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40 * Implements function to compute many autocorrelation functions
42 * \author David van der Spoel <david.vanderspoel@icm.uu.se>
43 * \ingroup module_correlationfunctions
55 #include "gromacs/correlationfunctions/expfit.h"
56 #include "gromacs/correlationfunctions/integrate.h"
57 #include "gromacs/correlationfunctions/manyautocorrelation.h"
58 #include "gromacs/correlationfunctions/polynomials.h"
59 #include "gromacs/fileio/xvgr.h"
60 #include "gromacs/math/functions.h"
61 #include "gromacs/math/vec.h"
62 #include "gromacs/utility/arraysize.h"
63 #include "gromacs/utility/fatalerror.h"
64 #include "gromacs/utility/futil.h"
65 #include "gromacs/utility/real.h"
66 #include "gromacs/utility/smalloc.h"
67 #include "gromacs/utility/strconvert.h"
69 /*! \brief Shortcut macro to select modes. */
70 #define MODE(x) ((mode & (x)) == (x))
75 int nrestart, nout, P, fitfn;
76 gmx_bool bFour, bNormalize;
77 real tbeginfit, tendfit;
80 /*! \brief Global variable set true if initialization routines are called. */
81 static gmx_bool bACFinit = FALSE;
83 /*! \brief Data structure for storing command line variables. */
93 /*! \brief Routine to compute ACF using FFT. */
94 static void low_do_four_core(int nframes, real c1[], real cfour[], int nCos)
97 std::vector<std::vector<real>> data;
99 data[0].resize(nframes, 0);
103 for (i = 0; (i < nframes); i++)
109 for (i = 0; (i < nframes); i++)
111 data[0][i] = cos(c1[i]);
115 for (i = 0; (i < nframes); i++)
117 data[0][i] = sin(c1[i]);
120 default: gmx_fatal(FARGS, "nCos = %d, %s %d", nCos, __FILE__, __LINE__);
123 many_auto_correl(&data);
124 for (i = 0; (i < nframes); i++)
126 cfour[i] = data[0][i];
130 /*! \brief Routine to comput ACF without FFT. */
131 static void do_ac_core(int nframes, int nout, real corr[], real c1[], int nrestart, unsigned long mode)
133 int j, k, j3, jk3, m, n;
139 printf("WARNING: setting number of restarts to 1\n");
144 fprintf(debug, "Starting do_ac_core: nframes=%d, nout=%d, nrestart=%d,mode=%lu\n", nframes, 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",
208 else if (MODE(eacP3))
212 corr[k] += LegendreP(cth, mmm); /* 1.5*cth*cth-0.5; */
214 else if (MODE(eacRcross))
217 for (m = 0; (m < DIM); m++)
224 corr[k] += iprod(rr, rr);
226 else if (MODE(eacVector))
228 for (m = 0; (m < DIM); m++)
239 gmx_fatal(FARGS, "\nInvalid mode (%lu) in do_ac_core", mode);
243 /* Correct for the number of points and copy results to the data array */
244 for (j = 0; (j < nout); j++)
246 n = (nframes - j + (nrestart - 1)) / nrestart;
251 /*! \brief Routine to normalize ACF, dividing by corr[0]. */
252 static void normalize_acf(int nout, real corr[])
259 fprintf(debug, "Before normalization\n");
260 for (j = 0; (j < nout); j++)
262 fprintf(debug, "%5d %10f\n", j, corr[j]);
266 /* Normalisation makes that c[0] = 1.0 and that other points are scaled
269 if (fabs(corr[0]) < 1e-5)
277 for (j = 0; (j < nout); j++)
284 fprintf(debug, "After normalization\n");
285 for (j = 0; (j < nout); j++)
287 fprintf(debug, "%5d %10f\n", j, corr[j]);
292 /*! \brief Routine that averages ACFs. */
293 static void average_acf(gmx_bool bVerbose, int n, int nitem, real** c1)
300 printf("Averaging correlation functions\n");
303 for (j = 0; (j < n); j++)
306 for (i = 0; (i < nitem); i++)
310 c1[0][j] = c0 / nitem;
314 /*! \brief Normalize ACFs. */
315 static void norm_and_scale_vectors(int nframes, real c1[], real scale)
320 for (j = 0; (j < nframes); j++)
322 rij = &(c1[j * DIM]);
324 for (m = 0; (m < DIM); m++)
331 /*! \brief Debugging */
332 static void dump_tmp(char* s, int n, real c[])
337 fp = gmx_ffopen(s, "w");
338 for (i = 0; (i < n); i++)
340 fprintf(fp, "%10d %10g\n", i, c[i]);
345 /*! \brief High level ACF routine. */
346 static void do_four_core(unsigned long mode, int nframes, real c1[], real csum[], real ctmp[])
353 snew(cfour, nframes);
357 /********************************************
359 ********************************************/
360 low_do_four_core(nframes, c1, csum, enNorm);
362 else if (MODE(eacCos))
364 /***************************************************
366 ***************************************************/
367 /* Copy the data to temp array. Since we need it twice
368 * we can't overwrite original.
370 for (j = 0; (j < nframes); j++)
375 /* Cosine term of AC function */
376 low_do_four_core(nframes, ctmp, cfour, enCos);
377 for (j = 0; (j < nframes); j++)
382 /* Sine term of AC function */
383 low_do_four_core(nframes, ctmp, cfour, enSin);
384 for (j = 0; (j < nframes); j++)
390 else if (MODE(eacP2))
392 /***************************************************
393 * Legendre polynomials
394 ***************************************************/
395 /* First normalize the vectors */
396 norm_and_scale_vectors(nframes, c1, 1.0);
398 /* For P2 thingies we have to do six FFT based correls
399 * First for XX^2, then for YY^2, then for ZZ^2
400 * Then we have to do XY, YZ and XZ (counting these twice)
401 * After that we sum them and normalise
402 * P2(x) = (3 * cos^2 (x) - 1)/2
403 * for unit vectors u and v we compute the cosine as the inner product
404 * cos(u,v) = uX vX + uY vY + uZ vZ
408 * C(t) = | (3 cos^2(u(t'),u(t'+t)) - 1)/2 dt'
413 * P2(u(0),u(t)) = [3 * (uX(0) uX(t) +
415 * uZ(0) uZ(t))^2 - 1]/2
416 * = [3 * ((uX(0) uX(t))^2 +
419 * 2(uX(0) uY(0) uX(t) uY(t)) +
420 * 2(uX(0) uZ(0) uX(t) uZ(t)) +
421 * 2(uY(0) uZ(0) uY(t) uZ(t))) - 1]/2
423 * = [(3/2) * (<uX^2> + <uY^2> + <uZ^2> +
424 * 2<uXuY> + 2<uXuZ> + 2<uYuZ>) - 0.5]
428 /* Because of normalization the number of -0.5 to subtract
429 * depends on the number of data points!
431 for (j = 0; (j < nframes); j++)
433 csum[j] = -0.5 * (nframes - j);
436 /***** DIAGONAL ELEMENTS ************/
437 for (m = 0; (m < DIM); m++)
439 /* Copy the vector data in a linear array */
440 for (j = 0; (j < nframes); j++)
442 ctmp[j] = gmx::square(c1[DIM * j + m]);
446 sprintf(buf, "c1diag%d.xvg", m);
447 dump_tmp(buf, nframes, ctmp);
450 low_do_four_core(nframes, ctmp, cfour, enNorm);
454 sprintf(buf, "c1dfout%d.xvg", m);
455 dump_tmp(buf, nframes, cfour);
458 for (j = 0; (j < nframes); j++)
460 csum[j] += fac * (cfour[j]);
463 /******* OFF-DIAGONAL ELEMENTS **********/
464 for (m = 0; (m < DIM); m++)
466 /* Copy the vector data in a linear array */
468 for (j = 0; (j < nframes); j++)
470 ctmp[j] = c1[DIM * j + m] * c1[DIM * j + m1];
475 sprintf(buf, "c1off%d.xvg", m);
476 dump_tmp(buf, nframes, ctmp);
478 low_do_four_core(nframes, ctmp, cfour, enNorm);
481 sprintf(buf, "c1ofout%d.xvg", m);
482 dump_tmp(buf, nframes, cfour);
485 for (j = 0; (j < nframes); j++)
487 csum[j] += fac * cfour[j];
491 else if (MODE(eacP1) || MODE(eacVector))
493 /***************************************************
495 ***************************************************/
498 /* First normalize the vectors */
499 norm_and_scale_vectors(nframes, c1, 1.0);
502 /* For vector thingies we have to do three FFT based correls
503 * First for XX, then for YY, then for ZZ
504 * After that we sum them and normalise
506 for (j = 0; (j < nframes); j++)
510 for (m = 0; (m < DIM); m++)
512 /* Copy the vector data in a linear array */
513 for (j = 0; (j < nframes); j++)
515 ctmp[j] = c1[DIM * j + m];
517 low_do_four_core(nframes, ctmp, cfour, enNorm);
518 for (j = 0; (j < nframes); j++)
526 gmx_fatal(FARGS, "\nUnknown mode in do_autocorr (%lu)", mode);
530 for (j = 0; (j < nframes); j++)
532 c1[j] = csum[j] / static_cast<real>(nframes - j);
536 void low_do_autocorr(const char* fn,
537 const gmx_output_env_t* oenv,
553 FILE * fp, *gp = nullptr;
557 real sum, Ct2av, Ctav;
558 gmx_bool bFour = acf.bFour;
560 /* Check flags and parameters */
561 nout = get_acfnout();
564 nout = acf.nout = (nframes + 1) / 2;
566 else if (nout > nframes)
571 if (MODE(eacCos) && MODE(eacVector))
573 gmx_fatal(FARGS, "Incompatible options bCos && bVector (%s, %d)", __FILE__, __LINE__);
575 if ((MODE(eacP3) || MODE(eacRcross)) && bFour)
579 fprintf(stderr, "Can't combine mode %lu with FFT, turning off FFT\n", mode);
583 if (MODE(eacNormal) && MODE(eacVector))
585 gmx_fatal(FARGS, "Incompatible mode bits: normal and vector (or Legendre)");
588 /* Print flags and parameters */
591 printf("Will calculate %s of %d thingies for %d frames\n", title ? title : "autocorrelation", nitem, nframes);
592 printf("bAver = %s, bFour = %s bNormalize= %s\n",
593 gmx::boolToString(bAver),
594 gmx::boolToString(bFour),
595 gmx::boolToString(bNormalize));
596 printf("mode = %lu, dt = %g, nrestart = %d\n", mode, dt, nrestart);
598 /* Allocate temp arrays */
602 /* Loop over items (e.g. molecules or dihedrals)
603 * In this loop the actual correlation functions are computed, but without
606 for (int i = 0; i < nitem; i++)
608 if (bVerbose && (((i % 100) == 0) || (i == nitem - 1)))
610 fprintf(stderr, "\rThingie %d", i + 1);
616 do_four_core(mode, nframes, c1[i], csum, ctmp);
620 do_ac_core(nframes, nout, ctmp, c1[i], nrestart, mode);
625 fprintf(stderr, "\n");
633 fp = xvgropen(fn, title, "Time (ps)", "C(t)", oenv);
644 average_acf(bVerbose, nframes, nitem, c1);
649 normalize_acf(nout, c1[0]);
652 if (eFitFn != effnNONE)
654 fit_acf(nout, eFitFn, oenv, fn != nullptr, tbeginfit, tendfit, dt, c1[0], fit);
655 sum = print_and_integrate(fp, nout, dt, c1[0], fit, 1);
659 sum = print_and_integrate(fp, nout, dt, c1[0], nullptr, 1);
663 printf("Correlation time (integral over corrfn): %g (ps)\n", sum);
668 /* Not averaging. Normalize individual ACFs */
672 gp = xvgropen("ct-distr.xvg", "Correlation times", "item", "time (ps)", oenv);
674 for (i = 0; i < nitem; i++)
678 normalize_acf(nout, c1[i]);
680 if (eFitFn != effnNONE)
682 fit_acf(nout, eFitFn, oenv, fn != nullptr, tbeginfit, tendfit, dt, c1[i], fit);
683 sum = print_and_integrate(fp, nout, dt, c1[i], fit, 1);
687 sum = print_and_integrate(fp, nout, dt, c1[i], nullptr, 1);
690 fprintf(debug, "CORRelation time (integral over corrfn %d): %g (ps)\n", i, sum);
697 fprintf(gp, "%5d %.3f\n", i, sum);
708 printf("Average correlation time %.3f Std. Dev. %.3f Error %.3f (ps)\n",
710 std::sqrt((Ct2av - gmx::square(Ctav))),
711 std::sqrt((Ct2av - gmx::square(Ctav)) / (nitem - 1)));
721 /*! \brief Legend for selecting Legendre polynomials. */
722 static const char* Leg[] = { nullptr, "0", "1", "2", "3", nullptr };
724 t_pargs* add_acf_pargs(int* npargs, t_pargs* pa)
731 "Length of the ACF, default is half the number of frames" },
732 { "-normalize", FALSE, etBOOL, { &acf.bNormalize }, "Normalize ACF" },
737 "HIDDENUse fast fourier transform for correlation function" },
742 "HIDDENNumber of frames between time origins for ACF when no FFT is used" },
743 { "-P", FALSE, etENUM, { Leg }, "Order of Legendre polynomial for ACF (0 indicates none)" },
744 { "-fitfn", FALSE, etENUM, { s_ffn }, "Fit function" },
749 "Time where to begin the exponential fit of the correlation function" },
754 "Time where to end the exponential fit of the correlation function, -1 is until the "
761 snew(ppa, *npargs + npa);
762 for (i = 0; (i < *npargs); i++)
766 for (i = 0; (i < npa); i++)
768 ppa[*npargs + i] = acfpa[i];
776 acf.fitfn = effnEXP1;
778 acf.bNormalize = TRUE;
787 void do_autocorr(const char* fn,
788 const gmx_output_env_t* oenv,
799 printf("ACF data structures have not been initialised. Call add_acf_pargs\n");
802 /* Handle enumerated types */
803 sscanf(Leg[0], "%d", &acf.P);
804 acf.fitfn = sffn2effn(s_ffn);
808 case 1: mode = mode | eacP1; break;
809 case 2: mode = mode | eacP2; break;
810 case 3: mode = mode | eacP3; break;
836 gmx_fatal(FARGS, "ACF data not initialized yet");
846 gmx_fatal(FARGS, "ACF data not initialized yet");
849 return sffn2effn(s_ffn);