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])
{
int i, j, smallest_g, smallest_index, sum_g, delta_g[3];
int bzgp[KPT_NUM_BZ_SEARCH_SPACE], bz_address_double[3];
modulo_i3(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 < KPT_NUM_BZ_SEARCH_SPACE; i++) {
for (j = 0; j < 3; j++) {
bz_address_double[j] = (bz_address[q_index][j] +
kpt_bz_search_space[i][j] * mesh[j]) * 2;
}
bzgp[i] = bz_map[kgd_get_grid_point_double_mesh(bz_address_double, bzmesh)];
}
for (i = 0; i < KPT_NUM_BZ_SEARCH_SPACE; i++) {
if (bzgp[i] != -1) {
goto escape;
}
}
escape:
smallest_g = 4;
smallest_index = 0;
for (i = 0; i < KPT_NUM_BZ_SEARCH_SPACE; i++) {
if (bzgp[i] > -1) { /* q'' is in BZ */
sum_g = (abs(delta_g[0] + kpt_bz_search_space[i][0]) +
abs(delta_g[1] + kpt_bz_search_space[i][1]) +
abs(delta_g[2] + kpt_bz_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] += kpt_bz_search_space[smallest_index][i] * mesh[i];
}
return smallest_g;
}
static int get_ir_reciprocal_mesh_distortion(int grid_address[][3],
int ir_mapping_table[],
const int mesh[3],
const int is_shift[3],
const MatINT *rot_reciprocal)
{
int i, j, k, grid_point_rot, indivisible;
int address_double[3], address_double_rot[3], divisor[3];
kgd_get_all_grid_addresses(grid_address, mesh);
for (i = 0; i < 3; i++) {
divisor[i] = mesh[(i + 1) % 3] * mesh[(i + 2) % 3];
}
#pragma omp parallel for private(j, k, grid_point_rot, address_double, address_double_rot)
for (i = 0; i < mesh[0] * mesh[1] * mesh[2]; i++) {
kgd_get_grid_address_double_mesh(address_double,
grid_address[i],
mesh,
is_shift);
for (j = 0; j < 3; j++) {
address_double[j] *= divisor[j];
}
ir_mapping_table[i] = i;
for (j = 0; j < rot_reciprocal->size; j++) {
mat_multiply_matrix_vector_i3(address_double_rot,
rot_reciprocal->mat[j],
address_double);
for (k = 0; k < 3; k++) {
indivisible = address_double_rot[k] % divisor[k];
if (indivisible) {break;}
address_double_rot[k] /= divisor[k];
if ((address_double_rot[k] % 2 != 0 && is_shift[k] == 0) ||
(address_double_rot[k] % 2 == 0 && is_shift[k] == 1)) {
indivisible = 1;
break;
}
}
if (indivisible) {continue;}
grid_point_rot = kgd_get_grid_point_double_mesh(address_double_rot, mesh);
if (grid_point_rot < ir_mapping_table[i]) {
#ifdef _OPENMP
ir_mapping_table[i] = grid_point_rot;
#else
ir_mapping_table[i] = ir_mapping_table[grid_point_rot];
break;
#endif
}
}
}
return get_num_ir(ir_mapping_table, mesh);
}
static int get_BZ_triplets_at_q(int triplets[][3],
const int grid_point,
PHPYCONST 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];
int *ir_grid_points;
for (i = 0; i < 3; i++) {
bzmesh[i] = mesh[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) == 0) {
break;
}
}
for (j = 0; j < 3; j++) {
for (k = 0; k < 3; k++) {
bz_address_double[k] = bz_address[j][k] * 2;
}
triplets[i][j] =
bz_map[kgd_get_grid_point_double_mesh(bz_address_double, bzmesh)];
}
}
free(ir_grid_points);
return num_ir;
}
/*---------*/
int spg_get_grid_point_from_address(const int grid_address[3],
const int mesh[3])
{
int address_double[3];
int is_shift[3];
is_shift[0] = 0;
is_shift[1] = 0;
is_shift[2] = 0;
kgd_get_grid_address_double_mesh(address_double,
grid_address,
mesh,
is_shift);
return kgd_get_grid_point_double_mesh(address_double, mesh);
}
static int get_ir_reciprocal_mesh_normal(int grid_address[][3],
int ir_mapping_table[],
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 */
/* ir_mapping_table: the mapping from each point to ir-point. */
int i, j, grid_point_rot;
int address_double[3], address_double_rot[3];
kgd_get_all_grid_addresses(grid_address, mesh);
#pragma omp parallel for private(j, grid_point_rot, address_double, address_double_rot)
for (i = 0; i < mesh[0] * mesh[1] * mesh[2]; i++) {
kgd_get_grid_address_double_mesh(address_double,
grid_address[i],
mesh,
is_shift);
ir_mapping_table[i] = i;
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 = kgd_get_grid_point_double_mesh(address_double_rot, mesh);
if (grid_point_rot < ir_mapping_table[i]) {
#ifdef _OPENMP
ir_mapping_table[i] = grid_point_rot;
#else
ir_mapping_table[i] = ir_mapping_table[grid_point_rot];
break;
#endif
}
}
}
return get_num_ir(ir_mapping_table, mesh);
}
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] = kgd_get_grid_point_double_mesh(address_double, mesh);
}
}
/* 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];
/* Multithreading doesn't work for this loop since gp calculated */
/* with boundary_num_gp is unstable to store bz_grid_address. */
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] + 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] + bz_search_space[j][k] * mesh[k];
bz_address_double[k] = bz_grid_address[gp][k] * 2 + is_shift[k];
}
bzgp = kgd_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 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 = kpt_get_point_group_reciprocal_with_q(rot_reciprocal,
tolerance,
1,
stabilizer_q);
num_ir_q = kpt_get_irreducible_reciprocal_mesh(grid_address,
map_q,
mesh,
is_shift,
rot_reciprocal_q);
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];
}
third_q[i] = kgd_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;
}
