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dihedral_table_omp.cpp
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/* ----------------------------------------------------------------------
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 "math.h"
#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"
using namespace LAMMPS_NS;
using namespace DIHEDRAL_TABLE_NS;
#define TOLERANCE 0.05
#define SMALL 0.001
/* ---------------------------------------------------------------------- */
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);
ev_setup_thr(eflag, vflag, nall, eatom, vatom, thr);
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);
}
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,i,m,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=vb12 x vb23 / |vb12 x vb23| ("x" is cross product)
double n234[g_dim]; //n234=vb34 x vb23 / |vb34 x vb23| ("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 = DotProduct(vb12, vb23);
double dot234 = DotProduct(vb23, vb34);
double L23sqr = DotProduct(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(DotProduct(perp12on23, perp12on23));
// Distance of atom 4 to central axis:
double perp34on23_len = sqrt(DotProduct(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];
}
#ifdef DIH_DEBUG_NUM
// ----- Numerical test? -----
cerr << " -- testing gradient for dihedral (n="<<n<<") for atoms ("
<< i1 << "," << i2 << "," << i3 << "," << i4 << ") --" << endl;
PrintGradientComparison(*this, dphi_dx1, dphi_dx2, dphi_dx3, dphi_dx4,
domain, x[i1], x[i2], x[i3], x[i4]);
for (int d=0; d < g_dim; ++d) {
// The sum of all the gradients should be near 0. (translational symmetry)
cerr <<"sum_gradients["<<d<<"]="<<dphi_dx1[d]<<"+"<<dphi_dx2[d]<<"+"<<dphi_dx3[d]<<"+"<<dphi_dx4[d]<<"="<<dphi_dx1[d]+dphi_dx2[d]+dphi_dx3[d]+dphi_dx4[d]<<endl;
// These should sum to zero
assert(abs(dphi_dx1[d]+dphi_dx2[d]+dphi_dx3[d]+dphi_dx4[d]) < 0.0002/L23);
}
#endif // #ifdef DIH_DEBUG_NUM
// ----- Step 3: Calculate the energy and force in the phi direction -----
// tabulated force & energy
double u, m_du_dphi; //u = energy. m_du_dphi = "minus" du/dphi
assert((0.0 <= phi) && (phi <= TWOPI));
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);
}
}

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