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sna.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 authors: Aidan Thompson, Christian Trott, SNL
------------------------------------------------------------------------- */
#include "sna.h"
#include "math.h"
#include "math_const.h"
#include "math_extra.h"
#include "string.h"
#include "stdlib.h"
#include "openmp_snap.h"
#include "memory.h"
#include "error.h"
#include "comm.h"
#include "atom.h"
using namespace std;
using namespace LAMMPS_NS;
using namespace MathConst;
/* ----------------------------------------------------------------------
this implementation is based on the method outlined
in Bartok[1], using formulae from VMK[2].
for the Clebsch-Gordan coefficients, we
convert the VMK half-integral labels
a, b, c, alpha, beta, gamma
to array offsets j1, j2, j, m1, m2, m
using the following relations:
j1 = 2*a
j2 = 2*b
j = 2*c
m1 = alpha+a 2*alpha = 2*m1 - j1
m2 = beta+b or 2*beta = 2*m2 - j2
m = gamma+c 2*gamma = 2*m - j
in this way:
-a <= alpha <= a
-b <= beta <= b
-c <= gamma <= c
becomes:
0 <= m1 <= j1
0 <= m2 <= j2
0 <= m <= j
and the requirement that
a+b+c be integral implies that
j1+j2+j must be even.
The requirement that:
gamma = alpha+beta
becomes:
2*m - j = 2*m1 - j1 + 2*m2 - j2
Similarly, for the Wigner U-functions U(J,m,m') we
convert the half-integral labels J,m,m' to
array offsets j,ma,mb:
j = 2*J
ma = J+m
mb = J+m'
so that:
0 <= j <= 2*Jmax
0 <= ma, mb <= j.
For the bispectrum components B(J1,J2,J) we convert to:
j1 = 2*J1
j2 = 2*J2
j = 2*J
and the requirement:
|J1-J2| <= J <= J1+J2, for j1+j2+j integral
becomes:
|j1-j2| <= j <= j1+j2, for j1+j2+j even integer
or
j = |j1-j2|, |j1-j2|+2,...,j1+j2-2,j1+j2
[1] Albert Bartok-Partay, "Gaussian Approximation..."
Doctoral Thesis, Cambrindge University, (2009)
[2] D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii,
"Quantum Theory of Angular Momentum," World Scientific (1988)
------------------------------------------------------------------------- */
SNA::SNA(LAMMPS* lmp, double rfac0_in,
int twojmax_in, int diagonalstyle_in, int use_shared_arrays_in,
double rmin0_in, int switch_flag_in) : Pointers(lmp)
{
wself = 1.0;
use_shared_arrays = use_shared_arrays_in;
rfac0 = rfac0_in;
rmin0 = rmin0_in;
switch_flag = switch_flag_in;
twojmax = twojmax_in;
diagonalstyle = diagonalstyle_in;
ncoeff = compute_ncoeff();
create_twojmax_arrays();
bvec = NULL;
dbvec = NULL;
memory->create(bvec, ncoeff, "pair:bvec");
memory->create(dbvec, ncoeff, 3, "pair:dbvec");
rij = NULL;
inside = NULL;
wj = NULL;
rcutij = NULL;
nmax = 0;
idxj = NULL;
#ifdef TIMING_INFO
timers = new double[20];
for(int i = 0; i < 20; i++) timers[i] = 0;
print = 0;
counter = 0;
#endif
build_indexlist();
}
/* ---------------------------------------------------------------------- */
SNA::~SNA()
{
if(!use_shared_arrays) {
destroy_twojmax_arrays();
memory->destroy(rij);
memory->destroy(inside);
memory->destroy(wj);
memory->destroy(rcutij);
memory->destroy(bvec);
memory->destroy(dbvec);
}
delete[] idxj;
}
void SNA::build_indexlist()
{
if(diagonalstyle == 0) {
int idxj_count = 0;
for(int j1 = 0; j1 <= twojmax; j1++)
for(int j2 = 0; j2 <= j1; j2++)
for(int j = abs(j1 - j2); j <= MIN(twojmax, j1 + j2); j += 2)
idxj_count++;
// indexList can be changed here
idxj = new SNA_LOOPINDICES[idxj_count];
idxj_max = idxj_count;
idxj_count = 0;
for(int j1 = 0; j1 <= twojmax; j1++)
for(int j2 = 0; j2 <= j1; j2++)
for(int j = abs(j1 - j2); j <= MIN(twojmax, j1 + j2); j += 2) {
idxj[idxj_count].j1 = j1;
idxj[idxj_count].j2 = j2;
idxj[idxj_count].j = j;
idxj_count++;
}
}
if(diagonalstyle == 1) {
int idxj_count = 0;
for(int j1 = 0; j1 <= twojmax; j1++)
for(int j = 0; j <= MIN(twojmax, 2 * j1); j += 2) {
idxj_count++;
}
// indexList can be changed here
idxj = new SNA_LOOPINDICES[idxj_count];
idxj_max = idxj_count;
idxj_count = 0;
for(int j1 = 0; j1 <= twojmax; j1++)
for(int j = 0; j <= MIN(twojmax, 2 * j1); j += 2) {
idxj[idxj_count].j1 = j1;
idxj[idxj_count].j2 = j1;
idxj[idxj_count].j = j;
idxj_count++;
}
}
if(diagonalstyle == 2) {
int idxj_count = 0;
for(int j1 = 0; j1 <= twojmax; j1++) {
idxj_count++;
}
// indexList can be changed here
idxj = new SNA_LOOPINDICES[idxj_count];
idxj_max = idxj_count;
idxj_count = 0;
for(int j1 = 0; j1 <= twojmax; j1++) {
idxj[idxj_count].j1 = j1;
idxj[idxj_count].j2 = j1;
idxj[idxj_count].j = j1;
idxj_count++;
}
}
if(diagonalstyle == 3) {
int idxj_count = 0;
for(int j1 = 0; j1 <= twojmax; j1++)
for(int j2 = 0; j2 <= j1; j2++)
for(int j = abs(j1 - j2); j <= MIN(twojmax, j1 + j2); j += 2)
if (j >= j1) idxj_count++;
// indexList can be changed here
idxj = new SNA_LOOPINDICES[idxj_count];
idxj_max = idxj_count;
idxj_count = 0;
for(int j1 = 0; j1 <= twojmax; j1++)
for(int j2 = 0; j2 <= j1; j2++)
for(int j = abs(j1 - j2); j <= MIN(twojmax, j1 + j2); j += 2)
if (j >= j1) {
idxj[idxj_count].j1 = j1;
idxj[idxj_count].j2 = j2;
idxj[idxj_count].j = j;
idxj_count++;
}
}
}
/* ---------------------------------------------------------------------- */
void SNA::init()
{
init_clebsch_gordan();
init_rootpqarray();
}
void SNA::grow_rij(int newnmax)
{
if(newnmax <= nmax) return;
nmax = newnmax;
if(!use_shared_arrays) {
memory->destroy(rij);
memory->destroy(inside);
memory->destroy(wj);
memory->destroy(rcutij);
memory->create(rij, nmax, 3, "pair:rij");
memory->create(inside, nmax, "pair:inside");
memory->create(wj, nmax, "pair:wj");
memory->create(rcutij, nmax, "pair:rcutij");
}
}
/* ----------------------------------------------------------------------
compute Ui by summing over neighbors j
------------------------------------------------------------------------- */
void SNA::compute_ui(int jnum)
{
double rsq, r, x, y, z, z0, theta0;
// utot(j,ma,mb) = 0 for all j,ma,ma
// utot(j,ma,ma) = 1 for all j,ma
// for j in neighbors of i:
// compute r0 = (x,y,z,z0)
// utot(j,ma,mb) += u(r0;j,ma,mb) for all j,ma,mb
zero_uarraytot();
addself_uarraytot(wself);
#ifdef TIMING_INFO
clock_gettime(CLOCK_REALTIME, &starttime);
#endif
for(int j = 0; j < jnum; j++) {
x = rij[j][0];
y = rij[j][1];
z = rij[j][2];
rsq = x * x + y * y + z * z;
r = sqrt(rsq);
theta0 = (r - rmin0) * rfac0 * MY_PI / (rcutij[j] - rmin0);
// theta0 = (r - rmin0) * rscale0;
z0 = r / tan(theta0);
compute_uarray(x, y, z, z0, r);
add_uarraytot(r, wj[j], rcutij[j]);
}
#ifdef TIMING_INFO
clock_gettime(CLOCK_REALTIME, &endtime);
timers[0] += (endtime.tv_sec - starttime.tv_sec + 1.0 *
(endtime.tv_nsec - starttime.tv_nsec) / 1000000000);
#endif
}
void SNA::compute_ui_omp(int jnum, int sub_threads)
{
double rsq, r, x, y, z, z0, theta0;
// utot(j,ma,mb) = 0 for all j,ma,ma
// utot(j,ma,ma) = 1 for all j,ma
// for j in neighbors of i:
// compute r0 = (x,y,z,z0)
// utot(j,ma,mb) += u(r0;j,ma,mb) for all j,ma,mb
zero_uarraytot();
addself_uarraytot(wself);
for(int j = 0; j < jnum; j++) {
x = rij[j][0];
y = rij[j][1];
z = rij[j][2];
rsq = x * x + y * y + z * z;
r = sqrt(rsq);
theta0 = (r - rmin0) * rfac0 * MY_PI / (rcutij[j] - rmin0);
// theta0 = (r - rmin0) * rscale0;
z0 = r / tan(theta0);
omp_set_num_threads(sub_threads);
#if defined(_OPENMP)
#pragma omp parallel shared(x,y,z,z0,r,sub_threads) default(none)
#endif
{
compute_uarray_omp(x, y, z, z0, r, sub_threads);
}
add_uarraytot(r, wj[j], rcutij[j]);
}
}
/* ----------------------------------------------------------------------
compute Zi by summing over products of Ui
------------------------------------------------------------------------- */
void SNA::compute_zi()
{
// for j1 = 0,...,twojmax
// for j2 = 0,twojmax
// for j = |j1-j2|,Min(twojmax,j1+j2),2
// for ma = 0,...,j
// for mb = 0,...,jmid
// z(j1,j2,j,ma,mb) = 0
// for ma1 = Max(0,ma+(j1-j2-j)/2),Min(j1,ma+(j1+j2-j)/2)
// sumb1 = 0
// ma2 = ma-ma1+(j1+j2-j)/2;
// for mb1 = Max(0,mb+(j1-j2-j)/2),Min(j1,mb+(j1+j2-j)/2)
// mb2 = mb-mb1+(j1+j2-j)/2;
// sumb1 += cg(j1,mb1,j2,mb2,j) *
// u(j1,ma1,mb1) * u(j2,ma2,mb2)
// z(j1,j2,j,ma,mb) += sumb1*cg(j1,ma1,j2,ma2,j)
#ifdef TIMING_INFO
clock_gettime(CLOCK_REALTIME, &starttime);
#endif
// compute_dbidrj() requires full j1/j2/j chunk of z elements
// use zarray j1/j2 symmetry
for(int j1 = 0; j1 <= twojmax; j1++)
for(int j2 = 0; j2 <= j1; j2++) {
for(int j = j1 - j2; j <= MIN(twojmax, j1 + j2); j += 2) {
double sumb1_r, sumb1_i;
int ma2, mb2;
for(int mb = 0; 2*mb <= j; mb++)
for(int ma = 0; ma <= j; ma++) {
zarray_r[j1][j2][j][ma][mb] = 0.0;
zarray_i[j1][j2][j][ma][mb] = 0.0;
for(int ma1 = MAX(0, (2 * ma - j - j2 + j1) / 2);
ma1 <= MIN(j1, (2 * ma - j + j2 + j1) / 2); ma1++) {
sumb1_r = 0.0;
sumb1_i = 0.0;
ma2 = (2 * ma - j - (2 * ma1 - j1) + j2) / 2;
for(int mb1 = MAX(0, (2 * mb - j - j2 + j1) / 2);
mb1 <= MIN(j1, (2 * mb - j + j2 + j1) / 2); mb1++) {
mb2 = (2 * mb - j - (2 * mb1 - j1) + j2) / 2;
sumb1_r += cgarray[j1][j2][j][mb1][mb2] *
(uarraytot_r[j1][ma1][mb1] * uarraytot_r[j2][ma2][mb2] -
uarraytot_i[j1][ma1][mb1] * uarraytot_i[j2][ma2][mb2]);
sumb1_i += cgarray[j1][j2][j][mb1][mb2] *
(uarraytot_r[j1][ma1][mb1] * uarraytot_i[j2][ma2][mb2] +
uarraytot_i[j1][ma1][mb1] * uarraytot_r[j2][ma2][mb2]);
} // end loop over mb1
zarray_r[j1][j2][j][ma][mb] +=
sumb1_r * cgarray[j1][j2][j][ma1][ma2];
zarray_i[j1][j2][j][ma][mb] +=
sumb1_i * cgarray[j1][j2][j][ma1][ma2];
} // end loop over ma1
} // end loop over ma, mb
} // end loop over j
} // end loop over j1, j2
#ifdef TIMING_INFO
clock_gettime(CLOCK_REALTIME, &endtime);
timers[1] += (endtime.tv_sec - starttime.tv_sec + 1.0 *
(endtime.tv_nsec - starttime.tv_nsec) / 1000000000);
#endif
}
void SNA::compute_zi_omp(int sub_threads)
{
// for j1 = 0,...,twojmax
// for j2 = 0,twojmax
// for j = |j1-j2|,Min(twojmax,j1+j2),2
// for ma = 0,...,j
// for mb = 0,...,j
// z(j1,j2,j,ma,mb) = 0
// for ma1 = Max(0,ma+(j1-j2-j)/2),Min(j1,ma+(j1+j2-j)/2)
// sumb1 = 0
// ma2 = ma-ma1+(j1+j2-j)/2;
// for mb1 = Max(0,mb+(j1-j2-j)/2),Min(j1,mb+(j1+j2-j)/2)
// mb2 = mb-mb1+(j1+j2-j)/2;
// sumb1 += cg(j1,mb1,j2,mb2,j) *
// u(j1,ma1,mb1) * u(j2,ma2,mb2)
// z(j1,j2,j,ma,mb) += sumb1*cg(j1,ma1,j2,ma2,j)
if(omp_in_parallel())
omp_set_num_threads(sub_threads);
// compute_dbidrj() requires full j1/j2/j chunk of z elements
// use zarray j1/j2 symmetry
#if defined(_OPENMP)
#pragma omp parallel for schedule(auto) default(none)
#endif
for(int j1 = 0; j1 <= twojmax; j1++)
for(int j2 = 0; j2 <= j1; j2++)
for(int j = abs(j1 - j2); j <= MIN(twojmax, j1 + j2); j += 2) {
double sumb1_r, sumb1_i;
int ma2, mb2;
for(int ma = 0; ma <= j; ma++)
for(int mb = 0; mb <= j; mb++) {
zarray_r[j1][j2][j][ma][mb] = 0.0;
zarray_i[j1][j2][j][ma][mb] = 0.0;
for(int ma1 = MAX(0, (2 * ma - j - j2 + j1) / 2);
ma1 <= MIN(j1, (2 * ma - j + j2 + j1) / 2); ma1++) {
sumb1_r = 0.0;
sumb1_i = 0.0;
ma2 = (2 * ma - j - (2 * ma1 - j1) + j2) / 2;
for(int mb1 = MAX(0, (2 * mb - j - j2 + j1) / 2);
mb1 <= MIN(j1, (2 * mb - j + j2 + j1) / 2); mb1++) {
mb2 = (2 * mb - j - (2 * mb1 - j1) + j2) / 2;
sumb1_r += cgarray[j1][j2][j][mb1][mb2] *
(uarraytot_r[j1][ma1][mb1] * uarraytot_r[j2][ma2][mb2] -
uarraytot_i[j1][ma1][mb1] * uarraytot_i[j2][ma2][mb2]);
sumb1_i += cgarray[j1][j2][j][mb1][mb2] *
(uarraytot_r[j1][ma1][mb1] * uarraytot_i[j2][ma2][mb2] +
uarraytot_i[j1][ma1][mb1] * uarraytot_r[j2][ma2][mb2]);
}
zarray_r[j1][j2][j][ma][mb] +=
sumb1_r * cgarray[j1][j2][j][ma1][ma2];
zarray_i[j1][j2][j][ma][mb] +=
sumb1_i * cgarray[j1][j2][j][ma1][ma2];
}
}
}
}
/* ----------------------------------------------------------------------
compute Bi by summing conj(Ui)*Zi
------------------------------------------------------------------------- */
void SNA::compute_bi()
{
// for j1 = 0,...,twojmax
// for j2 = 0,twojmax
// for j = |j1-j2|,Min(twojmax,j1+j2),2
// b(j1,j2,j) = 0
// for mb = 0,...,jmid
// for ma = 0,...,j
// b(j1,j2,j) +=
// 2*Conj(u(j,ma,mb))*z(j1,j2,j,ma,mb)
#ifdef TIMING_INFO
clock_gettime(CLOCK_REALTIME, &starttime);
#endif
for(int j1 = 0; j1 <= twojmax; j1++)
for(int j2 = 0; j2 <= j1; j2++) {
for(int j = abs(j1 - j2);
j <= MIN(twojmax, j1 + j2); j += 2) {
barray[j1][j2][j] = 0.0;
for(int mb = 0; 2*mb < j; mb++) {
for(int ma = 0; ma <= j; ma++) {
barray[j1][j2][j] +=
uarraytot_r[j][ma][mb] * zarray_r[j1][j2][j][ma][mb] +
uarraytot_i[j][ma][mb] * zarray_i[j1][j2][j][ma][mb];
}
}
// For j even, special treatment for middle column
if (j%2 == 0) {
int mb = j/2;
for(int ma = 0; ma < mb; ma++)
barray[j1][j2][j] +=
uarraytot_r[j][ma][mb] * zarray_r[j1][j2][j][ma][mb] +
uarraytot_i[j][ma][mb] * zarray_i[j1][j2][j][ma][mb];
int ma = mb;
barray[j1][j2][j] +=
(uarraytot_r[j][ma][mb] * zarray_r[j1][j2][j][ma][mb] +
uarraytot_i[j][ma][mb] * zarray_i[j1][j2][j][ma][mb])*0.5;
}
barray[j1][j2][j] *= 2.0;
}
}
#ifdef TIMING_INFO
clock_gettime(CLOCK_REALTIME, &endtime);
timers[2] += (endtime.tv_sec - starttime.tv_sec + 1.0 *
(endtime.tv_nsec - starttime.tv_nsec) / 1000000000);
#endif
}
/* ----------------------------------------------------------------------
copy Bi array to a vector
------------------------------------------------------------------------- */
void SNA::copy_bi2bvec()
{
int ncount, j1, j2, j;
ncount = 0;
for(j1 = 0; j1 <= twojmax; j1++)
if(diagonalstyle == 0) {
for(j2 = 0; j2 <= j1; j2++)
for(j = abs(j1 - j2);
j <= MIN(twojmax, j1 + j2); j += 2) {
bvec[ncount] = barray[j1][j2][j];
ncount++;
}
} else if(diagonalstyle == 1) {
j2 = j1;
for(j = abs(j1 - j2);
j <= MIN(twojmax, j1 + j2); j += 2) {
bvec[ncount] = barray[j1][j2][j];
ncount++;
}
} else if(diagonalstyle == 2) {
j = j2 = j1;
bvec[ncount] = barray[j1][j2][j];
ncount++;
} else if(diagonalstyle == 3) {
for(j2 = 0; j2 <= j1; j2++)
for(j = abs(j1 - j2);
j <= MIN(twojmax, j1 + j2); j += 2)
if (j >= j1) {
bvec[ncount] = barray[j1][j2][j];
ncount++;
}
}
}
/* ----------------------------------------------------------------------
calculate derivative of Ui w.r.t. atom j
------------------------------------------------------------------------- */
void SNA::compute_duidrj(double* rij, double wj, double rcut)
{
double rsq, r, x, y, z, z0, theta0, cs, sn;
double dz0dr;
x = rij[0];
y = rij[1];
z = rij[2];
rsq = x * x + y * y + z * z;
r = sqrt(rsq);
double rscale0 = rfac0 * MY_PI / (rcut - rmin0);
theta0 = (r - rmin0) * rscale0;
cs = cos(theta0);
sn = sin(theta0);
z0 = r * cs / sn;
dz0dr = z0 / r - (r*rscale0) * (rsq + z0 * z0) / rsq;
#ifdef TIMING_INFO
clock_gettime(CLOCK_REALTIME, &starttime);
#endif
compute_duarray(x, y, z, z0, r, dz0dr, wj, rcut);
#ifdef TIMING_INFO
clock_gettime(CLOCK_REALTIME, &endtime);
timers[3] += (endtime.tv_sec - starttime.tv_sec + 1.0 *
(endtime.tv_nsec - starttime.tv_nsec) / 1000000000);
#endif
}
/* ----------------------------------------------------------------------
calculate derivative of Bi w.r.t. atom j
variant using indexlist for j1,j2,j
variant not using symmetry relation
------------------------------------------------------------------------- */
void SNA::compute_dbidrj_nonsymm()
{
// for j1 = 0,...,twojmax
// for j2 = 0,twojmax
// for j = |j1-j2|,Min(twojmax,j1+j2),2
// dbdr(j1,j2,j) = 0
// for ma = 0,...,j
// for mb = 0,...,j
// dzdr = 0
// for ma1 = Max(0,ma+(j1-j2-j)/2),Min(j1,ma+(j1+j2-j)/2)
// sumb1 = 0
// ma2 = ma-ma1+(j1+j2-j)/2;
// for mb1 = Max(0,mb+(j1-j2-j)/2),Min(j1,mb+(j1+j2-j)/2)
// mb2 = mb-mb1+(j1+j2-j)/2;
// sumb1 += cg(j1,mb1,j2,mb2,j) *
// (dudr(j1,ma1,mb1) * u(j2,ma2,mb2) +
// u(j1,ma1,mb1) * dudr(j2,ma2,mb2))
// dzdr += sumb1*cg(j1,ma1,j2,ma2,j)
// dbdr(j1,j2,j) +=
// Conj(dudr(j,ma,mb))*z(j1,j2,j,ma,mb) +
// Conj(u(j,ma,mb))*dzdr
double* dbdr;
double* dudr_r, *dudr_i;
double sumb1_r[3], sumb1_i[3], dzdr_r[3], dzdr_i[3];
int ma2;
#ifdef TIMING_INFO
clock_gettime(CLOCK_REALTIME, &starttime);
#endif
for(int JJ = 0; JJ < idxj_max; JJ++) {
const int j1 = idxj[JJ].j1;
const int j2 = idxj[JJ].j2;
const int j = idxj[JJ].j;
dbdr = dbarray[j1][j2][j];
dbdr[0] = 0.0;
dbdr[1] = 0.0;
dbdr[2] = 0.0;
double** *j1duarray_r = duarray_r[j1];
double** *j2duarray_r = duarray_r[j2];
double** *j1duarray_i = duarray_i[j1];
double** *j2duarray_i = duarray_i[j2];
double** j1uarraytot_r = uarraytot_r[j1];
double** j2uarraytot_r = uarraytot_r[j2];
double** j1uarraytot_i = uarraytot_i[j1];
double** j2uarraytot_i = uarraytot_i[j2];
double** j1j2jcgarray = cgarray[j1][j2][j];
for(int ma = 0; ma <= j; ma++)
for(int mb = 0; mb <= j; mb++) {
dzdr_r[0] = 0.0;
dzdr_r[1] = 0.0;
dzdr_r[2] = 0.0;
dzdr_i[0] = 0.0;
dzdr_i[1] = 0.0;
dzdr_i[2] = 0.0;
const int max_mb1 = MIN(j1, (2 * mb - j + j2 + j1) / 2) + 1;
const int max_ma1 = MIN(j1, (2 * ma - j + j2 + j1) / 2) + 1;
for(int ma1 = MAX(0, (2 * ma - j - j2 + j1) / 2);
ma1 < max_ma1; ma1++) {
ma2 = (2 * ma - j - (2 * ma1 - j1) + j2) / 2;
sumb1_r[0] = 0.0;
sumb1_r[1] = 0.0;
sumb1_r[2] = 0.0;
sumb1_i[0] = 0.0;
sumb1_i[1] = 0.0;
sumb1_i[2] = 0.0;
//inside loop 54 operations (mul and add)
for(int mb1 = MAX(0, (2 * mb - j - j2 + j1) / 2),
mb2 = mb + (j1 + j2 - j) / 2 - mb1;
mb1 < max_mb1; mb1++, mb2--) {
double* dudr1_r, *dudr1_i, *dudr2_r, *dudr2_i;
dudr1_r = j1duarray_r[ma1][mb1];
dudr2_r = j2duarray_r[ma2][mb2];
dudr1_i = j1duarray_i[ma1][mb1];
dudr2_i = j2duarray_i[ma2][mb2];
const double cga_mb1mb2 = j1j2jcgarray[mb1][mb2];
const double uat_r_ma2mb2 = cga_mb1mb2 * j2uarraytot_r[ma2][mb2];
const double uat_r_ma1mb1 = cga_mb1mb2 * j1uarraytot_r[ma1][mb1];
const double uat_i_ma2mb2 = cga_mb1mb2 * j2uarraytot_i[ma2][mb2];
const double uat_i_ma1mb1 = cga_mb1mb2 * j1uarraytot_i[ma1][mb1];
for(int k = 0; k < 3; k++) {
sumb1_r[k] += dudr1_r[k] * uat_r_ma2mb2;
sumb1_r[k] -= dudr1_i[k] * uat_i_ma2mb2;
sumb1_i[k] += dudr1_r[k] * uat_i_ma2mb2;
sumb1_i[k] += dudr1_i[k] * uat_r_ma2mb2;
sumb1_r[k] += dudr2_r[k] * uat_r_ma1mb1;
sumb1_r[k] -= dudr2_i[k] * uat_i_ma1mb1;
sumb1_i[k] += dudr2_r[k] * uat_i_ma1mb1;
sumb1_i[k] += dudr2_i[k] * uat_r_ma1mb1;
}
} // end loop over mb1,mb2
// dzdr += sumb1*cg(j1,ma1,j2,ma2,j)
dzdr_r[0] += sumb1_r[0] * j1j2jcgarray[ma1][ma2];
dzdr_r[1] += sumb1_r[1] * j1j2jcgarray[ma1][ma2];
dzdr_r[2] += sumb1_r[2] * j1j2jcgarray[ma1][ma2];
dzdr_i[0] += sumb1_i[0] * j1j2jcgarray[ma1][ma2];
dzdr_i[1] += sumb1_i[1] * j1j2jcgarray[ma1][ma2];
dzdr_i[2] += sumb1_i[2] * j1j2jcgarray[ma1][ma2];
} // end loop over ma1,ma2
// dbdr(j1,j2,j) +=
// Conj(dudr(j,ma,mb))*z(j1,j2,j,ma,mb) +
// Conj(u(j,ma,mb))*dzdr
dudr_r = duarray_r[j][ma][mb];
dudr_i = duarray_i[j][ma][mb];
for(int k = 0; k < 3; k++)
dbdr[k] +=
(dudr_r[k] * zarray_r[j1][j2][j][ma][mb] +
dudr_i[k] * zarray_i[j1][j2][j][ma][mb]) +
(uarraytot_r[j][ma][mb] * dzdr_r[k] +
uarraytot_i[j][ma][mb] * dzdr_i[k]);
} //end loop over ma mb
} //end loop over j1 j2 j
#ifdef TIMING_INFO
clock_gettime(CLOCK_REALTIME, &endtime);
timers[4] += (endtime.tv_sec - starttime.tv_sec + 1.0 *
(endtime.tv_nsec - starttime.tv_nsec) / 1000000000);
#endif
}
/* ----------------------------------------------------------------------
calculate derivative of Bi w.r.t. atom j
variant using indexlist for j1,j2,j
variant using symmetry relation
------------------------------------------------------------------------- */
void SNA::compute_dbidrj()
{
// for j1 = 0,...,twojmax
// for j2 = 0,twojmax
// for j = |j1-j2|,Min(twojmax,j1+j2),2
// zdb = 0
// for mb = 0,...,jmid
// for ma = 0,...,j
// zdb +=
// Conj(dudr(j,ma,mb))*z(j1,j2,j,ma,mb)
// dbdr(j1,j2,j) += 2*zdb
// zdb = 0
// for mb1 = 0,...,j1mid
// for ma1 = 0,...,j1
// zdb +=
// Conj(dudr(j1,ma1,mb1))*z(j1,j2,j,ma1,mb1)
// dbdr(j1,j2,j) += 2*zdb*(j+1)/(j1+1)
// zdb = 0
// for mb2 = 0,...,j2mid
// for ma2 = 0,...,j2
// zdb +=
// Conj(dudr(j2,ma2,mb2))*z(j1,j,j2,ma2,mb2)
// dbdr(j1,j2,j) += 2*zdb*(j+1)/(j2+1)
double* dbdr;
double* dudr_r, *dudr_i;
double sumzdu_r[3];
double** jjjzarray_r;
double** jjjzarray_i;
double jjjmambzarray_r;
double jjjmambzarray_i;
#ifdef TIMING_INFO
clock_gettime(CLOCK_REALTIME, &starttime);
#endif
for(int JJ = 0; JJ < idxj_max; JJ++) {
const int j1 = idxj[JJ].j1;
const int j2 = idxj[JJ].j2;
const int j = idxj[JJ].j;
dbdr = dbarray[j1][j2][j];
dbdr[0] = 0.0;
dbdr[1] = 0.0;
dbdr[2] = 0.0;
// Sum terms Conj(dudr(j,ma,mb))*z(j1,j2,j,ma,mb)
for(int k = 0; k < 3; k++)
sumzdu_r[k] = 0.0;
// use zarray j1/j2 symmetry (optional)
if (j1 >= j2) {
jjjzarray_r = zarray_r[j1][j2][j];
jjjzarray_i = zarray_i[j1][j2][j];
} else {
jjjzarray_r = zarray_r[j2][j1][j];
jjjzarray_i = zarray_i[j2][j1][j];
}
for(int mb = 0; 2*mb < j; mb++)
for(int ma = 0; ma <= j; ma++) {
dudr_r = duarray_r[j][ma][mb];
dudr_i = duarray_i[j][ma][mb];
jjjmambzarray_r = jjjzarray_r[ma][mb];
jjjmambzarray_i = jjjzarray_i[ma][mb];
for(int k = 0; k < 3; k++)
sumzdu_r[k] +=
dudr_r[k] * jjjmambzarray_r +
dudr_i[k] * jjjmambzarray_i;
} //end loop over ma mb
// For j even, handle middle column
if (j%2 == 0) {
int mb = j/2;
for(int ma = 0; ma < mb; ma++) {
dudr_r = duarray_r[j][ma][mb];
dudr_i = duarray_i[j][ma][mb];
jjjmambzarray_r = jjjzarray_r[ma][mb];
jjjmambzarray_i = jjjzarray_i[ma][mb];
for(int k = 0; k < 3; k++)
sumzdu_r[k] +=
dudr_r[k] * jjjmambzarray_r +
dudr_i[k] * jjjmambzarray_i;
}
int ma = mb;
dudr_r = duarray_r[j][ma][mb];
dudr_i = duarray_i[j][ma][mb];
jjjmambzarray_r = jjjzarray_r[ma][mb];
jjjmambzarray_i = jjjzarray_i[ma][mb];
for(int k = 0; k < 3; k++)
sumzdu_r[k] +=
(dudr_r[k] * jjjmambzarray_r +
dudr_i[k] * jjjmambzarray_i)*0.5;
} // end if jeven
for(int k = 0; k < 3; k++)
dbdr[k] += 2.0*sumzdu_r[k];
// Sum over Conj(dudr(j1,ma1,mb1))*z(j,j2,j1,ma1,mb1)
double j1fac = (j+1)/(j1+1.0);
for(int k = 0; k < 3; k++)
sumzdu_r[k] = 0.0;
// use zarray j1/j2 symmetry (optional)
if (j >= j2) {
jjjzarray_r = zarray_r[j][j2][j1];
jjjzarray_i = zarray_i[j][j2][j1];
} else {
jjjzarray_r = zarray_r[j2][j][j1];
jjjzarray_i = zarray_i[j2][j][j1];
}
for(int mb1 = 0; 2*mb1 < j1; mb1++)
for(int ma1 = 0; ma1 <= j1; ma1++) {
dudr_r = duarray_r[j1][ma1][mb1];
dudr_i = duarray_i[j1][ma1][mb1];
jjjmambzarray_r = jjjzarray_r[ma1][mb1];
jjjmambzarray_i = jjjzarray_i[ma1][mb1];
for(int k = 0; k < 3; k++)
sumzdu_r[k] +=
dudr_r[k] * jjjmambzarray_r +
dudr_i[k] * jjjmambzarray_i;
} //end loop over ma1 mb1
// For j1 even, handle middle column
if (j1%2 == 0) {
int mb1 = j1/2;
for(int ma1 = 0; ma1 < mb1; ma1++) {
dudr_r = duarray_r[j1][ma1][mb1];
dudr_i = duarray_i[j1][ma1][mb1];
jjjmambzarray_r = jjjzarray_r[ma1][mb1];
jjjmambzarray_i = jjjzarray_i[ma1][mb1];
for(int k = 0; k < 3; k++)
sumzdu_r[k] +=
dudr_r[k] * jjjmambzarray_r +
dudr_i[k] * jjjmambzarray_i;
}
int ma1 = mb1;
dudr_r = duarray_r[j1][ma1][mb1];
dudr_i = duarray_i[j1][ma1][mb1];
jjjmambzarray_r = jjjzarray_r[ma1][mb1];
jjjmambzarray_i = jjjzarray_i[ma1][mb1];
for(int k = 0; k < 3; k++)
sumzdu_r[k] +=
(dudr_r[k] * jjjmambzarray_r +
dudr_i[k] * jjjmambzarray_i)*0.5;
} // end if j1even
for(int k = 0; k < 3; k++)
dbdr[k] += 2.0*sumzdu_r[k]*j1fac;
// Sum over Conj(dudr(j2,ma2,mb2))*z(j1,j,j2,ma2,mb2)
double j2fac = (j+1)/(j2+1.0);
for(int k = 0; k < 3; k++)
sumzdu_r[k] = 0.0;
// use zarray j1/j2 symmetry (optional)
if (j1 >= j) {
jjjzarray_r = zarray_r[j1][j][j2];
jjjzarray_i = zarray_i[j1][j][j2];
} else {
jjjzarray_r = zarray_r[j][j1][j2];
jjjzarray_i = zarray_i[j][j1][j2];
}
for(int mb2 = 0; 2*mb2 < j2; mb2++)
for(int ma2 = 0; ma2 <= j2; ma2++) {
dudr_r = duarray_r[j2][ma2][mb2];
dudr_i = duarray_i[j2][ma2][mb2];
jjjmambzarray_r = jjjzarray_r[ma2][mb2];
jjjmambzarray_i = jjjzarray_i[ma2][mb2];
for(int k = 0; k < 3; k++)
sumzdu_r[k] +=
dudr_r[k] * jjjmambzarray_r +
dudr_i[k] * jjjmambzarray_i;
} //end loop over ma2 mb2
// For j2 even, handle middle column
if (j2%2 == 0) {
int mb2 = j2/2;
for(int ma2 = 0; ma2 < mb2; ma2++) {
dudr_r = duarray_r[j2][ma2][mb2];
dudr_i = duarray_i[j2][ma2][mb2];
jjjmambzarray_r = jjjzarray_r[ma2][mb2];
jjjmambzarray_i = jjjzarray_i[ma2][mb2];
for(int k = 0; k < 3; k++)
sumzdu_r[k] +=
dudr_r[k] * jjjmambzarray_r +
dudr_i[k] * jjjmambzarray_i;
}
int ma2 = mb2;
dudr_r = duarray_r[j2][ma2][mb2];
dudr_i = duarray_i[j2][ma2][mb2];
jjjmambzarray_r = jjjzarray_r[ma2][mb2];
jjjmambzarray_i = jjjzarray_i[ma2][mb2];
for(int k = 0; k < 3; k++)
sumzdu_r[k] +=
(dudr_r[k] * jjjmambzarray_r +
dudr_i[k] * jjjmambzarray_i)*0.5;
} // end if j2even
for(int k = 0; k < 3; k++)
dbdr[k] += 2.0*sumzdu_r[k]*j2fac;
} //end loop over j1 j2 j
#ifdef TIMING_INFO
clock_gettime(CLOCK_REALTIME, &endtime);
timers[4] += (endtime.tv_sec - starttime.tv_sec + 1.0 *
(endtime.tv_nsec - starttime.tv_nsec) / 1000000000);
#endif
}
/* ----------------------------------------------------------------------
copy Bi derivatives into a vector
------------------------------------------------------------------------- */
void SNA::copy_dbi2dbvec()
{
int ncount, j1, j2, j;
ncount = 0;
for(j1 = 0; j1 <= twojmax; j1++) {
if(diagonalstyle == 0) {
for(j2 = 0; j2 <= j1; j2++)
for(j = abs(j1 - j2);
j <= MIN(twojmax, j1 + j2); j += 2) {
dbvec[ncount][0] = dbarray[j1][j2][j][0];
dbvec[ncount][1] = dbarray[j1][j2][j][1];
dbvec[ncount][2] = dbarray[j1][j2][j][2];
ncount++;
}
} else if(diagonalstyle == 1) {
j2 = j1;
for(j = abs(j1 - j2);
j <= MIN(twojmax, j1 + j2); j += 2) {
dbvec[ncount][0] = dbarray[j1][j2][j][0];
dbvec[ncount][1] = dbarray[j1][j2][j][1];
dbvec[ncount][2] = dbarray[j1][j2][j][2];
ncount++;
}
} else if(diagonalstyle == 2) {
j = j2 = j1;
dbvec[ncount][0] = dbarray[j1][j2][j][0];
dbvec[ncount][1] = dbarray[j1][j2][j][1];
dbvec[ncount][2] = dbarray[j1][j2][j][2];
ncount++;
} else if(diagonalstyle == 3) {
for(j2 = 0; j2 <= j1; j2++)
for(j = abs(j1 - j2);
j <= MIN(twojmax, j1 + j2); j += 2)
if (j >= j1) {
dbvec[ncount][0] = dbarray[j1][j2][j][0];
dbvec[ncount][1] = dbarray[j1][j2][j][1];
dbvec[ncount][2] = dbarray[j1][j2][j][2];
ncount++;
}
}
}
}
/* ---------------------------------------------------------------------- */
void SNA::zero_uarraytot()
{
for (int j = 0; j <= twojmax; j++)
for (int ma = 0; ma <= j; ma++)
for (int mb = 0; mb <= j; mb++) {
uarraytot_r[j][ma][mb] = 0.0;
uarraytot_i[j][ma][mb] = 0.0;
}
}
/* ---------------------------------------------------------------------- */
void SNA::addself_uarraytot(double wself_in)
{
for (int j = 0; j <= twojmax; j++)
for (int ma = 0; ma <= j; ma++) {
uarraytot_r[j][ma][ma] = wself_in;
uarraytot_i[j][ma][ma] = 0.0;
}
}
/* ----------------------------------------------------------------------
add Wigner U-functions for one neighbor to the total
------------------------------------------------------------------------- */
void SNA::add_uarraytot(double r, double wj, double rcut)
{
double sfac;
sfac = compute_sfac(r, rcut);
sfac *= wj;
for (int j = 0; j <= twojmax; j++)
for (int ma = 0; ma <= j; ma++)
for (int mb = 0; mb <= j; mb++) {
uarraytot_r[j][ma][mb] +=
sfac * uarray_r[j][ma][mb];
uarraytot_i[j][ma][mb] +=
sfac * uarray_i[j][ma][mb];
}
}
void SNA::add_uarraytot_omp(double r, double wj, double rcut)
{
double sfac;
sfac = compute_sfac(r, rcut);
sfac *= wj;
#if defined(_OPENMP)
#pragma omp for
#endif
for (int j = 0; j <= twojmax; j++)
for (int ma = 0; ma <= j; ma++)
for (int mb = 0; mb <= j; mb++) {
uarraytot_r[j][ma][mb] +=
sfac * uarray_r[j][ma][mb];
uarraytot_i[j][ma][mb] +=
sfac * uarray_i[j][ma][mb];
}
}
/* ----------------------------------------------------------------------
compute Wigner U-functions for one neighbor
------------------------------------------------------------------------- */
void SNA::compute_uarray(double x, double y, double z,
double z0, double r)
{
double r0inv;
double a_r, b_r, a_i, b_i;
double rootpq;
// compute Cayley-Klein parameters for unit quaternion
r0inv = 1.0 / sqrt(r * r + z0 * z0);
a_r = r0inv * z0;
a_i = -r0inv * z;
b_r = r0inv * y;
b_i = -r0inv * x;
// VMK Section 4.8.2
uarray_r[0][0][0] = 1.0;
uarray_i[0][0][0] = 0.0;
for (int j = 1; j <= twojmax; j++) {
// fill in left side of matrix layer from previous layer
for (int mb = 0; 2*mb <= j; mb++) {
uarray_r[j][0][mb] = 0.0;
uarray_i[j][0][mb] = 0.0;
for (int ma = 0; ma < j; ma++) {
rootpq = rootpqarray[j - ma][j - mb];
uarray_r[j][ma][mb] +=
rootpq *
(a_r * uarray_r[j - 1][ma][mb] +
a_i * uarray_i[j - 1][ma][mb]);
uarray_i[j][ma][mb] +=
rootpq *
(a_r * uarray_i[j - 1][ma][mb] -
a_i * uarray_r[j - 1][ma][mb]);
rootpq = rootpqarray[ma + 1][j - mb];
uarray_r[j][ma + 1][mb] =
-rootpq *
(b_r * uarray_r[j - 1][ma][mb] +
b_i * uarray_i[j - 1][ma][mb]);
uarray_i[j][ma + 1][mb] =
-rootpq *
(b_r * uarray_i[j - 1][ma][mb] -
b_i * uarray_r[j - 1][ma][mb]);
}
}
// copy left side to right side with inversion symmetry VMK 4.4(2)
// u[ma-j][mb-j] = (-1)^(ma-mb)*Conj([u[ma][mb])
int mbpar = -1;
for (int mb = 0; 2*mb <= j; mb++) {
mbpar = -mbpar;
int mapar = -mbpar;
for (int ma = 0; ma <= j; ma++) {
mapar = -mapar;
if (mapar == 1) {
uarray_r[j][j-ma][j-mb] = uarray_r[j][ma][mb];
uarray_i[j][j-ma][j-mb] = -uarray_i[j][ma][mb];
} else {
uarray_r[j][j-ma][j-mb] = -uarray_r[j][ma][mb];
uarray_i[j][j-ma][j-mb] = uarray_i[j][ma][mb];
}
}
}
}
}
void SNA::compute_uarray_omp(double x, double y, double z,
double z0, double r, int sub_threads)
{
double r0inv;
double a_r, b_r, a_i, b_i;
double rootpq;
// compute Cayley-Klein parameters for unit quaternion
r0inv = 1.0 / sqrt(r * r + z0 * z0);
a_r = r0inv * z0;
a_i = -r0inv * z;
b_r = r0inv * y;
b_i = -r0inv * x;
// VMK Section 4.8.2
uarray_r[0][0][0] = 1.0;
uarray_i[0][0][0] = 0.0;
for (int j = 1; j <= twojmax; j++) {
#if defined(_OPENMP)
#pragma omp for
#endif
for (int mb = 0; mb < j; mb++) {
uarray_r[j][0][mb] = 0.0;
uarray_i[j][0][mb] = 0.0;
for (int ma = 0; ma < j; ma++) {
rootpq = rootpqarray[j - ma][j - mb];
uarray_r[j][ma][mb] +=
rootpq *
(a_r * uarray_r[j - 1][ma][mb] +
a_i * uarray_i[j - 1][ma][mb]);
uarray_i[j][ma][mb] +=
rootpq *
(a_r * uarray_i[j - 1][ma][mb] -
a_i * uarray_r[j - 1][ma][mb]);
rootpq = rootpqarray[ma + 1][j - mb];
uarray_r[j][ma + 1][mb] =
-rootpq *
(b_r * uarray_r[j - 1][ma][mb] +
b_i * uarray_i[j - 1][ma][mb]);
uarray_i[j][ma + 1][mb] =
-rootpq *
(b_r * uarray_i[j - 1][ma][mb] -
b_i * uarray_r[j - 1][ma][mb]);
}
}
int mb = j;
uarray_r[j][0][mb] = 0.0;
uarray_i[j][0][mb] = 0.0;
#if defined(_OPENMP)
#pragma omp for
#endif
for (int ma = 0; ma < j; ma++) {
rootpq = rootpqarray[j - ma][mb];
uarray_r[j][ma][mb] +=
rootpq *
(b_r * uarray_r[j - 1][ma][mb - 1] -
b_i * uarray_i[j - 1][ma][mb - 1]);
uarray_i[j][ma][mb] +=
rootpq *
(b_r * uarray_i[j - 1][ma][mb - 1] +
b_i * uarray_r[j - 1][ma][mb - 1]);
rootpq = rootpqarray[ma + 1][mb];
uarray_r[j][ma + 1][mb] =
rootpq *
(a_r * uarray_r[j - 1][ma][mb - 1] -
a_i * uarray_i[j - 1][ma][mb - 1]);
uarray_i[j][ma + 1][mb] =
rootpq *
(a_r * uarray_i[j - 1][ma][mb - 1] +
a_i * uarray_r[j - 1][ma][mb - 1]);
}
}
}
/* ----------------------------------------------------------------------
compute derivatives of Wigner U-functions for one neighbor
see comments in compute_uarray()
------------------------------------------------------------------------- */
void SNA::compute_duarray(double x, double y, double z,
double z0, double r, double dz0dr,
double wj, double rcut)
{
double r0inv;
double a_r, a_i, b_r, b_i;
double da_r[3], da_i[3], db_r[3], db_i[3];
double dz0[3], dr0inv[3], dr0invdr;
double rootpq;
double rinv = 1.0 / r;
double ux = x * rinv;
double uy = y * rinv;
double uz = z * rinv;
r0inv = 1.0 / sqrt(r * r + z0 * z0);
a_r = z0 * r0inv;
a_i = -z * r0inv;
b_r = y * r0inv;
b_i = -x * r0inv;
dr0invdr = -pow(r0inv, 3.0) * (r + z0 * dz0dr);
dr0inv[0] = dr0invdr * ux;
dr0inv[1] = dr0invdr * uy;
dr0inv[2] = dr0invdr * uz;
dz0[0] = dz0dr * ux;
dz0[1] = dz0dr * uy;
dz0[2] = dz0dr * uz;
for (int k = 0; k < 3; k++) {
da_r[k] = dz0[k] * r0inv + z0 * dr0inv[k];
da_i[k] = -z * dr0inv[k];
}
da_i[2] += -r0inv;
for (int k = 0; k < 3; k++) {
db_r[k] = y * dr0inv[k];
db_i[k] = -x * dr0inv[k];
}
db_i[0] += -r0inv;
db_r[1] += r0inv;
uarray_r[0][0][0] = 1.0;
duarray_r[0][0][0][0] = 0.0;
duarray_r[0][0][0][1] = 0.0;
duarray_r[0][0][0][2] = 0.0;
uarray_i[0][0][0] = 0.0;
duarray_i[0][0][0][0] = 0.0;
duarray_i[0][0][0][1] = 0.0;
duarray_i[0][0][0][2] = 0.0;
for (int j = 1; j <= twojmax; j++) {
for (int mb = 0; 2*mb <= j; mb++) {
uarray_r[j][0][mb] = 0.0;
duarray_r[j][0][mb][0] = 0.0;
duarray_r[j][0][mb][1] = 0.0;
duarray_r[j][0][mb][2] = 0.0;
uarray_i[j][0][mb] = 0.0;
duarray_i[j][0][mb][0] = 0.0;
duarray_i[j][0][mb][1] = 0.0;
duarray_i[j][0][mb][2] = 0.0;
for (int ma = 0; ma < j; ma++) {
rootpq = rootpqarray[j - ma][j - mb];
uarray_r[j][ma][mb] += rootpq *
(a_r * uarray_r[j - 1][ma][mb] +
a_i * uarray_i[j - 1][ma][mb]);
uarray_i[j][ma][mb] += rootpq *
(a_r * uarray_i[j - 1][ma][mb] -
a_i * uarray_r[j - 1][ma][mb]);
for (int k = 0; k < 3; k++) {
duarray_r[j][ma][mb][k] +=
rootpq * (da_r[k] * uarray_r[j - 1][ma][mb] +
da_i[k] * uarray_i[j - 1][ma][mb] +
a_r * duarray_r[j - 1][ma][mb][k] +
a_i * duarray_i[j - 1][ma][mb][k]);
duarray_i[j][ma][mb][k] +=
rootpq * (da_r[k] * uarray_i[j - 1][ma][mb] -
da_i[k] * uarray_r[j - 1][ma][mb] +
a_r * duarray_i[j - 1][ma][mb][k] -
a_i * duarray_r[j - 1][ma][mb][k]);
}
rootpq = rootpqarray[ma + 1][j - mb];
uarray_r[j][ma + 1][mb] =
-rootpq * (b_r * uarray_r[j - 1][ma][mb] +
b_i * uarray_i[j - 1][ma][mb]);
uarray_i[j][ma + 1][mb] =
-rootpq * (b_r * uarray_i[j - 1][ma][mb] -
b_i * uarray_r[j - 1][ma][mb]);
for (int k = 0; k < 3; k++) {
duarray_r[j][ma + 1][mb][k] =
-rootpq * (db_r[k] * uarray_r[j - 1][ma][mb] +
db_i[k] * uarray_i[j - 1][ma][mb] +
b_r * duarray_r[j - 1][ma][mb][k] +
b_i * duarray_i[j - 1][ma][mb][k]);
duarray_i[j][ma + 1][mb][k] =
-rootpq * (db_r[k] * uarray_i[j - 1][ma][mb] -
db_i[k] * uarray_r[j - 1][ma][mb] +
b_r * duarray_i[j - 1][ma][mb][k] -
b_i * duarray_r[j - 1][ma][mb][k]);
}
}
}
int mbpar = -1;
for (int mb = 0; 2*mb <= j; mb++) {
mbpar = -mbpar;
int mapar = -mbpar;
for (int ma = 0; ma <= j; ma++) {
mapar = -mapar;
if (mapar == 1) {
uarray_r[j][j-ma][j-mb] = uarray_r[j][ma][mb];
uarray_i[j][j-ma][j-mb] = -uarray_i[j][ma][mb];
for (int k = 0; k < 3; k++) {
duarray_r[j][j-ma][j-mb][k] = duarray_r[j][ma][mb][k];
duarray_i[j][j-ma][j-mb][k] = -duarray_i[j][ma][mb][k];
}
} else {
uarray_r[j][j-ma][j-mb] = -uarray_r[j][ma][mb];
uarray_i[j][j-ma][j-mb] = uarray_i[j][ma][mb];
for (int k = 0; k < 3; k++) {
duarray_r[j][j-ma][j-mb][k] = -duarray_r[j][ma][mb][k];
duarray_i[j][j-ma][j-mb][k] = duarray_i[j][ma][mb][k];
}
}
}
}
}
double sfac = compute_sfac(r, rcut);
double dsfac = compute_dsfac(r, rcut);
sfac *= wj;
dsfac *= wj;
for (int j = 0; j <= twojmax; j++)
for (int ma = 0; ma <= j; ma++)
for (int mb = 0; mb <= j; mb++) {
duarray_r[j][ma][mb][0] = dsfac * uarray_r[j][ma][mb] * ux +
sfac * duarray_r[j][ma][mb][0];
duarray_i[j][ma][mb][0] = dsfac * uarray_i[j][ma][mb] * ux +
sfac * duarray_i[j][ma][mb][0];
duarray_r[j][ma][mb][1] = dsfac * uarray_r[j][ma][mb] * uy +
sfac * duarray_r[j][ma][mb][1];
duarray_i[j][ma][mb][1] = dsfac * uarray_i[j][ma][mb] * uy +
sfac * duarray_i[j][ma][mb][1];
duarray_r[j][ma][mb][2] = dsfac * uarray_r[j][ma][mb] * uz +
sfac * duarray_r[j][ma][mb][2];
duarray_i[j][ma][mb][2] = dsfac * uarray_i[j][ma][mb] * uz +
sfac * duarray_i[j][ma][mb][2];
}
}
/* ----------------------------------------------------------------------
memory usage of arrays
------------------------------------------------------------------------- */
double SNA::memory_usage()
{
int jdim = twojmax + 1;
double bytes;
bytes = jdim * jdim * jdim * jdim * jdim * sizeof(double);
bytes += 2 * jdim * jdim * jdim * sizeof(complex<double>);
bytes += 2 * jdim * jdim * jdim * sizeof(double);
bytes += jdim * jdim * jdim * 3 * sizeof(complex<double>);
bytes += jdim * jdim * jdim * 3 * sizeof(double);
bytes += ncoeff * sizeof(double);
bytes += jdim * jdim * jdim * jdim * jdim * sizeof(complex<double>);
return bytes;
}
/* ---------------------------------------------------------------------- */
void SNA::create_twojmax_arrays()
{
int jdim = twojmax + 1;
memory->create(cgarray, jdim, jdim, jdim, jdim, jdim,
"sna:cgarray");
memory->create(rootpqarray, jdim+1, jdim+1,
"sna:rootpqarray");
memory->create(barray, jdim, jdim, jdim,
"sna:barray");
memory->create(dbarray, jdim, jdim, jdim, 3,
"sna:dbarray");
memory->create(duarray_r, jdim, jdim, jdim, 3,
"sna:duarray");
memory->create(duarray_i, jdim, jdim, jdim, 3,
"sna:duarray");
memory->create(uarray_r, jdim, jdim, jdim,
"sna:uarray");
memory->create(uarray_i, jdim, jdim, jdim,
"sna:uarray");
if(!use_shared_arrays) {
memory->create(uarraytot_r, jdim, jdim, jdim,
"sna:uarraytot");
memory->create(zarray_r, jdim, jdim, jdim, jdim, jdim,
"sna:zarray");
memory->create(uarraytot_i, jdim, jdim, jdim,
"sna:uarraytot");
memory->create(zarray_i, jdim, jdim, jdim, jdim, jdim,
"sna:zarray");
}
}
/* ---------------------------------------------------------------------- */
void SNA::destroy_twojmax_arrays()
{
memory->destroy(cgarray);
memory->destroy(rootpqarray);
memory->destroy(barray);
memory->destroy(dbarray);
memory->destroy(duarray_r);
memory->destroy(duarray_i);
memory->destroy(uarray_r);
memory->destroy(uarray_i);
if(!use_shared_arrays) {
memory->destroy(uarraytot_r);
memory->destroy(zarray_r);
memory->destroy(uarraytot_i);
memory->destroy(zarray_i);
}
}
/* ----------------------------------------------------------------------
store n! and return it as needed
------------------------------------------------------------------------- */
double SNA::factorial(int n)
{
const int nmax = 167; // Largest n supported
double nfac_table[nmax+1] = {
1,
1,
2,
6,
24,
120,
720,
5040,
40320,
362880,
3628800,
39916800,
479001600,
6227020800,
87178291200,
1307674368000,
20922789888000,
355687428096000,
6.402373705728e+15,
1.21645100408832e+17,
2.43290200817664e+18,
5.10909421717094e+19,
1.12400072777761e+21,
2.5852016738885e+22,
6.20448401733239e+23,
1.5511210043331e+25,
4.03291461126606e+26,
1.08888694504184e+28,
3.04888344611714e+29,
8.8417619937397e+30,
2.65252859812191e+32,
8.22283865417792e+33,
2.63130836933694e+35,
8.68331761881189e+36,
2.95232799039604e+38,
1.03331479663861e+40,
3.71993326789901e+41,
1.37637530912263e+43,
5.23022617466601e+44,
2.03978820811974e+46,
8.15915283247898e+47,
3.34525266131638e+49,
1.40500611775288e+51,
6.04152630633738e+52,
2.65827157478845e+54,
1.1962222086548e+56,
5.50262215981209e+57,
2.58623241511168e+59,
1.24139155925361e+61,
6.08281864034268e+62,
3.04140932017134e+64,
1.55111875328738e+66,
8.06581751709439e+67,
4.27488328406003e+69,
2.30843697339241e+71,
1.26964033536583e+73,
7.10998587804863e+74,
4.05269195048772e+76,
2.35056133128288e+78,
1.3868311854569e+80,
8.32098711274139e+81,
5.07580213877225e+83,
3.14699732603879e+85,
1.98260831540444e+87,
1.26886932185884e+89,
8.24765059208247e+90,
5.44344939077443e+92,
3.64711109181887e+94,
2.48003554243683e+96,
1.71122452428141e+98,
1.19785716699699e+100,
8.50478588567862e+101,
6.12344583768861e+103,
4.47011546151268e+105,
3.30788544151939e+107,
2.48091408113954e+109,
1.88549470166605e+111,
1.45183092028286e+113,
1.13242811782063e+115,
8.94618213078297e+116,
7.15694570462638e+118,
5.79712602074737e+120,
4.75364333701284e+122,
3.94552396972066e+124,
3.31424013456535e+126,
2.81710411438055e+128,
2.42270953836727e+130,
2.10775729837953e+132,
1.85482642257398e+134,
1.65079551609085e+136,
1.48571596448176e+138,
1.3520015276784e+140,
1.24384140546413e+142,
1.15677250708164e+144,
1.08736615665674e+146,
1.03299784882391e+148,
9.91677934870949e+149,
9.61927596824821e+151,
9.42689044888324e+153,
9.33262154439441e+155,
9.33262154439441e+157,
9.42594775983835e+159,
9.61446671503512e+161,
9.90290071648618e+163,
1.02990167451456e+166,
1.08139675824029e+168,
1.14628056373471e+170,
1.22652020319614e+172,
1.32464181945183e+174,
1.44385958320249e+176,
1.58824554152274e+178,
1.76295255109024e+180,
1.97450685722107e+182,
2.23119274865981e+184,
2.54355973347219e+186,
2.92509369349301e+188,
3.3931086844519e+190,
3.96993716080872e+192,
4.68452584975429e+194,
5.5745857612076e+196,
6.68950291344912e+198,
8.09429852527344e+200,
9.8750442008336e+202,
1.21463043670253e+205,
1.50614174151114e+207,
1.88267717688893e+209,
2.37217324288005e+211,
3.01266001845766e+213,
3.8562048236258e+215,
4.97450422247729e+217,
6.46685548922047e+219,
8.47158069087882e+221,
1.118248651196e+224,
1.48727070609069e+226,
1.99294274616152e+228,
2.69047270731805e+230,
3.65904288195255e+232,
5.01288874827499e+234,
6.91778647261949e+236,
9.61572319694109e+238,
1.34620124757175e+241,
1.89814375907617e+243,
2.69536413788816e+245,
3.85437071718007e+247,
5.5502938327393e+249,
8.04792605747199e+251,
1.17499720439091e+254,
1.72724589045464e+256,
2.55632391787286e+258,
3.80892263763057e+260,
5.71338395644585e+262,
8.62720977423323e+264,
1.31133588568345e+267,
2.00634390509568e+269,
3.08976961384735e+271,
4.78914290146339e+273,
7.47106292628289e+275,
1.17295687942641e+278,
1.85327186949373e+280,
2.94670227249504e+282,
4.71472363599206e+284,
7.59070505394721e+286,
1.22969421873945e+289,
2.0044015765453e+291,
3.28721858553429e+293,
5.42391066613159e+295,
9.00369170577843e+297,
1.503616514865e+300,
};
if(n < 0 || n > nmax) {
char str[128];
sprintf(str, "Invalid argument to factorial %d", n);
error->all(FLERR, str);
}
return nfac_table[n];
}
/* ----------------------------------------------------------------------
the function delta given by VMK Eq. 8.2(1)
------------------------------------------------------------------------- */
double SNA::deltacg(int j1, int j2, int j)
{
double sfaccg = factorial((j1 + j2 + j) / 2 + 1);
return sqrt(factorial((j1 + j2 - j) / 2) *
factorial((j1 - j2 + j) / 2) *
factorial((-j1 + j2 + j) / 2) / sfaccg);
}
/* ----------------------------------------------------------------------
assign Clebsch-Gordan coefficients using
the quasi-binomial formula VMK 8.2.1(3)
------------------------------------------------------------------------- */
void SNA::init_clebsch_gordan()
{
double sum,dcg,sfaccg;
int m, aa2, bb2, cc2;
int ifac;
for (int j1 = 0; j1 <= twojmax; j1++)
for (int j2 = 0; j2 <= twojmax; j2++)
for (int j = abs(j1 - j2); j <= MIN(twojmax, j1 + j2); j += 2)
for (int m1 = 0; m1 <= j1; m1 += 1) {
aa2 = 2 * m1 - j1;
for (int m2 = 0; m2 <= j2; m2 += 1) {
// -c <= cc <= c
bb2 = 2 * m2 - j2;
m = (aa2 + bb2 + j) / 2;
if(m < 0 || m > j) continue;
sum = 0.0;
for (int z = MAX(0, MAX(-(j - j2 + aa2)
/ 2, -(j - j1 - bb2) / 2));
z <= MIN((j1 + j2 - j) / 2,
MIN((j1 - aa2) / 2, (j2 + bb2) / 2));
z++) {
ifac = z % 2 ? -1 : 1;
sum += ifac /
(factorial(z) *
factorial((j1 + j2 - j) / 2 - z) *
factorial((j1 - aa2) / 2 - z) *
factorial((j2 + bb2) / 2 - z) *
factorial((j - j2 + aa2) / 2 + z) *
factorial((j - j1 - bb2) / 2 + z));
}
cc2 = 2 * m - j;
dcg = deltacg(j1, j2, j);
sfaccg = sqrt(factorial((j1 + aa2) / 2) *
factorial((j1 - aa2) / 2) *
factorial((j2 + bb2) / 2) *
factorial((j2 - bb2) / 2) *
factorial((j + cc2) / 2) *
factorial((j - cc2) / 2) *
(j + 1));
cgarray[j1][j2][j][m1][m2] = sum * dcg * sfaccg;
}
}
}
/* ----------------------------------------------------------------------
pre-compute table of sqrt[p/m2], p, q = 1,twojmax
the p = 0, q = 0 entries are allocated and skipped for convenience.
------------------------------------------------------------------------- */
void SNA::init_rootpqarray()
{
for (int p = 1; p <= twojmax; p++)
for (int q = 1; q <= twojmax; q++)
rootpqarray[p][q] = sqrt(static_cast<double>(p)/q);
}
/* ----------------------------------------------------------------------
a = j/2
------------------------------------------------------------------------- */
void SNA::jtostr(char* str, int j)
{
if(j % 2 == 0)
sprintf(str, "%d", j / 2);
else
sprintf(str, "%d/2", j);
}
/* ----------------------------------------------------------------------
aa = m - j/2
------------------------------------------------------------------------- */
void SNA::mtostr(char* str, int j, int m)
{
if(j % 2 == 0)
sprintf(str, "%d", m - j / 2);
else
sprintf(str, "%d/2", 2 * m - j);
}
/* ----------------------------------------------------------------------
list values of Clebsch-Gordan coefficients
using notation of VMK Table 8.11
------------------------------------------------------------------------- */
void SNA::print_clebsch_gordan(FILE* file)
{
char stra[20], strb[20], strc[20], straa[20], strbb[20], strcc[20];
int m, aa2, bb2;
fprintf(file, "a, aa, b, bb, c, cc, c(a,aa,b,bb,c,cc) \n");
for (int j1 = 0; j1 <= twojmax; j1++) {
jtostr(stra, j1);
for (int j2 = 0; j2 <= twojmax; j2++) {
jtostr(strb, j2);
for (int j = abs(j1 - j2); j <= MIN(twojmax, j1 + j2); j += 2) {
jtostr(strc, j);
for (int m1 = 0; m1 <= j1; m1 += 1) {
mtostr(straa, j1, m1);
aa2 = 2 * m1 - j1;
for (int m2 = 0; m2 <= j2; m2 += 1) {
bb2 = 2 * m2 - j2;
m = (aa2 + bb2 + j) / 2;
if(m < 0 || m > j) continue;
mtostr(strbb, j2, m2);
mtostr(strcc, j, m);
fprintf(file, "%s\t%s\t%s\t%s\t%s\t%s\t%g\n",
stra, straa, strb, strbb, strc, strcc,
cgarray[j1][j2][j][m1][m2]);
}
}
}
}
}
}
/* ---------------------------------------------------------------------- */
int SNA::compute_ncoeff()
{
int ncount;
ncount = 0;
for (int j1 = 0; j1 <= twojmax; j1++)
if(diagonalstyle == 0) {
for (int j2 = 0; j2 <= j1; j2++)
for (int j = abs(j1 - j2);
j <= MIN(twojmax, j1 + j2); j += 2)
ncount++;
} else if(diagonalstyle == 1) {
int j2 = j1;
for (int j = abs(j1 - j2);
j <= MIN(twojmax, j1 + j2); j += 2)
ncount++;
} else if(diagonalstyle == 2) {
ncount++;
} else if(diagonalstyle == 3) {
for (int j2 = 0; j2 <= j1; j2++)
for (int j = abs(j1 - j2);
j <= MIN(twojmax, j1 + j2); j += 2)
if (j >= j1) ncount++;
}
return ncount;
}
/* ---------------------------------------------------------------------- */
double SNA::compute_sfac(double r, double rcut)
{
if (switch_flag == 0) return 1.0;
if (switch_flag == 1) {
if(r <= rmin0) return 1.0;
else if(r > rcut) return 0.0;
else {
double rcutfac = MY_PI / (rcut - rmin0);
return 0.5 * (cos((r - rmin0) * rcutfac) + 1.0);
}
}
return 0.0;
}
/* ---------------------------------------------------------------------- */
double SNA::compute_dsfac(double r, double rcut)
{
if (switch_flag == 0) return 0.0;
if (switch_flag == 1) {
if(r <= rmin0) return 0.0;
else if(r > rcut) return 0.0;
else {
double rcutfac = MY_PI / (rcut - rmin0);
return -0.5 * sin((r - rmin0) * rcutfac) * rcutfac;
}
}
return 0.0;
}

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