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39 * Implements function to compute many autocorrelation functions
41 * \author David van der Spoel <david.vanderspoel@icm.uu.se>
42 * \ingroup module_correlationfunctions
52 #include "gromacs/correlationfunctions/expfit.h"
53 #include "gromacs/correlationfunctions/integrate.h"
54 #include "gromacs/correlationfunctions/manyautocorrelation.h"
55 #include "gromacs/correlationfunctions/polynomials.h"
56 #include "gromacs/fileio/xvgr.h"
57 #include "gromacs/legacyheaders/macros.h"
58 #include "gromacs/legacyheaders/names.h"
59 #include "gromacs/math/vec.h"
60 #include "gromacs/utility/fatalerror.h"
61 #include "gromacs/utility/futil.h"
62 #include "gromacs/utility/real.h"
63 #include "gromacs/utility/smalloc.h"
65 /*! \brief Shortcut macro to select modes. */
66 #define MODE(x) ((mode & (x)) == (x))
70 int nrestart, nout, P, fitfn;
71 gmx_bool bFour, bNormalize;
72 real tbeginfit, tendfit;
75 /*! \brief Global variable set true if initialization routines are called. */
76 static gmx_bool bACFinit = FALSE;
78 /*! \brief Data structure for storing command line variables. */
85 /*! \brief Routine to compute ACF using FFT. */
86 static void low_do_four_core(int nfour, int nframes, real c1[], real cfour[],
97 for (i = 0; (i < nframes); i++)
104 for (i = 0; (i < nframes); i++)
106 cfour[i] = cos(c1[i]);
110 for (i = 0; (i < nframes); i++)
112 cfour[i] = sin(c1[i]);
116 gmx_fatal(FARGS, "nCos = %d, %s %d", nCos, __FILE__, __LINE__);
119 fftcode = many_auto_correl(1, nframes, nfour, &cfour);
122 /*! \brief Routine to comput ACF without FFT. */
123 static void do_ac_core(int nframes, int nout,
124 real corr[], real c1[], int nrestart,
127 int j, k, j3, jk3, m, n;
133 printf("WARNING: setting number of restarts to 1\n");
139 "Starting do_ac_core: nframes=%d, nout=%d, nrestart=%d,mode=%lu\n",
140 nframes, nout, nrestart, mode);
143 for (j = 0; (j < nout); j++)
148 /* Loop over starting points. */
149 for (j = 0; (j < nframes); j += nrestart)
153 /* Loop over the correlation length for this starting point */
154 for (k = 0; (k < nout) && (j+k < nframes); k++)
158 /* Switch over possible ACF types.
159 * It might be more efficient to put the loops inside the switch,
160 * but this is more clear, and save development time!
164 corr[k] += c1[j]*c1[j+k];
166 else if (MODE(eacCos))
168 /* Compute the cos (phi(t)-phi(t+dt)) */
169 corr[k] += cos(c1[j]-c1[j+k]);
171 else if (MODE(eacIden))
173 /* Check equality (phi(t)==phi(t+dt)) */
174 corr[k] += (c1[j] == c1[j+k]) ? 1 : 0;
176 else if (MODE(eacP1) || MODE(eacP2) || MODE(eacP3))
180 for (m = 0; (m < DIM); m++)
185 cth = cos_angle(xj, xk);
187 if (cth-1.0 > 1.0e-15)
189 printf("j: %d, k: %d, xj:(%g,%g,%g), xk:(%g,%g,%g)\n",
190 j, k, xj[XX], xj[YY], xj[ZZ], xk[XX], xk[YY], xk[ZZ]);
197 else if (MODE(eacP3))
201 corr[k] += LegendreP(cth, mmm); /* 1.5*cth*cth-0.5; */
203 else if (MODE(eacRcross))
206 for (m = 0; (m < DIM); m++)
213 corr[k] += iprod(rr, rr);
215 else if (MODE(eacVector))
217 for (m = 0; (m < DIM); m++)
228 gmx_fatal(FARGS, "\nInvalid mode (%d) in do_ac_core", mode);
232 /* Correct for the number of points and copy results to the data array */
233 for (j = 0; (j < nout); j++)
235 n = (nframes-j+(nrestart-1))/nrestart;
240 /*! \brief Routine to normalize ACF, dividing by corr[0]. */
241 void normalize_acf(int nout, real corr[])
248 fprintf(debug, "Before normalization\n");
249 for (j = 0; (j < nout); j++)
251 fprintf(debug, "%5d %10f\n", j, corr[j]);
255 /* Normalisation makes that c[0] = 1.0 and that other points are scaled
258 if (fabs(corr[0]) < 1e-5)
266 for (j = 0; (j < nout); j++)
273 fprintf(debug, "After normalization\n");
274 for (j = 0; (j < nout); j++)
276 fprintf(debug, "%5d %10f\n", j, corr[j]);
281 /*! \brief Routine that averages ACFs. */
282 void average_acf(gmx_bool bVerbose, int n, int nitem, real **c1)
289 printf("Averaging correlation functions\n");
292 for (j = 0; (j < n); j++)
295 for (i = 0; (i < nitem); i++)
303 /*! \brief Normalize ACFs. */
304 void norm_and_scale_vectors(int nframes, real c1[], real scale)
309 for (j = 0; (j < nframes); j++)
313 for (m = 0; (m < DIM); m++)
320 /*! \brief Debugging */
321 static void dump_tmp(char *s, int n, real c[])
326 fp = gmx_ffopen(s, "w");
327 for (i = 0; (i < n); i++)
329 fprintf(fp, "%10d %10g\n", i, c[i]);
334 /*! \brief High level ACF routine. */
335 void do_four_core(unsigned long mode, int nfour, int nf2, int nframes,
336 real c1[], real csum[], real ctmp[])
347 /********************************************
349 ********************************************/
350 low_do_four_core(nfour, nf2, c1, csum, enNorm);
352 else if (MODE(eacCos))
354 /***************************************************
356 ***************************************************/
357 /* Copy the data to temp array. Since we need it twice
358 * we can't overwrite original.
360 for (j = 0; (j < nf2); j++)
365 /* Cosine term of AC function */
366 low_do_four_core(nfour, nf2, ctmp, cfour, enCos);
367 for (j = 0; (j < nf2); j++)
372 /* Sine term of AC function */
373 low_do_four_core(nfour, nf2, ctmp, cfour, enSin);
374 for (j = 0; (j < nf2); j++)
380 else if (MODE(eacP2))
382 /***************************************************
383 * Legendre polynomials
384 ***************************************************/
385 /* First normalize the vectors */
386 norm_and_scale_vectors(nframes, c1, 1.0);
388 /* For P2 thingies we have to do six FFT based correls
389 * First for XX^2, then for YY^2, then for ZZ^2
390 * Then we have to do XY, YZ and XZ (counting these twice)
391 * After that we sum them and normalise
392 * P2(x) = (3 * cos^2 (x) - 1)/2
393 * for unit vectors u and v we compute the cosine as the inner product
394 * cos(u,v) = uX vX + uY vY + uZ vZ
398 * C(t) = | (3 cos^2(u(t'),u(t'+t)) - 1)/2 dt'
403 * P2(u(0),u(t)) = [3 * (uX(0) uX(t) +
405 * uZ(0) uZ(t))^2 - 1]/2
406 * = [3 * ((uX(0) uX(t))^2 +
409 * 2(uX(0) uY(0) uX(t) uY(t)) +
410 * 2(uX(0) uZ(0) uX(t) uZ(t)) +
411 * 2(uY(0) uZ(0) uY(t) uZ(t))) - 1]/2
413 * = [(3/2) * (<uX^2> + <uY^2> + <uZ^2> +
414 * 2<uXuY> + 2<uXuZ> + 2<uYuZ>) - 0.5]
418 /* Because of normalization the number of -0.5 to subtract
419 * depends on the number of data points!
421 for (j = 0; (j < nf2); j++)
423 csum[j] = -0.5*(nf2-j);
426 /***** DIAGONAL ELEMENTS ************/
427 for (m = 0; (m < DIM); m++)
429 /* Copy the vector data in a linear array */
430 for (j = 0; (j < nf2); j++)
432 ctmp[j] = sqr(c1[DIM*j+m]);
436 sprintf(buf, "c1diag%d.xvg", m);
437 dump_tmp(buf, nf2, ctmp);
440 low_do_four_core(nfour, nf2, ctmp, cfour, enNorm);
444 sprintf(buf, "c1dfout%d.xvg", m);
445 dump_tmp(buf, nf2, cfour);
448 for (j = 0; (j < nf2); j++)
450 csum[j] += fac*(cfour[j]);
453 /******* OFF-DIAGONAL ELEMENTS **********/
454 for (m = 0; (m < DIM); m++)
456 /* Copy the vector data in a linear array */
458 for (j = 0; (j < nf2); j++)
460 ctmp[j] = c1[DIM*j+m]*c1[DIM*j+m1];
465 sprintf(buf, "c1off%d.xvg", m);
466 dump_tmp(buf, nf2, ctmp);
468 low_do_four_core(nfour, nf2, ctmp, cfour, enNorm);
471 sprintf(buf, "c1ofout%d.xvg", m);
472 dump_tmp(buf, nf2, cfour);
475 for (j = 0; (j < nf2); j++)
477 csum[j] += fac*cfour[j];
481 else if (MODE(eacP1) || MODE(eacVector))
483 /***************************************************
485 ***************************************************/
488 /* First normalize the vectors */
489 norm_and_scale_vectors(nframes, c1, 1.0);
492 /* For vector thingies we have to do three FFT based correls
493 * First for XX, then for YY, then for ZZ
494 * After that we sum them and normalise
496 for (j = 0; (j < nf2); j++)
500 for (m = 0; (m < DIM); m++)
502 /* Copy the vector data in a linear array */
503 for (j = 0; (j < nf2); j++)
505 ctmp[j] = c1[DIM*j+m];
507 low_do_four_core(nfour, nf2, ctmp, cfour, enNorm);
508 for (j = 0; (j < nf2); j++)
516 gmx_fatal(FARGS, "\nUnknown mode in do_autocorr (%d)", mode);
520 for (j = 0; (j < nf2); j++)
522 c1[j] = csum[j]/(real)(nframes-j);
526 void low_do_autocorr(const char *fn, const output_env_t oenv, const char *title,
527 int nframes, int nitem, int nout, real **c1,
528 real dt, unsigned long mode, int nrestart,
529 gmx_bool bAver, gmx_bool bNormalize,
530 gmx_bool bVerbose, real tbeginfit, real tendfit,
533 FILE *fp, *gp = NULL;
537 real c0, sum, Ct2av, Ctav;
538 gmx_bool bFour = acf.bFour;
540 /* Check flags and parameters */
541 nout = get_acfnout();
544 nout = acf.nout = (nframes+1)/2;
546 else if (nout > nframes)
551 if (MODE(eacCos) && MODE(eacVector))
553 gmx_fatal(FARGS, "Incompatible options bCos && bVector (%s, %d)",
556 if ((MODE(eacP3) || MODE(eacRcross)) && bFour)
560 fprintf(stderr, "Can't combine mode %lu with FFT, turning off FFT\n", mode);
564 if (MODE(eacNormal) && MODE(eacVector))
566 gmx_fatal(FARGS, "Incompatible mode bits: normal and vector (or Legendre)");
569 /* Print flags and parameters */
572 printf("Will calculate %s of %d thingies for %d frames\n",
573 title ? title : "autocorrelation", nitem, nframes);
574 printf("bAver = %s, bFour = %s bNormalize= %s\n",
575 bool_names[bAver], bool_names[bFour], bool_names[bNormalize]);
576 printf("mode = %lu, dt = %g, nrestart = %d\n", mode, dt, nrestart);
580 c0 = log((double)nframes)/log(2.0);
590 fprintf(debug, "Using FFT to calculate %s, #points for FFT = %d\n",
594 /* Allocate temp arrays */
600 nfour = 0; /* To keep the compiler happy */
605 /* Loop over items (e.g. molecules or dihedrals)
606 * In this loop the actual correlation functions are computed, but without
609 k = max(1, pow(10, (int)(log(nitem)/log(100))));
610 for (i = 0; i < nitem; i++)
612 if (bVerbose && ((i%k == 0 || i == nitem-1)))
614 fprintf(stderr, "\rThingie %d", i+1);
619 do_four_core(mode, nfour, nframes, nframes, c1[i], csum, ctmp);
623 do_ac_core(nframes, nout, ctmp, c1[i], nrestart, mode);
628 fprintf(stderr, "\n");
636 fp = xvgropen(fn, title, "Time (ps)", "C(t)", oenv);
647 average_acf(bVerbose, nframes, nitem, c1);
652 normalize_acf(nout, c1[0]);
655 if (eFitFn != effnNONE)
657 fit_acf(nout, eFitFn, oenv, fn != NULL, tbeginfit, tendfit, dt, c1[0], fit);
658 sum = print_and_integrate(fp, nout, dt, c1[0], fit, 1);
662 sum = print_and_integrate(fp, nout, dt, c1[0], NULL, 1);
665 printf("Correlation time (integral over corrfn): %g (ps)\n", sum);
671 /* Not averaging. Normalize individual ACFs */
675 gp = xvgropen("ct-distr.xvg", "Correlation times", "item", "time (ps)", oenv);
677 for (i = 0; i < nitem; i++)
681 normalize_acf(nout, c1[i]);
683 if (eFitFn != effnNONE)
685 fit_acf(nout, eFitFn, oenv, fn != NULL, tbeginfit, tendfit, dt, c1[i], fit);
686 sum = print_and_integrate(fp, nout, dt, c1[i], fit, 1);
690 sum = print_and_integrate(fp, nout, dt, c1[i], NULL, 1);
694 "CORRelation time (integral over corrfn %d): %g (ps)\n",
702 fprintf(gp, "%5d %.3f\n", i, sum);
713 printf("Average correlation time %.3f Std. Dev. %.3f Error %.3f (ps)\n",
714 Ctav, sqrt((Ct2av - sqr(Ctav))),
715 sqrt((Ct2av - sqr(Ctav))/(nitem-1)));
725 /*! \brief Legend for selecting Legendre polynomials. */
726 static const char *Leg[] = { NULL, "0", "1", "2", "3", NULL };
728 t_pargs *add_acf_pargs(int *npargs, t_pargs *pa)
731 { "-acflen", FALSE, etINT, {&acf.nout},
732 "Length of the ACF, default is half the number of frames" },
733 { "-normalize", FALSE, etBOOL, {&acf.bNormalize},
735 { "-fftcorr", FALSE, etBOOL, {&acf.bFour},
736 "HIDDENUse fast fourier transform for correlation function" },
737 { "-nrestart", FALSE, etINT, {&acf.nrestart},
738 "HIDDENNumber of frames between time origins for ACF when no FFT is used" },
739 { "-P", FALSE, etENUM, {Leg},
740 "Order of Legendre polynomial for ACF (0 indicates none)" },
741 { "-fitfn", FALSE, etENUM, {s_ffn},
743 { "-beginfit", FALSE, etREAL, {&acf.tbeginfit},
744 "Time where to begin the exponential fit of the correlation function" },
745 { "-endfit", FALSE, etREAL, {&acf.tendfit},
746 "Time where to end the exponential fit of the correlation function, -1 is until the end" },
752 snew(ppa, *npargs+npa);
753 for (i = 0; (i < *npargs); i++)
757 for (i = 0; (i < npa); i++)
759 ppa[*npargs+i] = acfpa[i];
767 acf.fitfn = effnEXP1;
769 acf.bNormalize = TRUE;
778 void do_autocorr(const char *fn, const output_env_t oenv, const char *title,
779 int nframes, int nitem, real **c1,
780 real dt, unsigned long mode, gmx_bool bAver)
784 printf("ACF data structures have not been initialised. Call add_acf_pargs\n");
787 /* Handle enumerated types */
788 sscanf(Leg[0], "%d", &acf.P);
789 acf.fitfn = sffn2effn(s_ffn);
806 low_do_autocorr(fn, oenv, title, nframes, nitem, acf.nout, c1, dt, mode,
807 acf.nrestart, bAver, acf.bNormalize,
808 bDebugMode(), acf.tbeginfit, acf.tendfit,
812 int get_acfnout(void)
816 gmx_fatal(FARGS, "ACF data not initialized yet");
822 int get_acffitfn(void)
826 gmx_fatal(FARGS, "ACF data not initialized yet");
829 return sffn2effn(s_ffn);