void kpt_get_neighboring_grid_points(int neighboring_grid_points[],
const int grid_point,
SPGCONST int relative_grid_address[][3],
const int num_relative_grid_address,
const int mesh[3],
SPGCONST int bz_grid_address[][3],
const int bz_map[])
{
int mesh_double[3], bzmesh[3], bzmesh_double[3],
address_double[3], bz_address_double[3];
int i, j, bz_gp;
for (i = 0; i < 3; i++) {
mesh_double[i] = mesh[i] * 2;
bzmesh[i] = mesh[i] * 2;
bzmesh_double[i] = bzmesh[i] * 2;
}
for (i = 0; i < num_relative_grid_address; i++) {
for (j = 0; j < 3; j++) {
address_double[j] = (bz_grid_address[grid_point][j] +
relative_grid_address[i][j]) * 2;
bz_address_double[j] = address_double[j];
}
get_vector_modulo(bz_address_double, bzmesh_double);
bz_gp = bz_map[get_grid_point_double_mesh(bz_address_double, bzmesh)];
if (bz_gp == -1) {
get_vector_modulo(address_double, mesh_double);
neighboring_grid_points[i] =
get_grid_point_double_mesh(address_double, mesh);
} else {
neighboring_grid_points[i] = bz_gp;
}
}
}
void kpt_get_grid_points_by_rotations(int rot_grid_points[],
const int address_orig[3],
const MatINT * rot_reciprocal,
const int mesh[3],
const int is_shift[3])
{
int i;
int address_double_orig[3], address_double[3];
for (i = 0; i < 3; i++) {
address_double_orig[i] = address_orig[i] * 2 + is_shift[i];
}
for (i = 0; i < rot_reciprocal->size; i++) {
mat_multiply_matrix_vector_i3(address_double,
rot_reciprocal->mat[i],
address_double_orig);
rot_grid_points[i] = get_grid_point_double_mesh(address_double, mesh);
}
}
void kpt_get_BZ_grid_points_by_rotations(int rot_grid_points[],
const int address_orig[3],
const MatINT * rot_reciprocal,
const int mesh[3],
const int is_shift[3],
const int bz_map[])
{
int i;
int address_double_orig[3], address_double[3], mesh_double[3], bzmesh_double[3];
for (i = 0; i < 3; i++) {
mesh_double[i] = mesh[i] * 2;
bzmesh_double[i] = mesh[i] * 4;
address_double_orig[i] = address_orig[i] * 2 + is_shift[i];
}
for (i = 0; i < rot_reciprocal->size; i++) {
mat_multiply_matrix_vector_i3(address_double,
rot_reciprocal->mat[i],
address_double_orig);
get_vector_modulo(address_double, bzmesh_double);
rot_grid_points[i] =
bz_map[get_grid_point_double_mesh(address_double, mesh_double)];
}
}
static int get_ir_reciprocal_mesh(int grid_address[][3],
int map[],
const int mesh[3],
const int is_shift[3],
const MatINT *rot_reciprocal)
{
/* In the following loop, mesh is doubled. */
/* Even and odd mesh numbers correspond to */
/* is_shift[i] are 0 or 1, respectively. */
/* is_shift = [0,0,0] gives Gamma center mesh. */
/* grid: reducible grid points */
/* map: the mapping from each point to ir-point. */
int i, j, k, l, grid_point, grid_point_rot, num_ir = 0;
int address[3], address_double[3], address_double_rot[3];
/* "-1" means the element is not touched yet. */
for (i = 0; i < mesh[0] * mesh[1] * mesh[2]; i++) {
map[i] = -1;
}
#ifndef GRID_ORDER_XYZ
for (i = 0; i < mesh[2]; i++) {
for (j = 0; j < mesh[1]; j++) {
for (k = 0; k < mesh[0]; k++) {
address[0] = k;
address[1] = j;
address[2] = i;
#else
for (i = 0; i < mesh[0]; i++) {
for (j = 0; j < mesh[1]; j++) {
for (k = 0; k < mesh[2]; k++) {
address[0] = i;
address[1] = j;
address[2] = k;
#endif
for (l = 0; l < 3; l++) {
address_double[l] = address[l] * 2 + is_shift[l];
}
grid_point = get_grid_point_double_mesh(address_double, mesh);
reduce_grid_address(grid_address[grid_point], address, mesh);
for (l = 0; l < rot_reciprocal->size; l++) {
mat_multiply_matrix_vector_i3(address_double_rot,
rot_reciprocal->mat[l],
address_double);
grid_point_rot = get_grid_point_double_mesh(address_double_rot, mesh);
if (grid_point_rot > -1) { /* Invalid if even --> odd or odd --> even */
if (map[grid_point_rot] > -1) {
map[grid_point] = map[grid_point_rot];
break;
}
}
}
if (map[grid_point] == -1) {
map[grid_point] = grid_point;
num_ir++;
}
}
}
}
return num_ir;
}
static int
get_ir_reciprocal_mesh_openmp(int grid_address[][3],
int map[],
const int mesh[3],
const int is_shift[3],
const MatINT * rot_reciprocal)
{
int i, j, grid_point, grid_point_rot, num_ir;
int address[3], address_double[3], address_double_rot[3];
#pragma omp parallel for private(j, grid_point, grid_point_rot, address, address_double, address_double_rot)
for (i = 0; i < mesh[0] * mesh[1] * mesh[2]; i++) {
#ifndef GRID_ORDER_XYZ
/* address[2] * mesh[0] * mesh[1] + address[1] * mesh[0] + address[0]; */
address[0] = i % mesh[0];
address[2] = i / (mesh[0] * mesh[1]);
address[1] = (i - address[2] * mesh[0] * mesh[1]) / mesh[0];
#else
/* address[0] * mesh[1] * mesh[2] + address[1] * mesh[2] + address[2]; */
address[2] = i % mesh[2];
address[0] = i / (mesh[1] * mesh[2]);
address[1] = (i - address[0] * mesh[1] * mesh[2]) / mesh[2];
#endif
for (j = 0; j < 3; j++) {
address_double[j] = address[j] * 2 + is_shift[j];
}
grid_point = get_grid_point_double_mesh(address_double, mesh);
map[grid_point] = grid_point;
reduce_grid_address(grid_address[grid_point], address, mesh);
for (j = 0; j < rot_reciprocal->size; j++) {
mat_multiply_matrix_vector_i3(address_double_rot,
rot_reciprocal->mat[j],
address_double);
grid_point_rot = get_grid_point_double_mesh(address_double_rot, mesh);
if (grid_point_rot > -1) { /* Invalid if even --> odd or odd --> even */
if (grid_point_rot < map[grid_point]) {
map[grid_point] = grid_point_rot;
}
}
}
}
num_ir = 0;
#pragma omp parallel for reduction(+:num_ir)
for (i = 0; i < mesh[0] * mesh[1] * mesh[2]; i++) {
if (map[i] == i) {
num_ir++;
}
}
return num_ir;
}
/* Relocate grid addresses to first Brillouin zone */
/* bz_grid_address[prod(mesh + 1)][3] */
/* bz_map[prod(mesh * 2)] */
static int relocate_BZ_grid_address(int bz_grid_address[][3],
int bz_map[],
SPGCONST int grid_address[][3],
const int mesh[3],
SPGCONST double rec_lattice[3][3],
const int is_shift[3])
{
double tolerance, min_distance;
double q_vector[3], distance[KPT_NUM_BZ_SEARCH_SPACE];
int bzmesh[3], bz_address_double[3];
int i, j, k, min_index, boundary_num_gp, total_num_gp, bzgp, gp;
tolerance = get_tolerance_for_BZ_reduction(rec_lattice, mesh);
for (i = 0; i < 3; i++) {
bzmesh[i] = mesh[i] * 2;
}
for (i = 0; i < bzmesh[0] * bzmesh[1] * bzmesh[2]; i++) {
bz_map[i] = -1;
}
boundary_num_gp = 0;
total_num_gp = mesh[0] * mesh[1] * mesh[2];
for (i = 0; i < total_num_gp; i++) {
for (j = 0; j < KPT_NUM_BZ_SEARCH_SPACE; j++) {
for (k = 0; k < 3; k++) {
q_vector[k] =
((grid_address[i][k] + kpt_bz_search_space[j][k] * mesh[k]) * 2 +
is_shift[k]) / ((double)mesh[k]) / 2;
}
mat_multiply_matrix_vector_d3(q_vector, rec_lattice, q_vector);
distance[j] = mat_norm_squared_d3(q_vector);
}
min_distance = distance[0];
min_index = 0;
for (j = 1; j < KPT_NUM_BZ_SEARCH_SPACE; j++) {
if (distance[j] < min_distance) {
min_distance = distance[j];
min_index = j;
}
}
for (j = 0; j < KPT_NUM_BZ_SEARCH_SPACE; j++) {
if (distance[j] < min_distance + tolerance) {
if (j == min_index) {
gp = i;
} else {
gp = boundary_num_gp + total_num_gp;
}
for (k = 0; k < 3; k++) {
bz_grid_address[gp][k] =
grid_address[i][k] + kpt_bz_search_space[j][k] * mesh[k];
bz_address_double[k] = bz_grid_address[gp][k] * 2 + is_shift[k];
}
bzgp = get_grid_point_double_mesh(bz_address_double, bzmesh);
bz_map[bzgp] = gp;
if (j != min_index) {
boundary_num_gp++;
}
}
}
}
return boundary_num_gp + total_num_gp;
}
static double get_tolerance_for_BZ_reduction(SPGCONST double rec_lattice[3][3],
const int mesh[3])
{
int i, j;
double tolerance;
double length[3];
for (i = 0; i < 3; i++) {
length[i] = 0;
for (j = 0; j < 3; j++) {
length[i] += rec_lattice[j][i] * rec_lattice[j][i];
}
length[i] /= mesh[i] * mesh[i];
}
tolerance = length[0];
for (i = 1; i < 3; i++) {
if (tolerance < length[i]) {
tolerance = length[i];
}
}
tolerance *= 0.01;
return tolerance;
}
int kpt_get_grid_point_double_mesh(const int address_double[3],
const int mesh[3])
{
return get_grid_point_double_mesh(address_double, mesh);
}
static int get_ir_reciprocal_mesh(int grid_address[][3],
int map[],
const int mesh[3],
const int is_shift[3],
const MatINT *rot_reciprocal)
{
/* In the following loop, mesh is doubled. */
/* Even and odd mesh numbers correspond to */
/* is_shift[i] are 0 or 1, respectively. */
/* is_shift = [0,0,0] gives Gamma center mesh. */
/* grid: reducible grid points */
/* map: the mapping from each point to ir-point. */
int i, j, k, l, grid_point, grid_point_rot, num_ir = 0;
int address_double[3], address_rot[3], mesh_double[3];
for (i = 0; i < 3; i++) {
mesh_double[i] = mesh[i] * 2;
}
/* "-1" means the element is not touched yet. */
for (i = 0; i < mesh[0] * mesh[1] * mesh[2]; i++) {
map[i] = -1;
}
#ifndef GRID_ORDER_XYZ
for (i = 0; i < mesh[2]; i++) {
for (j = 0; j < mesh[1]; j++) {
for (k = 0; k < mesh[0]; k++) {
address_double[0] = k * 2 + is_shift[0];
address_double[1] = j * 2 + is_shift[1];
address_double[2] = i * 2 + is_shift[2];
#else
for (i = 0; i < mesh[0]; i++) {
for (j = 0; j < mesh[1]; j++) {
for (k = 0; k < mesh[2]; k++) {
address_double[0] = i * 2 + is_shift[0];
address_double[1] = j * 2 + is_shift[1];
address_double[2] = k * 2 + is_shift[2];
#endif
grid_point = get_grid_point_double_mesh(address_double, mesh);
get_grid_address(grid_address[grid_point], address_double, mesh);
for (l = 0; l < rot_reciprocal->size; l++) {
mat_multiply_matrix_vector_i3(address_rot,
rot_reciprocal->mat[l],
address_double);
get_vector_modulo(address_rot, mesh_double);
grid_point_rot = get_grid_point_double_mesh(address_rot, mesh);
if (grid_point_rot > -1) { /* Invalid if even --> odd or odd --> even */
if (map[grid_point_rot] > -1) {
map[grid_point] = map[grid_point_rot];
break;
}
}
}
if (map[grid_point] == -1) {
map[grid_point] = grid_point;
num_ir++;
}
}
}
}
return num_ir;
}
static int
get_ir_reciprocal_mesh_openmp(int grid_address[][3],
int map[],
const int mesh[3],
const int is_shift[3],
const MatINT * rot_reciprocal)
{
int i, j, k, l, grid_point, grid_point_rot, num_ir;
int address_double[3], address_rot[3], mesh_double[3];
for (i = 0; i < 3; i++) {
mesh_double[i] = mesh[i] * 2;
}
#ifndef GRID_ORDER_XYZ
#pragma omp parallel for private(j, k, l, grid_point, grid_point_rot, address_double, address_rot)
for (i = 0; i < mesh[2]; i++) {
for (j = 0; j < mesh[1]; j++) {
for (k = 0; k < mesh[0]; k++) {
address_double[0] = k * 2 + is_shift[0];
address_double[1] = j * 2 + is_shift[1];
address_double[2] = i * 2 + is_shift[2];
#else
#pragma omp parallel for private(j, k, l, grid_point, grid_point_rot, address_double, address_rot)
for (i = 0; i < mesh[0]; i++) {
for (j = 0; j < mesh[1]; j++) {
for (k = 0; k < mesh[2]; k++) {
address_double[0] = i * 2 + is_shift[0];
address_double[1] = j * 2 + is_shift[1];
address_double[2] = k * 2 + is_shift[2];
#endif
grid_point = get_grid_point_double_mesh(address_double, mesh);
map[grid_point] = grid_point;
get_grid_address(grid_address[grid_point], address_double, mesh);
for (l = 0; l < rot_reciprocal->size; l++) {
mat_multiply_matrix_vector_i3(address_rot,
rot_reciprocal->mat[l],
address_double);
get_vector_modulo(address_rot, mesh_double);
grid_point_rot = get_grid_point_double_mesh(address_rot, mesh);
if (grid_point_rot > -1) { /* Invalid if even --> odd or odd --> even */
if (grid_point_rot < map[grid_point]) {
map[grid_point] = grid_point_rot;
}
}
}
}
}
}
num_ir = 0;
#pragma omp parallel for reduction(+:num_ir)
for (i = 0; i < mesh[0] * mesh[1] * mesh[2]; i++) {
if (map[i] == i) {
num_ir++;
}
}
return num_ir;
}
/* Relocate grid addresses to first Brillouin zone */
/* bz_grid_address[prod(mesh + 1)][3] */
/* bz_map[prod(mesh * 2)] */
static int relocate_BZ_grid_address(int bz_grid_address[][3],
int bz_map[],
SPGCONST int grid_address[][3],
const int mesh[3],
SPGCONST double rec_lattice[3][3],
const int is_shift[3])
{
double tolerance, min_distance;
double q_vector[3], distance[NUM_DIM_SEARCH];
int bzmesh[3], bzmesh_double[3], bz_address_double[3];
int i, j, k, min_index, boundary_num_gp, total_num_gp, bzgp, gp;
tolerance = get_tolerance_for_BZ_reduction(rec_lattice, mesh);
for (i = 0; i < 3; i++) {
bzmesh[i] = mesh[i] * 2;
bzmesh_double[i] = bzmesh[i] * 2;
}
for (i = 0; i < bzmesh[0] * bzmesh[1] * bzmesh[2]; i++) {
bz_map[i] = -1;
}
boundary_num_gp = 0;
total_num_gp = mesh[0] * mesh[1] * mesh[2];
for (i = 0; i < total_num_gp; i++) {
for (j = 0; j < NUM_DIM_SEARCH; j++) {
for (k = 0; k < 3; k++) {
q_vector[k] =
((grid_address[i][k] + search_space[j][k] * mesh[k]) * 2 +
is_shift[k]) / ((double)mesh[k]) / 2;
}
mat_multiply_matrix_vector_d3(q_vector, rec_lattice, q_vector);
distance[j] = mat_norm_squared_d3(q_vector);
}
min_distance = distance[0];
min_index = 0;
for (j = 1; j < NUM_DIM_SEARCH; j++) {
if (distance[j] < min_distance) {
min_distance = distance[j];
min_index = j;
}
}
for (j = 0; j < NUM_DIM_SEARCH; j++) {
if (distance[j] < min_distance + tolerance) {
if (j == min_index) {
gp = i;
} else {
gp = boundary_num_gp + total_num_gp;
}
for (k = 0; k < 3; k++) {
bz_grid_address[gp][k] =
grid_address[i][k] + search_space[j][k] * mesh[k];
bz_address_double[k] = bz_grid_address[gp][k] * 2 + is_shift[k];
}
get_vector_modulo(bz_address_double, bzmesh_double);
bzgp = get_grid_point_double_mesh(bz_address_double, bzmesh);
bz_map[bzgp] = gp;
if (j != min_index) {
boundary_num_gp++;
}
}
}
}
return boundary_num_gp + total_num_gp;
}
static double get_tolerance_for_BZ_reduction(SPGCONST double rec_lattice[3][3],
const int mesh[3])
{
int i, j;
double tolerance;
double length[3];
for (i = 0; i < 3; i++) {
length[i] = 0;
for (j = 0; j < 3; j++) {
length[i] += rec_lattice[j][i] * rec_lattice[j][i];
}
length[i] /= mesh[i] * mesh[i];
}
tolerance = length[0];
for (i = 1; i < 3; i++) {
if (tolerance < length[i]) {
tolerance = length[i];
}
}
tolerance *= 0.01;
return tolerance;
}
static int get_ir_triplets_at_q(int map_triplets[],
int map_q[],
int grid_address[][3],
const int grid_point,
const int mesh[3],
const MatINT * rot_reciprocal)
{
int i, j, num_grid, q_2, num_ir_q, num_ir_triplets, ir_grid_point;
int mesh_double[3], is_shift[3];
int address_double0[3], address_double1[3], address_double2[3];
int *ir_grid_points, *third_q;
double tolerance;
double stabilizer_q[1][3];
MatINT *rot_reciprocal_q;
tolerance = 0.01 / (mesh[0] + mesh[1] + mesh[2]);
num_grid = mesh[0] * mesh[1] * mesh[2];
for (i = 0; i < 3; i++) {
/* Only consider the gamma-point */
is_shift[i] = 0;
mesh_double[i] = mesh[i] * 2;
}
/* Search irreducible q-points (map_q) with a stabilizer */
/* q */
grid_point_to_address_double(address_double0, grid_point, mesh, is_shift);
for (i = 0; i < 3; i++) {
stabilizer_q[0][i] =
(double)address_double0[i] / mesh_double[i] - (address_double0[i] > mesh[i]);
}
rot_reciprocal_q = get_point_group_reciprocal_with_q(rot_reciprocal,
tolerance,
1,
stabilizer_q);
#ifdef _OPENMP
num_ir_q = get_ir_reciprocal_mesh_openmp(grid_address,
map_q,
mesh,
is_shift,
rot_reciprocal_q);
#else
num_ir_q = get_ir_reciprocal_mesh(grid_address,
map_q,
mesh,
is_shift,
rot_reciprocal_q);
#endif
mat_free_MatINT(rot_reciprocal_q);
third_q = (int*) malloc(sizeof(int) * num_ir_q);
ir_grid_points = (int*) malloc(sizeof(int) * num_ir_q);
num_ir_q = 0;
for (i = 0; i < num_grid; i++) {
if (map_q[i] == i) {
ir_grid_points[num_ir_q] = i;
num_ir_q++;
}
map_triplets[i] = -1;
}
#pragma omp parallel for private(j, address_double1, address_double2)
for (i = 0; i < num_ir_q; i++) {
grid_point_to_address_double(address_double1,
ir_grid_points[i],
mesh,
is_shift); /* q' */
for (j = 0; j < 3; j++) { /* q'' */
address_double2[j] = - address_double0[j] - address_double1[j];
}
get_vector_modulo(address_double2, mesh_double);
third_q[i] = get_grid_point_double_mesh(address_double2, mesh);
}
num_ir_triplets = 0;
for (i = 0; i < num_ir_q; i++) {
ir_grid_point = ir_grid_points[i];
q_2 = third_q[i];
if (map_triplets[map_q[q_2]] > -1) {
map_triplets[ir_grid_point] = map_q[q_2];
} else {
map_triplets[ir_grid_point] = ir_grid_point;
num_ir_triplets++;
}
}
#pragma omp parallel for
for (i = 0; i < num_grid; i++) {
map_triplets[i] = map_triplets[map_q[i]];
}
free(third_q);
third_q = NULL;
free(ir_grid_points);
ir_grid_points = NULL;
return num_ir_triplets;
}
static int get_BZ_triplets_at_q(int triplets[][3],
const int grid_point,
SPGCONST int bz_grid_address[][3],
const int bz_map[],
const int map_triplets[],
const int num_map_triplets,
const int mesh[3])
{
int i, j, k, num_ir;
int bz_address[3][3], bz_address_double[3], bzmesh[3], bzmesh_double[3];
int *ir_grid_points;
for (i = 0; i < 3; i++) {
bzmesh[i] = mesh[i] * 2;
bzmesh_double[i] = bzmesh[i] * 2;
}
num_ir = 0;
ir_grid_points = (int*) malloc(sizeof(int) * num_map_triplets);
for (i = 0; i < num_map_triplets; i++) {
if (map_triplets[i] == i) {
ir_grid_points[num_ir] = i;
num_ir++;
}
}
#pragma omp parallel for private(j, k, bz_address, bz_address_double)
for (i = 0; i < num_ir; i++) {
for (j = 0; j < 3; j++) {
bz_address[0][j] = bz_grid_address[grid_point][j];
bz_address[1][j] = bz_grid_address[ir_grid_points[i]][j];
bz_address[2][j] = - bz_address[0][j] - bz_address[1][j];
}
for (j = 2; j > -1; j--) {
if (get_third_q_of_triplets_at_q(bz_address,
j,
bz_map,
mesh,
bzmesh,
bzmesh_double) == 0) {
break;
}
}
for (j = 0; j < 3; j++) {
for (k = 0; k < 3; k++) {
bz_address_double[k] = bz_address[j][k] * 2;
}
get_vector_modulo(bz_address_double, bzmesh_double);
triplets[i][j] =
bz_map[get_grid_point_double_mesh(bz_address_double, bzmesh)];
}
}
free(ir_grid_points);
return num_ir;
}
static int get_third_q_of_triplets_at_q(int bz_address[3][3],
const int q_index,
const int bz_map[],
const int mesh[3],
const int bzmesh[3],
const int bzmesh_double[3])
{
int i, j, smallest_g, smallest_index, sum_g, delta_g[3];
int bzgp[NUM_DIM_SEARCH], bz_address_double[3];
get_vector_modulo(bz_address[q_index], mesh);
for (i = 0; i < 3; i++) {
delta_g[i] = 0;
for (j = 0; j < 3; j++) {
delta_g[i] += bz_address[j][i];
}
delta_g[i] /= mesh[i];
}
for (i = 0; i < NUM_DIM_SEARCH; i++) {
for (j = 0; j < 3; j++) {
bz_address_double[j] = (bz_address[q_index][j] +
search_space[i][j] * mesh[j]) * 2;
}
for (j = 0; j < 3; j++) {
if (bz_address_double[j] < 0) {
bz_address_double[j] += bzmesh_double[j];
}
}
get_vector_modulo(bz_address_double, bzmesh_double);
bzgp[i] = bz_map[get_grid_point_double_mesh(bz_address_double, bzmesh)];
}
for (i = 0; i < NUM_DIM_SEARCH; i++) {
if (bzgp[i] != -1) {
goto escape;
}
}
warning_print("******* Warning *******\n");
warning_print(" No third-q was found.\n");
warning_print("******* Warning *******\n");
escape:
smallest_g = 4;
smallest_index = 0;
for (i = 0; i < NUM_DIM_SEARCH; i++) {
if (bzgp[i] > -1) { /* q'' is in BZ */
sum_g = (abs(delta_g[0] + search_space[i][0]) +
abs(delta_g[1] + search_space[i][1]) +
abs(delta_g[2] + search_space[i][2]));
if (sum_g < smallest_g) {
smallest_index = i;
smallest_g = sum_g;
}
}
}
for (i = 0; i < 3; i++) {
bz_address[q_index][i] += search_space[smallest_index][i] * mesh[i];
}
return smallest_g;
}