/* ----------------------------------------------------------------------
   LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
   http://lammps.sandia.gov, Sandia National Laboratories
   Steve Plimpton, sjplimp@sandia.gov

   Copyright (2003) Sandia Corporation.  Under the terms of Contract
   DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
   certain rights in this software.  This software is distributed under
   the GNU General Public License.

   See the README file in the top-level LAMMPS directory.
------------------------------------------------------------------------- */

/* ----------------------------------------------------------------------
   Contributing author: Axel Kohlmeyer (Temple U)
------------------------------------------------------------------------- */

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

#include "dihedral_table_omp.h"
#include "atom.h"
#include "comm.h"
#include "neighbor.h"
#include "domain.h"
#include "force.h"
#include "update.h"
#include "error.h"

#include "math_const.h"
#include "math_extra.h"

#include "suffix.h"

using namespace LAMMPS_NS;
using namespace MathConst;
using namespace MathExtra;

#define TOLERANCE 0.05
#define SMALL     0.001

// --------------------------------------------
// ------- Calculate the dihedral angle -------
// --------------------------------------------
static const int g_dim=3;

static double Phi(double const *x1, //array holding x,y,z coords atom 1
                  double const *x2, // :       :      :      :        2
                  double const *x3, // :       :      :      :        3
                  double const *x4, // :       :      :      :        4
                  Domain *domain, //<-periodic boundary information
                  // The following arrays are of doubles with g_dim elements.
                  // (g_dim is a constant known at compile time, usually 3).
                  // Their contents is calculated by this function.
                  // Space for these vectors must be allocated in advance.
                  // (This is not hidden internally because these vectors
                  //  may be needed outside the function, later on.)
                  double *vb12, // will store x2-x1
                  double *vb23, // will store x3-x2
                  double *vb34, // will store x4-x3
                  double *n123, // will store normal to plane x1,x2,x3
                  double *n234) // will store normal to plane x2,x3,x4
{

  for (int d=0; d < g_dim; ++d) {
    vb12[d] = x2[d] - x1[d]; // 1st bond
    vb23[d] = x3[d] - x2[d]; // 2nd bond
    vb34[d] = x4[d] - x3[d]; // 3rd bond
  }

  //Consider periodic boundary conditions:
  domain->minimum_image(vb12[0],vb12[1],vb12[2]);
  domain->minimum_image(vb23[0],vb23[1],vb23[2]);
  domain->minimum_image(vb34[0],vb34[1],vb34[2]);

  //--- Compute the normal to the planes formed by atoms 1,2,3 and 2,3,4 ---

  cross3(vb23, vb12, n123);        // <- n123=vb23 x vb12
  cross3(vb23, vb34, n234);        // <- n234=vb23 x vb34

  norm3(n123);
  norm3(n234);

  double cos_phi = -dot3(n123, n234);

  if (cos_phi > 1.0)
    cos_phi = 1.0;
  else if (cos_phi < -1.0)
    cos_phi = -1.0;

  double phi = acos(cos_phi);

  if (dot3(n123, vb34) > 0.0) {
    phi = -phi;   //(Note: Negative dihedral angles are possible only in 3-D.)
    phi += MY_2PI; //<- This insure phi is always in the range 0 to 2*PI
  }
  return phi;
} // DihedralTable::Phi()


/* ---------------------------------------------------------------------- */

DihedralTableOMP::DihedralTableOMP(class LAMMPS *lmp)
  : DihedralTable(lmp), ThrOMP(lmp,THR_DIHEDRAL)
{
  suffix_flag |= Suffix::OMP;
}

/* ---------------------------------------------------------------------- */

void DihedralTableOMP::compute(int eflag, int vflag)
{

  if (eflag || vflag) {
    ev_setup(eflag,vflag);
  } else evflag = 0;

  const int nall = atom->nlocal + atom->nghost;
  const int nthreads = comm->nthreads;
  const int inum = neighbor->ndihedrallist;

#if defined(_OPENMP)
#pragma omp parallel default(none) shared(eflag,vflag)
#endif
  {
    int ifrom, ito, tid;

    loop_setup_thr(ifrom, ito, tid, inum, nthreads);
    ThrData *thr = fix->get_thr(tid);
    thr->timer(Timer::START);
    ev_setup_thr(eflag, vflag, nall, eatom, vatom, thr);

    if (inum > 0) {
      if (evflag) {
        if (eflag) {
          if (force->newton_bond) eval<1,1,1>(ifrom, ito, thr);
          else eval<1,1,0>(ifrom, ito, thr);
        } else {
          if (force->newton_bond) eval<1,0,1>(ifrom, ito, thr);
          else eval<1,0,0>(ifrom, ito, thr);
        }
      } else {
        if (force->newton_bond) eval<0,0,1>(ifrom, ito, thr);
        else eval<0,0,0>(ifrom, ito, thr);
      }
    }
    thr->timer(Timer::BOND);
    reduce_thr(this, eflag, vflag, thr);
  } // end of omp parallel region
}

template <int EVFLAG, int EFLAG, int NEWTON_BOND>
void DihedralTableOMP::eval(int nfrom, int nto, ThrData * const thr)
{
  int i1,i2,i3,i4,n,type;
  double edihedral,f1[3],f2[3],f3[3],f4[3];

  const double * const * const x = atom->x;
  double * const * const f = thr->get_f();
  const int * const * const dihedrallist = neighbor->dihedrallist;
  const int nlocal = atom->nlocal;

  // The dihedral angle "phi" is the angle between n123 and n234
  // the planes defined by atoms i1,i2,i3, and i2,i3,i4.
  //
  // Definitions of vectors: vb12, vb23, vb34, perp12on23
  //                         proj12on23, perp43on32, proj43on32
  //
  //  Note: The positions of the 4 atoms are labeled x[i1], x[i2], x[i3], x[i4]
  //        (which are also vectors)
  //
  //             proj12on23                          proj34on23
  //             --------->                         ----------->
  //                           .
  //                          .
  //                         .
  //                  x[i2] .                       x[i3]
  //    .                __@----------vb23-------->@ . . . .           .
  //   /|\                /|                        \                  |
  //    |                /                           \                 |
  //    |               /                             \                |
  // perp12vs23        /                               \               |
  //    |             /                                 \          perp34vs23
  //    |          vb12                                  \             |
  //    |           /                                   vb34           |
  //    |          /                                       \           |
  //    |         /                                         \          |
  //    |        /                                           \         |
  //            @                                             \        |
  //                                                          _\|     \|/
  //         x[i1]                                              @
  //
  //                                                           x[i4]
  //

  double vb12[g_dim]; // displacement vector from atom i1 towards atom i2
  //     vb12[d]       = x[i2][d] - x[i1][d]      (for d=0,1,2)
  double vb23[g_dim]; // displacement vector from atom i2 towards atom i3
  //     vb23[d]       = x[i3][d] - x[i2][d]      (for d=0,1,2)
  double vb34[g_dim]; // displacement vector from atom i3 towards atom i4
  //     vb34[d]       = x[i4][d] - x[i3][d]      (for d=0,1,2)

  //  n123 & n234: These two unit vectors are normal to the planes
  //               defined by atoms 1,2,3 and 2,3,4.
  double n123[g_dim]; //n123=vb23 x vb12 / |vb23 x vb12|  ("x" is cross product)
  double n234[g_dim]; //n234=vb23 x vb34 / |vb23 x vb34|  ("x" is cross product)

  double proj12on23[g_dim];
  //    proj12on23[d] = (vb23[d]/|vb23|) * DotProduct(vb12,vb23)/|vb12|*|vb23|
  double proj34on23[g_dim];
  //    proj34on23[d] = (vb34[d]/|vb23|) * DotProduct(vb34,vb23)/|vb34|*|vb23|
  double perp12on23[g_dim];
  //    perp12on23[d] = v12[d] - proj12on23[d]
  double perp34on23[g_dim];
  //    perp34on23[d] = v34[d] - proj34on23[d]

  edihedral = 0.0;

  for (n = nfrom; n < nto; n++) {

    i1 = dihedrallist[n][0];
    i2 = dihedrallist[n][1];
    i3 = dihedrallist[n][2];
    i4 = dihedrallist[n][3];
    type = dihedrallist[n][4];

    // ------ Step 1: Compute the dihedral angle "phi" ------
    //

    // Phi() calculates the dihedral angle.
    // This function also calculates the vectors:
    // vb12, vb23, vb34, n123, and n234, which we will need later.


    double phi = Phi(x[i1], x[i2], x[i3], x[i4], domain,
                     vb12, vb23, vb34, n123, n234);


    // ------ Step 2: Compute the gradient of phi with atomic position: ------
    //
    // Gradient variables:
    //
    // dphi_dx1, dphi_dx2, dphi_dx3, dphi_dx4 are the gradients of phi with
    // respect to the atomic positions of atoms i1, i2, i3, i4, respectively.
    // As an example, consider dphi_dx1.  The d'th element is:
    double dphi_dx1[g_dim]; //                 d phi
    double dphi_dx2[g_dim]; // dphi_dx1[d] = ----------    (partial derivatives)
    double dphi_dx3[g_dim]; //               d x[i1][d]
    double dphi_dx4[g_dim]; //where d=0,1,2 corresponds to x,y,z  (if g_dim==3)

    double dot123             = dot3(vb12, vb23);
    double dot234             = dot3(vb23, vb34);
    double L23sqr             = dot3(vb23, vb23);
    double L23                = sqrt(L23sqr);   // (central bond length)
    double inv_L23sqr = 0.0;
    double inv_L23    = 0.0;
    if (L23sqr != 0.0) {
      inv_L23sqr = 1.0 / L23sqr;
      inv_L23 = 1.0 / L23;
    }
    double neg_inv_L23        = -inv_L23;
    double dot123_over_L23sqr = dot123 * inv_L23sqr;
    double dot234_over_L23sqr = dot234 * inv_L23sqr;

    for (int d=0; d < g_dim; ++d) {
      // See figure above for a visual definitions of these vectors:
      proj12on23[d] = vb23[d] * dot123_over_L23sqr;
      proj34on23[d] = vb23[d] * dot234_over_L23sqr;
      perp12on23[d] = vb12[d] - proj12on23[d];
      perp34on23[d] = vb34[d] - proj34on23[d];
    }

    // --- Compute the gradient vectors dphi/dx1 and dphi/dx4: ---

    // These two gradients point in the direction of n123 and n234,
    // and are scaled by the distances of atoms 1 and 4 from the central axis.
    // Distance of atom 1 to central axis:
    double perp12on23_len = sqrt(dot3(perp12on23, perp12on23));
    // Distance of atom 4 to central axis:
    double perp34on23_len = sqrt(dot3(perp34on23, perp34on23));

    double inv_perp12on23 = 0.0;
    if (perp12on23_len != 0.0) inv_perp12on23 = 1.0 / perp12on23_len;
    double inv_perp34on23 = 0.0;
    if (perp34on23_len != 0.0) inv_perp34on23 = 1.0 / perp34on23_len;

    for (int d=0; d < g_dim; ++d) {
      dphi_dx1[d] =  n123[d] * inv_perp12on23;
      dphi_dx4[d] =  n234[d] * inv_perp34on23;
    }

    // --- Compute the gradient vectors dphi/dx2 and dphi/dx3: ---
    //
    // This is more tricky because atoms 2 and 3 are shared by both planes
    // 123 and 234 (the angle between which defines "phi").  Moving either
    // one of these atoms effects both the 123 and 234 planes
    // Both the 123 and 234 planes intersect with the plane perpendicular to the
    // central bond axis (vb23).  The two lines where these intersections occur
    // will shift when you move either atom 2 or atom 3.  The angle between
    // these lines is the dihedral angle, phi.  We can define four quantities:
    // dphi123_dx2 is the change in "phi" due to the movement of the 123 plane
    //             ...as a result of moving atom 2.
    // dphi234_dx2 is the change in "phi" due to the movement of the 234 plane
    //             ...as a result of moving atom 2.
    // dphi123_dx3 is the change in "phi" due to the movement of the 123 plane
    //             ...as a result of moving atom 3.
    // dphi234_dx3 is the change in "phi" due to the movement of the 234 plane
    //             ...as a result of moving atom 3.

    double proj12on23_len = dot123 * inv_L23;
    double proj34on23_len = dot234 * inv_L23;
    // Interpretation:
    //The magnitude of "proj12on23_len" is the length of the proj12on23 vector.
    //The sign is positive if it points in the same direction as the central
    //bond (vb23).  Otherwise it is negative.  The same goes for "proj34on23".
    //(In the example figure in the comment above, both variables are positive.)

    // The forumula used in the 8 lines below explained here:
    //   "supporting_information/doc/gradient_formula_explanation/"
    double dphi123_dx2_coef = neg_inv_L23 * (L23 + proj12on23_len);
    double dphi234_dx2_coef = inv_L23 * proj34on23_len;

    double dphi234_dx3_coef = neg_inv_L23 * (L23 + proj34on23_len);
    double dphi123_dx3_coef = inv_L23 * proj12on23_len;

    for (int d=0; d < g_dim; ++d) {
      // Recall that the n123 and n234 plane normal vectors are proportional to
      // the dphi/dx1 and dphi/dx2 gradients vectors
      // It turns out we can save slightly more CPU cycles by expressing
      // dphi/dx2 and dphi/dx3 as linear combinations of dphi/dx1 and dphi/dx2
      // which we computed already (instead of n123 & n234).
      dphi_dx2[d] = dphi123_dx2_coef*dphi_dx1[d] + dphi234_dx2_coef*dphi_dx4[d];
      dphi_dx3[d] = dphi123_dx3_coef*dphi_dx1[d] + dphi234_dx3_coef*dphi_dx4[d];
    }


    // ----- Step 3: Calculate the energy and force in the phi direction -----

    // tabulated force & energy
    double u=0.0, m_du_dphi=0.0; //u = energy.   m_du_dphi = "minus" du/dphi

    uf_lookup(type, phi, u, m_du_dphi);


    if (EFLAG) edihedral = u;

    // ----- Step 4: Calculate the force direction in real space -----

    // chain rule:
    //          d U          d U      d phi
    // -f  =   -----   =    -----  *  -----
    //          d x         d phi      d x
    for(int d=0; d < g_dim; ++d) {
      f1[d] = m_du_dphi * dphi_dx1[d];
      f2[d] = m_du_dphi * dphi_dx2[d];
      f3[d] = m_du_dphi * dphi_dx3[d];
      f4[d] = m_du_dphi * dphi_dx4[d];
    }

    // apply force to each of 4 atoms

    if (NEWTON_BOND || i1 < nlocal) {
      f[i1][0] += f1[0];
      f[i1][1] += f1[1];
      f[i1][2] += f1[2];
    }

    if (NEWTON_BOND || i2 < nlocal) {
      f[i2][0] += f2[0];
      f[i2][1] += f2[1];
      f[i2][2] += f2[2];
    }

    if (NEWTON_BOND || i3 < nlocal) {
      f[i3][0] += f3[0];
      f[i3][1] += f3[1];
      f[i3][2] += f3[2];
    }

    if (NEWTON_BOND || i4 < nlocal) {
      f[i4][0] += f4[0];
      f[i4][1] += f4[1];
      f[i4][2] += f4[2];
    }

    if (EVFLAG)
      ev_tally_thr(this,i1,i2,i3,i4,nlocal,NEWTON_BOND,edihedral,f1,f3,f4,
                   vb12[0],vb12[1],vb12[2],vb23[0],vb23[1],vb23[2],vb34[0],
                   vb34[1],vb34[2],thr);
  }
}
