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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
54 #include "gromacs/correlationfunctions/expfit.h"
55 #include "gromacs/correlationfunctions/integrate.h"
56 #include "gromacs/correlationfunctions/manyautocorrelation.h"
57 #include "gromacs/correlationfunctions/polynomials.h"
58 #include "gromacs/fileio/xvgr.h"
59 #include "gromacs/math/functions.h"
60 #include "gromacs/math/vec.h"
61 #include "gromacs/utility/arraysize.h"
62 #include "gromacs/utility/fatalerror.h"
63 #include "gromacs/utility/futil.h"
64 #include "gromacs/utility/real.h"
65 #include "gromacs/utility/smalloc.h"
66 #include "gromacs/utility/strconvert.h"
68 /*! \brief Shortcut macro to select modes. */
69 #define MODE(x) ((mode & (x)) == (x))
74 int nrestart, nout, P, fitfn;
75 gmx_bool bFour, bNormalize;
76 real tbeginfit, tendfit;
79 /*! \brief Global variable set true if initialization routines are called. */
80 static gmx_bool bACFinit = FALSE;
82 /*! \brief Data structure for storing command line variables. */
92 /*! \brief Routine to compute ACF using FFT. */
93 static void low_do_four_core(int nframes, real c1[], real cfour[], int nCos)
96 std::vector<std::vector<real>> data;
98 data[0].resize(nframes, 0);
102 for (i = 0; (i < nframes); i++)
108 for (i = 0; (i < nframes); i++)
110 data[0][i] = cos(c1[i]);
114 for (i = 0; (i < nframes); i++)
116 data[0][i] = sin(c1[i]);
119 default: gmx_fatal(FARGS, "nCos = %d, %s %d", nCos, __FILE__, __LINE__);
122 many_auto_correl(&data);
123 for (i = 0; (i < nframes); i++)
125 cfour[i] = data[0][i];
129 /*! \brief Routine to comput ACF without FFT. */
130 static void do_ac_core(int nframes, int nout, real corr[], real c1[], int nrestart, unsigned long mode)
132 int j, k, j3, jk3, m, n;
138 printf("WARNING: setting number of restarts to 1\n");
143 fprintf(debug, "Starting do_ac_core: nframes=%d, nout=%d, nrestart=%d,mode=%lu\n", nframes,
144 nout, nrestart, mode);
147 for (j = 0; (j < nout); j++)
152 /* Loop over starting points. */
153 for (j = 0; (j < nframes); j += nrestart)
157 /* Loop over the correlation length for this starting point */
158 for (k = 0; (k < nout) && (j + k < nframes); k++)
162 /* Switch over possible ACF types.
163 * It might be more efficient to put the loops inside the switch,
164 * but this is more clear, and save development time!
168 corr[k] += c1[j] * c1[j + k];
170 else if (MODE(eacCos))
172 /* Compute the cos (phi(t)-phi(t+dt)) */
173 corr[k] += std::cos(c1[j] - c1[j + k]);
175 else if (MODE(eacIden))
177 /* Check equality (phi(t)==phi(t+dt)) */
178 corr[k] += (c1[j] == c1[j + k]) ? 1 : 0;
180 else if (MODE(eacP1) || MODE(eacP2) || MODE(eacP3))
184 for (m = 0; (m < DIM); m++)
189 cth = cos_angle(xj, xk);
191 if (cth - 1.0 > 1.0e-15)
193 printf("j: %d, k: %d, xj:(%g,%g,%g), xk:(%g,%g,%g)\n", j, k, xj[XX], xj[YY],
194 xj[ZZ], xk[XX], xk[YY], xk[ZZ]);
201 else if (MODE(eacP3))
205 corr[k] += LegendreP(cth, mmm); /* 1.5*cth*cth-0.5; */
207 else if (MODE(eacRcross))
210 for (m = 0; (m < DIM); m++)
217 corr[k] += iprod(rr, rr);
219 else if (MODE(eacVector))
221 for (m = 0; (m < DIM); m++)
232 gmx_fatal(FARGS, "\nInvalid mode (%lu) in do_ac_core", mode);
236 /* Correct for the number of points and copy results to the data array */
237 for (j = 0; (j < nout); j++)
239 n = (nframes - j + (nrestart - 1)) / nrestart;
244 /*! \brief Routine to normalize ACF, dividing by corr[0]. */
245 static void normalize_acf(int nout, real corr[])
252 fprintf(debug, "Before normalization\n");
253 for (j = 0; (j < nout); j++)
255 fprintf(debug, "%5d %10f\n", j, corr[j]);
259 /* Normalisation makes that c[0] = 1.0 and that other points are scaled
262 if (fabs(corr[0]) < 1e-5)
270 for (j = 0; (j < nout); j++)
277 fprintf(debug, "After normalization\n");
278 for (j = 0; (j < nout); j++)
280 fprintf(debug, "%5d %10f\n", j, corr[j]);
285 /*! \brief Routine that averages ACFs. */
286 static void average_acf(gmx_bool bVerbose, int n, int nitem, real** c1)
293 printf("Averaging correlation functions\n");
296 for (j = 0; (j < n); j++)
299 for (i = 0; (i < nitem); i++)
303 c1[0][j] = c0 / nitem;
307 /*! \brief Normalize ACFs. */
308 static void norm_and_scale_vectors(int nframes, real c1[], real scale)
313 for (j = 0; (j < nframes); j++)
315 rij = &(c1[j * DIM]);
317 for (m = 0; (m < DIM); m++)
324 /*! \brief Debugging */
325 static void dump_tmp(char* s, int n, real c[])
330 fp = gmx_ffopen(s, "w");
331 for (i = 0; (i < n); i++)
333 fprintf(fp, "%10d %10g\n", i, c[i]);
338 /*! \brief High level ACF routine. */
339 static void do_four_core(unsigned long mode, int nframes, real c1[], real csum[], real ctmp[])
346 snew(cfour, nframes);
350 /********************************************
352 ********************************************/
353 low_do_four_core(nframes, c1, csum, enNorm);
355 else if (MODE(eacCos))
357 /***************************************************
359 ***************************************************/
360 /* Copy the data to temp array. Since we need it twice
361 * we can't overwrite original.
363 for (j = 0; (j < nframes); j++)
368 /* Cosine term of AC function */
369 low_do_four_core(nframes, ctmp, cfour, enCos);
370 for (j = 0; (j < nframes); j++)
375 /* Sine term of AC function */
376 low_do_four_core(nframes, ctmp, cfour, enSin);
377 for (j = 0; (j < nframes); j++)
383 else if (MODE(eacP2))
385 /***************************************************
386 * Legendre polynomials
387 ***************************************************/
388 /* First normalize the vectors */
389 norm_and_scale_vectors(nframes, c1, 1.0);
391 /* For P2 thingies we have to do six FFT based correls
392 * First for XX^2, then for YY^2, then for ZZ^2
393 * Then we have to do XY, YZ and XZ (counting these twice)
394 * After that we sum them and normalise
395 * P2(x) = (3 * cos^2 (x) - 1)/2
396 * for unit vectors u and v we compute the cosine as the inner product
397 * cos(u,v) = uX vX + uY vY + uZ vZ
401 * C(t) = | (3 cos^2(u(t'),u(t'+t)) - 1)/2 dt'
406 * P2(u(0),u(t)) = [3 * (uX(0) uX(t) +
408 * uZ(0) uZ(t))^2 - 1]/2
409 * = [3 * ((uX(0) uX(t))^2 +
412 * 2(uX(0) uY(0) uX(t) uY(t)) +
413 * 2(uX(0) uZ(0) uX(t) uZ(t)) +
414 * 2(uY(0) uZ(0) uY(t) uZ(t))) - 1]/2
416 * = [(3/2) * (<uX^2> + <uY^2> + <uZ^2> +
417 * 2<uXuY> + 2<uXuZ> + 2<uYuZ>) - 0.5]
421 /* Because of normalization the number of -0.5 to subtract
422 * depends on the number of data points!
424 for (j = 0; (j < nframes); j++)
426 csum[j] = -0.5 * (nframes - j);
429 /***** DIAGONAL ELEMENTS ************/
430 for (m = 0; (m < DIM); m++)
432 /* Copy the vector data in a linear array */
433 for (j = 0; (j < nframes); j++)
435 ctmp[j] = gmx::square(c1[DIM * j + m]);
439 sprintf(buf, "c1diag%d.xvg", m);
440 dump_tmp(buf, nframes, ctmp);
443 low_do_four_core(nframes, ctmp, cfour, enNorm);
447 sprintf(buf, "c1dfout%d.xvg", m);
448 dump_tmp(buf, nframes, cfour);
451 for (j = 0; (j < nframes); j++)
453 csum[j] += fac * (cfour[j]);
456 /******* OFF-DIAGONAL ELEMENTS **********/
457 for (m = 0; (m < DIM); m++)
459 /* Copy the vector data in a linear array */
461 for (j = 0; (j < nframes); j++)
463 ctmp[j] = c1[DIM * j + m] * c1[DIM * j + m1];
468 sprintf(buf, "c1off%d.xvg", m);
469 dump_tmp(buf, nframes, ctmp);
471 low_do_four_core(nframes, ctmp, cfour, enNorm);
474 sprintf(buf, "c1ofout%d.xvg", m);
475 dump_tmp(buf, nframes, cfour);
478 for (j = 0; (j < nframes); j++)
480 csum[j] += fac * cfour[j];
484 else if (MODE(eacP1) || MODE(eacVector))
486 /***************************************************
488 ***************************************************/
491 /* First normalize the vectors */
492 norm_and_scale_vectors(nframes, c1, 1.0);
495 /* For vector thingies we have to do three FFT based correls
496 * First for XX, then for YY, then for ZZ
497 * After that we sum them and normalise
499 for (j = 0; (j < nframes); j++)
503 for (m = 0; (m < DIM); m++)
505 /* Copy the vector data in a linear array */
506 for (j = 0; (j < nframes); j++)
508 ctmp[j] = c1[DIM * j + m];
510 low_do_four_core(nframes, ctmp, cfour, enNorm);
511 for (j = 0; (j < nframes); j++)
519 gmx_fatal(FARGS, "\nUnknown mode in do_autocorr (%lu)", mode);
523 for (j = 0; (j < nframes); j++)
525 c1[j] = csum[j] / static_cast<real>(nframes - j);
529 void low_do_autocorr(const char* fn,
530 const gmx_output_env_t* oenv,
546 FILE * fp, *gp = nullptr;
550 real sum, Ct2av, Ctav;
551 gmx_bool bFour = acf.bFour;
553 /* Check flags and parameters */
554 nout = get_acfnout();
557 nout = acf.nout = (nframes + 1) / 2;
559 else if (nout > nframes)
564 if (MODE(eacCos) && MODE(eacVector))
566 gmx_fatal(FARGS, "Incompatible options bCos && bVector (%s, %d)", __FILE__, __LINE__);
568 if ((MODE(eacP3) || MODE(eacRcross)) && bFour)
572 fprintf(stderr, "Can't combine mode %lu with FFT, turning off FFT\n", mode);
576 if (MODE(eacNormal) && MODE(eacVector))
578 gmx_fatal(FARGS, "Incompatible mode bits: normal and vector (or Legendre)");
581 /* Print flags and parameters */
584 printf("Will calculate %s of %d thingies for %d frames\n",
585 title ? title : "autocorrelation", nitem, nframes);
586 printf("bAver = %s, bFour = %s bNormalize= %s\n", gmx::boolToString(bAver),
587 gmx::boolToString(bFour), gmx::boolToString(bNormalize));
588 printf("mode = %lu, dt = %g, nrestart = %d\n", mode, dt, nrestart);
590 /* Allocate temp arrays */
594 /* Loop over items (e.g. molecules or dihedrals)
595 * In this loop the actual correlation functions are computed, but without
598 for (int i = 0; i < nitem; i++)
600 if (bVerbose && (((i % 100) == 0) || (i == nitem - 1)))
602 fprintf(stderr, "\rThingie %d", i + 1);
608 do_four_core(mode, nframes, c1[i], csum, ctmp);
612 do_ac_core(nframes, nout, ctmp, c1[i], nrestart, mode);
617 fprintf(stderr, "\n");
625 fp = xvgropen(fn, title, "Time (ps)", "C(t)", oenv);
636 average_acf(bVerbose, nframes, nitem, c1);
641 normalize_acf(nout, c1[0]);
644 if (eFitFn != effnNONE)
646 fit_acf(nout, eFitFn, oenv, fn != nullptr, tbeginfit, tendfit, dt, c1[0], fit);
647 sum = print_and_integrate(fp, nout, dt, c1[0], fit, 1);
651 sum = print_and_integrate(fp, nout, dt, c1[0], nullptr, 1);
655 printf("Correlation time (integral over corrfn): %g (ps)\n", sum);
660 /* Not averaging. Normalize individual ACFs */
664 gp = xvgropen("ct-distr.xvg", "Correlation times", "item", "time (ps)", oenv);
666 for (i = 0; i < nitem; i++)
670 normalize_acf(nout, c1[i]);
672 if (eFitFn != effnNONE)
674 fit_acf(nout, eFitFn, oenv, fn != nullptr, tbeginfit, tendfit, dt, c1[i], fit);
675 sum = print_and_integrate(fp, nout, dt, c1[i], fit, 1);
679 sum = print_and_integrate(fp, nout, dt, c1[i], nullptr, 1);
682 fprintf(debug, "CORRelation time (integral over corrfn %d): %g (ps)\n", i, sum);
689 fprintf(gp, "%5d %.3f\n", i, sum);
700 printf("Average correlation time %.3f Std. Dev. %.3f Error %.3f (ps)\n", Ctav,
701 std::sqrt((Ct2av - gmx::square(Ctav))),
702 std::sqrt((Ct2av - gmx::square(Ctav)) / (nitem - 1)));
712 /*! \brief Legend for selecting Legendre polynomials. */
713 static const char* Leg[] = { nullptr, "0", "1", "2", "3", nullptr };
715 t_pargs* add_acf_pargs(int* npargs, t_pargs* pa)
722 "Length of the ACF, default is half the number of frames" },
723 { "-normalize", FALSE, etBOOL, { &acf.bNormalize }, "Normalize ACF" },
728 "HIDDENUse fast fourier transform for correlation function" },
733 "HIDDENNumber of frames between time origins for ACF when no FFT is used" },
734 { "-P", FALSE, etENUM, { Leg }, "Order of Legendre polynomial for ACF (0 indicates none)" },
735 { "-fitfn", FALSE, etENUM, { s_ffn }, "Fit function" },
740 "Time where to begin the exponential fit of the correlation function" },
745 "Time where to end the exponential fit of the correlation function, -1 is until the "
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,
779 const gmx_output_env_t* oenv,
790 printf("ACF data structures have not been initialised. Call add_acf_pargs\n");
793 /* Handle enumerated types */
794 sscanf(Leg[0], "%d", &acf.P);
795 acf.fitfn = sffn2effn(s_ffn);
799 case 1: mode = mode | eacP1; break;
800 case 2: mode = mode | eacP2; break;
801 case 3: mode = mode | eacP3; break;
805 low_do_autocorr(fn, oenv, title, nframes, nitem, acf.nout, c1, dt, mode, acf.nrestart, bAver,
806 acf.bNormalize, bDebugMode(), acf.tbeginfit, acf.tendfit, acf.fitfn);
813 gmx_fatal(FARGS, "ACF data not initialized yet");
823 gmx_fatal(FARGS, "ACF data not initialized yet");
826 return sffn2effn(s_ffn);