/*
 * This file is part of the GROMACS molecular simulation package.
 *
 * Copyright 1991- The GROMACS Authors
 * and the project initiators Erik Lindahl, Berk Hess and David van der Spoel.
 * Consult the AUTHORS/COPYING files and https://www.gromacs.org for details.
 *
 * GROMACS is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public License
 * as published by the Free Software Foundation; either version 2.1
 * of the License, or (at your option) any later version.
 *
 * GROMACS is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 * Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public
 * License along with GROMACS; if not, see
 * https://www.gnu.org/licenses, or write to the Free Software Foundation,
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 * If you want to redistribute modifications to GROMACS, please
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 */
#include "gmxpre.h"

#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>

#include <algorithm>

#include "gromacs/commandline/viewit.h"
#include "gromacs/correlationfunctions/expfit.h"
#include "gromacs/correlationfunctions/integrate.h"
#include "gromacs/fft/fft.h"
#include "gromacs/fileio/xvgr.h"
#include "gromacs/gmxana/gmx_ana.h"
#include "gromacs/gmxana/gstat.h"
#include "gromacs/math/gmxcomplex.h"
#include "gromacs/math/units.h"
#include "gromacs/math/utilities.h"
#include "gromacs/utility/arraysize.h"
#include "gromacs/utility/fatalerror.h"
#include "gromacs/utility/futil.h"
#include "gromacs/utility/pleasecite.h"
#include "gromacs/utility/smalloc.h"

/* Determines at which point in the array the fit should start */
static int calc_nbegin(int nx, real x[], real tbegin)
{
    int nbegin;

    /* Assume input x is sorted */
    for (nbegin = 0; (nbegin < nx) && (x[nbegin] <= tbegin); nbegin++)
    {
        // Deliberately left empty
    }
    if ((nbegin == nx) || (nbegin == 0))
    {
        gmx_fatal(FARGS, "Begin time %f not in x-domain [%f through %f]\n", tbegin, x[0], x[nx - 1]);
    }

    /* Take the one closest to tbegin */
    if (std::abs(x[nbegin] - tbegin) > std::abs(x[nbegin - 1] - tbegin))
    {
        nbegin--;
    }

    printf("nbegin = %d, x[nbegin] = %g, tbegin = %g\n", nbegin, x[nbegin], tbegin);

    return nbegin;
}

static real
numerical_deriv(int nx, real x[], const real y[], const real fity[], real combined[], real dy[], real tendInt, int nsmooth)
{
    FILE* tmpfp;
    int   i, nbegin, i0, i1;
    real  fac, fx, fy, integralSmth;

    nbegin = calc_nbegin(nx, x, tendInt);
    if (nsmooth == 0)
    {
        for (i = 0; (i < nbegin); i++)
        {
            combined[i] = y[i];
        }
        fac = y[nbegin] / fity[nbegin];
        printf("scaling fitted curve by %g\n", fac);
        for (i = nbegin; (i < nx); i++)
        {
            combined[i] = fity[i] * fac;
        }
    }
    else
    {
        i0 = std::max(0, nbegin);
        i1 = std::min(nx - 1, nbegin + nsmooth);
        printf("Making smooth transition from %d through %d\n", i0, i1);
        for (i = 0; (i < i0); i++)
        {
            combined[i] = y[i];
        }
        for (i = i0; (i <= i1); i++)
        {
            fx = static_cast<real>(i1 - i) / (i1 - i0);
            fy = static_cast<real>(i - i0) / (i1 - i0);
            if (debug)
            {
                fprintf(debug, "x: %g factors for smoothing: %10g %10g\n", x[i], fx, fy);
            }
            combined[i] = fx * y[i] + fy * fity[i];
        }
        for (i = i1 + 1; (i < nx); i++)
        {
            combined[i] = fity[i];
        }
    }

    tmpfp        = gmx_ffopen("integral_smth.xvg", "w");
    integralSmth = print_and_integrate(tmpfp, nx, x[1] - x[0], combined, nullptr, 1);
    printf("SMOOTH integral = %10.5e\n", integralSmth);

    dy[0] = (combined[1] - combined[0]) / (x[1] - x[0]);
    for (i = 1; (i < nx - 1); i++)
    {
        dy[i] = (combined[i + 1] - combined[i - 1]) / (x[i + 1] - x[i - 1]);
    }
    dy[nx - 1] = (combined[nx - 1] - combined[nx - 2]) / (x[nx - 1] - x[nx - 2]);

    for (i = 0; (i < nx); i++)
    {
        dy[i] *= -1;
    }

    return integralSmth;
}

static void do_four(const char*             fn,
                    const char*             cn,
                    int                     nx,
                    const real              x[],
                    const real              dy[],
                    real                    eps0,
                    real                    epsRF,
                    const gmx_output_env_t* oenv)
{
    FILE *     fp, *cp;
    t_complex *tmp, gw, hw, kw;
    int        i, nnx, nxsav;
    real       fac, nu, dt, maxeps, numax;
    gmx_fft_t  fft;
    int        fftcode;

    nxsav = nx;
    /*while ((dy[nx-1] == 0.0) && (nx > 0))
       nx--;*/
    if (nx == 0)
    {
        gmx_fatal(FARGS, "Empty dataset in %s, line %d!", __FILE__, __LINE__);
    }

    nnx = 1;
    while (nnx < 2 * nx)
    {
        nnx *= 2;
    }

    snew(tmp, 2 * nnx);
    printf("Doing FFT of %d points\n", nnx);
    for (i = 0; (i < nx); i++)
    {
        tmp[i].re = dy[i];
    }
    if ((fftcode = gmx_fft_init_1d_real(&fft, nnx, GMX_FFT_FLAG_NONE)) != 0)
    {
        gmx_fatal(FARGS, "gmx_fft_init_1d_real returned %d", fftcode);
    }
    if ((fftcode = gmx_fft_1d_real(fft, GMX_FFT_COMPLEX_TO_REAL, tmp, tmp)) != 0)
    {
        gmx_fatal(FARGS, "gmx_fft_1d_real returned %d", fftcode);
    }
    gmx_fft_destroy(fft);
    dt = x[1] - x[0];
    if (epsRF == 0)
    {
        fac = (eps0 - 1) / tmp[0].re;
    }
    else
    {
        fac = ((eps0 - 1) / (2 * epsRF + eps0)) / tmp[0].re;
    }
    fp     = xvgropen(fn, "Epsilon(\\8w\\4)", "Freq. (GHz)", "eps", oenv);
    cp     = xvgropen(cn, "Cole-Cole plot", "Eps'", "Eps''", oenv);
    maxeps = 0;
    numax  = 0;
    for (i = 0; (i < nxsav); i++)
    {
        if (epsRF == 0)
        {
            kw.re = 1 + fac * tmp[i].re;
            kw.im = 1 + fac * tmp[i].im;
        }
        else
        {
            gw = rcmul(fac, tmp[i]);
            hw = rcmul(2 * epsRF, gw);
            hw.re += 1.0;
            gw.re = 1.0 - gw.re;
            gw.im = -gw.im;
            kw    = cdiv(hw, gw);
        }
        kw.im *= -1;

        nu = (i + 1) * 1000.0 / (nnx * dt);
        if (kw.im > maxeps)
        {
            maxeps = kw.im;
            numax  = nu;
        }

        fprintf(fp, "%10.5e  %10.5e  %10.5e\n", nu, kw.re, kw.im);
        fprintf(cp, "%10.5e  %10.5e\n", kw.re, kw.im);
    }
    printf("MAXEPS = %10.5e at frequency %10.5e GHz (tauD = %8.1f ps)\n",
           maxeps,
           numax,
           1000 / (2 * M_PI * numax));
    xvgrclose(fp);
    xvgrclose(cp);
    sfree(tmp);
}

int gmx_dielectric(int argc, char* argv[])
{
    const char* desc[] = {
        "[THISMODULE] calculates frequency dependent dielectric constants",
        "from the autocorrelation function of the total dipole moment in",
        "your simulation. This ACF can be generated by [gmx-dipoles].",
        "The functional forms of the available functions are:",
        "",
        " * One parameter:    y = [EXP]-a[SUB]1[sub] x[exp],",
        " * Two parameters:   y = a[SUB]2[sub] [EXP]-a[SUB]1[sub] x[exp],",
        " * Three parameters: y = a[SUB]2[sub] [EXP]-a[SUB]1[sub] x[exp] + (1 - ",
        "   a[SUB]2[sub]) [EXP]-a[SUB]3[sub] x[exp].",
        "",
        "Start values for the fit procedure can be given on the command line.",
        "It is also possible to fix parameters at their start value, use [TT]-fix[tt]",
        "with the number of the parameter you want to fix.",
        "[PAR]",
        "Three output files are generated, the first contains the ACF,",
        "an exponential fit to it with 1, 2 or 3 parameters, and the",
        "numerical derivative of the combination data/fit.",
        "The second file contains the real and imaginary parts of the",
        "frequency-dependent dielectric constant, the last gives a plot",
        "known as the Cole-Cole plot, in which the imaginary",
        "component is plotted as a function of the real component.",
        "For a pure exponential relaxation (Debye relaxation) the latter",
        "plot should be one half of a circle."
    };
    t_filenm fnm[] = { { efXVG, "-f", "dipcorr", ffREAD },
                       { efXVG, "-d", "deriv", ffWRITE },
                       { efXVG, "-o", "epsw", ffWRITE },
                       { efXVG, "-c", "cole", ffWRITE } };
#define NFILE asize(fnm)
    gmx_output_env_t*          oenv;
    int                        i, j, nx, ny, nxtail, eFitFn, nfitparm;
    real                       dt, integral, fitintegral, fac, rffac;
    double*                    fitparms;
    double**                   yd;
    real**                     y;
    std::array<std::string, 5> legend = {
        "Correlation", "Std. Dev.", "Fit", "Combined", "Derivative"
    };
    static int  fix = 0, bX = 1, nsmooth = 3;
    static real tendInt = 5.0, tbegin = 5.0, tend = 500.0;
    static real A = 0.5, tau1 = 10.0, tau2 = 1.0, eps0 = 80, epsRF = 78.5, tail = 500.0;
    real        lambda;
    t_pargs     pa[] = {
        { "-x1",
          FALSE,
          etBOOL,
          { &bX },
          "use first column as [IT]x[it]-axis rather than first data set" },
        { "-eint",
          FALSE,
          etREAL,
          { &tendInt },
          "Time to end the integration of the data and start to use the fit" },
        { "-bfit", FALSE, etREAL, { &tbegin }, "Begin time of fit" },
        { "-efit", FALSE, etREAL, { &tend }, "End time of fit" },
        { "-tail", FALSE, etREAL, { &tail }, "Length of function including data and tail from fit" },
        { "-A", FALSE, etREAL, { &A }, "Start value for fit parameter A" },
        { "-tau1", FALSE, etREAL, { &tau1 }, "Start value for fit parameter [GRK]tau[grk]1" },
        { "-tau2", FALSE, etREAL, { &tau2 }, "Start value for fit parameter [GRK]tau[grk]2" },
        { "-eps0", FALSE, etREAL, { &eps0 }, "[GRK]epsilon[grk]0 of your liquid" },
        { "-epsRF",
          FALSE,
          etREAL,
          { &epsRF },
          "[GRK]epsilon[grk] of the reaction field used in your simulation. A value of 0 means "
          "infinity." },
        { "-fix",
          FALSE,
          etINT,
          { &fix },
          "Fix parameters at their start values, A (2), tau1 (1), or tau2 (4)" },
        { "-ffn", FALSE, etENUM, { s_ffn }, "Fit function" },
        { "-nsmooth", FALSE, etINT, { &nsmooth }, "Number of points for smoothing" }
    };

    if (!parse_common_args(
                &argc, argv, PCA_CAN_TIME | PCA_CAN_VIEW, NFILE, fnm, asize(pa), pa, asize(desc), desc, 0, nullptr, &oenv))
    {
        return 0;
    }
    please_cite(stdout, "Spoel98a");
    printf("WARNING: non-polarizable models can never yield an infinite\n"
           "dielectric constant that is different from 1. This is incorrect\n"
           "in the reference given above (Spoel98a).\n\n");


    nx     = read_xvg(opt2fn("-f", NFILE, fnm), &yd, &ny);
    dt     = yd[0][1] - yd[0][0];
    nxtail = std::min(static_cast<int>(tail / dt), nx);

    printf("Read data set containing %d columns and %d rows\n", ny, nx);
    printf("Assuming (from data) that timestep is %g, nxtail = %d\n", dt, nxtail);
    snew(y, 6);
    for (i = 0; (i < ny); i++)
    {
        snew(y[i], std::max(nx, nxtail));
    }
    for (i = 0; (i < nx); i++)
    {
        y[0][i] = yd[0][i];
        for (j = 1; (j < ny); j++)
        {
            y[j][i] = yd[j][i];
        }
    }
    if (nxtail > nx)
    {
        for (i = nx; (i < nxtail); i++)
        {
            y[0][i] = dt * i + y[0][0];
            for (j = 1; (j < ny); j++)
            {
                y[j][i] = 0.0;
            }
        }
        nx = nxtail;
    }


    /* We have read a file WITHOUT standard deviations, so we make our own... */
    if (ny == 2)
    {
        printf("Creating standard deviation numbers ...\n");
        snew(y[2], nx);

        fac = 1.0 / nx;
        for (i = 0; (i < nx); i++)
        {
            y[2][i] = fac;
        }
    }

    eFitFn   = sffn2effn(s_ffn);
    nfitparm = effnNparams(eFitFn);
    snew(fitparms, 4);
    fitparms[0] = tau1;
    if (nfitparm > 1)
    {
        fitparms[1] = A;
    }
    if (nfitparm > 2)
    {
        fitparms[2] = tau2;
    }


    snew(y[3], nx);
    snew(y[4], nx);
    snew(y[5], nx);

    integral = print_and_integrate(nullptr, calc_nbegin(nx, y[0], tbegin), dt, y[1], nullptr, 1);
    integral += do_lmfit(nx, y[1], y[2], dt, y[0], tbegin, tend, oenv, TRUE, eFitFn, fitparms, fix, nullptr);
    for (i = 0; i < nx; i++)
    {
        y[3][i] = fit_function(eFitFn, fitparms, y[0][i]);
    }

    if (epsRF == 0)
    {
        /* This means infinity! */
        lambda = 0;
        rffac  = 1;
    }
    else
    {
        lambda = (eps0 - 1.0) / (2 * epsRF - 1.0);
        rffac  = (2 * epsRF + eps0) / (2 * epsRF + 1);
    }
    printf("DATA INTEGRAL: %5.1f, tauD(old) = %5.1f ps, "
           "tau_slope = %5.1f, tau_slope,D = %5.1f ps\n",
           integral,
           integral * rffac,
           fitparms[0],
           fitparms[0] * rffac);

    printf("tau_D from tau1 = %8.3g , eps(Infty) = %8.3f\n",
           fitparms[0] * (1 + fitparms[1] * lambda),
           1 + ((1 - fitparms[1]) * (eps0 - 1)) / (1 + fitparms[1] * lambda));

    fitintegral = numerical_deriv(nx, y[0], y[1], y[3], y[4], y[5], tendInt, nsmooth);
    printf("FIT INTEGRAL (tau_M): %5.1f, tau_D = %5.1f\n", fitintegral, fitintegral * rffac);

    /* Now we have the negative gradient of <Phi(0) Phi(t)> */
    write_xvg(opt2fn("-d", NFILE, fnm), "Data", nx - 1, 6, y, legend, oenv);

    /* Do FFT and analysis */
    do_four(opt2fn("-o", NFILE, fnm), opt2fn("-c", NFILE, fnm), nx - 1, y[0], y[5], eps0, epsRF, oenv);

    do_view(oenv, opt2fn("-o", NFILE, fnm), "-nxy");
    do_view(oenv, opt2fn("-c", NFILE, fnm), nullptr);
    do_view(oenv, opt2fn("-d", NFILE, fnm), "-nxy");

    return 0;
}
