static int get_rotation_axis(SPGCONST int proper_rot[3][3])
{
int i, axis = -1;
int vec[3];
/* No specific axis for I and -I */
if (mat_check_identity_matrix_i3(proper_rot, identity)) {
goto end;
}
/* Look for eigenvector = rotation axis */
for (i = 0; i < NUM_ROT_AXES; i++) {
mat_multiply_matrix_vector_i3(vec, proper_rot, rot_axes[i]);
if (vec[0] == rot_axes[i][0] &&
vec[1] == rot_axes[i][1] &&
vec[2] == rot_axes[i][2]) {
axis = i;
break;
}
}
end:
#ifdef SPGDEBUG
if (axis == -1) {
printf("rotation axis cound not found.\n");
}
#endif
return axis;
}
static int get_orthogonal_axis(int ortho_axes[],
SPGCONST int proper_rot[3][3],
const int rot_order)
{
int i, num_ortho_axis;
int vec[3];
int sum_rot[3][3], rot[3][3];
num_ortho_axis = 0;
mat_copy_matrix_i3(sum_rot, identity);
mat_copy_matrix_i3(rot, identity);
for (i = 0; i < rot_order - 1; i++) {
mat_multiply_matrix_i3(rot, proper_rot, rot);
mat_add_matrix_i3(sum_rot, rot, sum_rot);
}
for (i = 0; i < NUM_ROT_AXES; i++) {
mat_multiply_matrix_vector_i3(vec, sum_rot, rot_axes[i]);
if (vec[0] == 0 &&
vec[1] == 0 &&
vec[2] == 0) {
ortho_axes[num_ortho_axis] = i;
num_ortho_axis++;
}
}
return num_ortho_axis;
}
static int laue4m(int axes[3],
SPGCONST PointSymmetry * pointsym)
{
int i, num_ortho_axis, norm, min_norm, is_found, tmpval;
int axis_vec[3];
int prop_rot[3][3], t_mat[3][3];
int ortho_axes[NUM_ROT_AXES];
for (i = 0; i < pointsym->size; i++) {
get_proper_rotation(prop_rot, pointsym->rot[i]);
/* Search foud-fold rotation */
if ( mat_get_trace_i3(prop_rot) == 1) {
/* The first axis */
axes[2] = get_rotation_axis(prop_rot);
break;
}
}
/* The second axis */
num_ortho_axis = get_orthogonal_axis(ortho_axes, prop_rot, 4);
if (! num_ortho_axis) { goto err; }
min_norm = 8;
is_found = 0;
for (i = 0; i < num_ortho_axis; i++) {
norm = mat_norm_squared_i3(rot_axes[ortho_axes[i]]);
if (norm < min_norm) {
min_norm = norm;
axes[0] = ortho_axes[i];
is_found = 1;
}
}
if (! is_found) { goto err; }
/* The third axis */
mat_multiply_matrix_vector_i3(axis_vec, prop_rot, rot_axes[axes[0]]);
is_found = 0;
for (i = 0; i < NUM_ROT_AXES; i++) {
if (is_exist_axis(axis_vec, i)) {
is_found = 1;
axes[1] = i;
break;
}
}
if (! is_found) { goto err; }
set_transformation_matrix(t_mat, axes);
if (mat_get_determinant_i3(t_mat) < 0) {
tmpval = axes[0];
axes[0] = axes[1];
axes[1] = tmpval;
}
return 1;
err:
return 0;
}
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);
}
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);
}
}
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_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 laue3m(int axes[3],
SPGCONST PointSymmetry * pointsym)
{
int i, is_found, tmpval, axis;
int prop_rot[3][3], prop_rot2[3][3], t_mat[3][3];
int axis_vec[3];
for (i = 0; i < pointsym->size; i++) {
get_proper_rotation(prop_rot, pointsym->rot[i]);
/* Search three-fold rotation */
if (mat_get_trace_i3(prop_rot) == 0) {
/* The first axis */
axes[2] = get_rotation_axis(prop_rot);
debug_print("laue3m prop_rot\n");
debug_print_matrix_i3(prop_rot);
break;
}
}
is_found = 0;
for (i = 0; i < pointsym->size; i++) {
get_proper_rotation(prop_rot2, pointsym->rot[i]);
/* Search two-fold rotation */
if (! (mat_get_trace_i3(prop_rot2) == -1)) {
continue;
}
/* The second axis */
axis = get_rotation_axis(prop_rot2);
if (! (axis == axes[2])) {
axes[0] = axis;
is_found = 1;
break;
}
}
if (! is_found) { goto err; }
/* The third axis */
mat_multiply_matrix_vector_i3(axis_vec, prop_rot, rot_axes[axes[0]]);
is_found = 0;
for (i = 0; i < NUM_ROT_AXES; i++) {
is_found = is_exist_axis(axis_vec, i);
if (is_found == 1) {
axes[1] = i;
break;
}
if (is_found == -1) {
axes[1] = i + NUM_ROT_AXES;
break;
}
}
if (! is_found) { goto err; }
set_transformation_matrix(t_mat, axes);
if (mat_get_determinant_i3(t_mat) < 0) {
tmpval = axes[0];
axes[0] = axes[1];
axes[1] = tmpval;
}
return 1;
err:
return 0;
}
static int laue_one_axis(int axes[3],
SPGCONST PointSymmetry * pointsym,
const int rot_order)
{
int i, j, num_ortho_axis, det, is_found, tmpval;
int axis_vec[3], tmp_axes[3];
int prop_rot[3][3], t_mat[3][3];
int ortho_axes[NUM_ROT_AXES];
debug_print("laue_one_axis with rot_order %d\n", rot_order);
for (i = 0; i < pointsym->size; i++) {
get_proper_rotation(prop_rot, pointsym->rot[i]);
/* Search foud-fold rotation */
if (rot_order == 4) {
if (mat_get_trace_i3(prop_rot) == 1) {
/* The first axis */
axes[2] = get_rotation_axis(prop_rot);
break;
}
}
/* Search three-fold rotation */
if (rot_order == 3) {
if (mat_get_trace_i3(prop_rot) == 0) {
/* The first axis */
axes[2] = get_rotation_axis(prop_rot);
break;
}
}
}
/* Candidates of the second axis */
num_ortho_axis = get_orthogonal_axis(ortho_axes, prop_rot, rot_order);
if (! num_ortho_axis) { goto err; }
tmp_axes[1] = -1;
tmp_axes[2] = axes[2];
for (i = 0; i < num_ortho_axis; i++) {
is_found = 0;
tmp_axes[0] = ortho_axes[i];
mat_multiply_matrix_vector_i3(axis_vec,
prop_rot,
rot_axes[tmp_axes[0]]);
for (j = 0; j < num_ortho_axis; j++) {
is_found = is_exist_axis(axis_vec, ortho_axes[j]);
if (is_found == 1) {
tmp_axes[1] = ortho_axes[j];
break;
}
if (is_found == -1) {
tmp_axes[1] = ortho_axes[j] + NUM_ROT_AXES;
break;
}
}
if (!is_found) { continue; }
set_transformation_matrix(t_mat, tmp_axes);
det = abs(mat_get_determinant_i3(t_mat));
if (det < 4) { /* to avoid F-center choice det=4 */
axes[0] = tmp_axes[0];
axes[1] = tmp_axes[1];
goto end;
}
}
err: /* axes are not correctly found. */
warning_print("spglib: Secondary axis is not found.");
warning_print("(line %d, %s).\n", __LINE__, __FILE__);
return 0;
end:
set_transformation_matrix(t_mat, axes);
if (mat_get_determinant_i3(t_mat) < 0) {
tmpval = axes[0];
axes[0] = axes[1];
axes[1] = tmpval;
}
debug_print("axes[0] = %d\n", axes[0]);
debug_print("axes[1] = %d\n", axes[1]);
debug_print("axes[2] = %d\n", axes[2]);
return 1;
}
static int laue_one_axis( int axes[3],
const Symmetry * symmetry,
const int rot_order )
{
int i, j, num_ortho_axis, det, min_det, is_found, tmpval;
int axis_vec[3], tmp_axes[3];
int prop_rot[3][3], t_mat[3][3];
int ortho_axes[NUM_ROT_AXES];
for ( i = 0; i < symmetry->size; i++ ) {
get_proper_rotation( prop_rot, symmetry->rot[i] );
/* Search foud-fold rotation */
if ( rot_order == 4 ) {
if ( mat_get_trace_i3( prop_rot ) == 1 ) {
/* The first axis */
axes[2] = get_rotation_axis( prop_rot );
break;
}
}
/* Search three-fold rotation */
if ( rot_order == 3 ) {
if ( mat_get_trace_i3( prop_rot ) == 0 ) {
/* The first axis */
axes[2] = get_rotation_axis( prop_rot );
break;
}
}
}
/* Candidates of the second axis */
num_ortho_axis = get_orthogonal_axis( ortho_axes, prop_rot, rot_order );
if ( ! num_ortho_axis ) { goto err; }
tmp_axes[2] = axes[2];
min_det = 4;
is_found = 0;
for ( i = 0; i < num_ortho_axis; i++ ) {
tmp_axes[0] = ortho_axes[i];
mat_multiply_matrix_vector_i3( axis_vec, prop_rot,
rot_axes[tmp_axes[0]] );
for ( j = 0; j < num_ortho_axis; j++ ) {
is_found = is_exist_axis( axis_vec, ortho_axes[j] );
if ( is_found == 1 ) {
tmp_axes[1] = ortho_axes[j];
break;
}
if ( is_found == -1 ) {
tmp_axes[1] = ortho_axes[j] + NUM_ROT_AXES;
break;
}
}
get_transform_matrix( t_mat, tmp_axes );
det = mat_get_determinant_i3( t_mat );
if ( det < 0 ) { det = -det; }
if ( det < min_det ) {
min_det = det;
axes[0] = tmp_axes[0];
axes[1] = tmp_axes[1];
}
}
if ( ! is_found ) { goto err; }
get_transform_matrix( t_mat, axes );
if ( mat_get_determinant_i3( t_mat ) < 0 ) {
tmpval = axes[0];
axes[0] = axes[1];
axes[1] = tmpval;
}
return 1;
err:
return 0;
}
static int laue4mmm( int axes[3],
const Symmetry * symmetry )
{
int i, is_found, tmpval, axis;
int prop_rot[3][3], prop_rot2[3][3], t_mat[3][3];
int axis_vec[3];
for ( i = 0; i < symmetry->size; i++ ) {
get_proper_rotation( prop_rot, symmetry->rot[i] );
/* Search foud-fold rotation */
if ( mat_get_trace_i3( prop_rot ) == 1 ) {
/* The first axis */
axes[2] = get_rotation_axis( prop_rot );
break;
}
}
is_found = 0;
for ( i = 0; i < symmetry->size; i++ ) {
get_proper_rotation( prop_rot2, symmetry->rot[i] );
/* Search two-fold rotation */
if ( ! ( mat_get_trace_i3( prop_rot2 ) == -1 ) ) {
continue;
}
/* The second axis */
axis = get_rotation_axis( prop_rot2 );
if ( ! ( axis == axes[2] ) ) {
axes[0] = axis;
is_found = 1;
break;
}
}
if ( ! is_found ) { goto err; }
/* The third axis */
mat_multiply_matrix_vector_i3( axis_vec, prop_rot, rot_axes[axes[0]] );
is_found = 0;
for ( i = 0; i < NUM_ROT_AXES; i++ ) {
if ( is_exist_axis( axis_vec, i ) ) {
is_found = 1;
axes[1] = i;
break;
}
}
if ( ! is_found ) { goto err; }
get_transform_matrix( t_mat, axes );
if ( mat_get_determinant_i3( t_mat ) < 0 ) {
tmpval = axes[0];
axes[0] = axes[1];
axes[1] = tmpval;
}
return 1;
err:
return 0;
}
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;
}
static int get_ir_reciprocal_mesh(int grid_points[][3],
int map[],
const int mesh[3],
const int is_shift[3],
SPGCONST PointSymmetry * point_symmetry)
{
/* In the following loop, mesh is doubled. */
/* Even and odd mesh numbers correspond to */
/* is_shift[i] = 0 and 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, address, address_rot, num_ir = 0;
int grid_double[3], grid_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++) {
grid_double[0] = k * 2 + is_shift[0];
grid_double[1] = j * 2 + is_shift[1];
grid_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++) {
grid_double[0] = i * 2 + is_shift[0];
grid_double[1] = j * 2 + is_shift[1];
grid_double[2] = k * 2 + is_shift[2];
#endif
address = grid_to_address(grid_double, mesh, is_shift);
get_grid_points(grid_points[address], grid_double, mesh);
for (l = 0; l < point_symmetry->size; l++) {
mat_multiply_matrix_vector_i3(grid_rot,
point_symmetry->rot[l], grid_double);
get_vector_modulo(grid_rot, mesh_double);
address_rot = grid_to_address(grid_rot, mesh, is_shift);
if (address_rot > -1) { /* Invalid if even --> odd or odd --> even */
if (map[address_rot] > -1) {
map[address] = map[address_rot];
break;
}
}
}
if (map[address] == -1) {
map[address] = address;
num_ir++;
}
}
}
}
return num_ir;
}
static int
get_ir_reciprocal_mesh_openmp(int grid_points[][3],
int map[],
const int mesh[3],
const int is_shift[3],
SPGCONST PointSymmetry * point_symmetry)
{
int i, j, k, l, address, address_rot, num_ir;
int grid_double[3], grid_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, address, address_rot, grid_double, grid_rot)
for (i = 0; i < mesh[2]; i++) {
for (j = 0; j < mesh[1]; j++) {
for (k = 0; k < mesh[0]; k++) {
grid_double[0] = k * 2 + is_shift[0];
grid_double[1] = j * 2 + is_shift[1];
grid_double[2] = i * 2 + is_shift[2];
#else
#pragma omp parallel for private(j, k, l, address, address_rot, grid_double, grid_rot)
for (i = 0; i < mesh[0]; i++) {
for (j = 0; j < mesh[1]; j++) {
for (k = 0; k < mesh[2]; k++) {
grid_double[0] = i * 2 + is_shift[0];
grid_double[1] = j * 2 + is_shift[1];
grid_double[2] = k * 2 + is_shift[2];
#endif
address = grid_to_address(grid_double, mesh, is_shift);
map[address] = address;
get_grid_points(grid_points[address], grid_double, mesh);
for (l = 0; l < point_symmetry->size; l++) {
mat_multiply_matrix_vector_i3(grid_rot,
point_symmetry->rot[l], grid_double);
get_vector_modulo(grid_rot, mesh_double);
address_rot = grid_to_address(grid_rot, mesh, is_shift);
if (address_rot > -1) { /* Invalid if even --> odd or odd --> even */
if (address_rot < map[address]) {
map[address] = address_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;
}
static int get_ir_triplets_at_q(int weights[],
int grid_points[][3],
int third_q[],
const int grid_point,
const int mesh[3],
SPGCONST PointSymmetry * pointgroup)
{
int i, j, num_grid, q_2, num_ir_q, num_ir_triplets, ir_address;
int mesh_double[3], is_shift[3];
int grid_double0[3], grid_double1[3], grid_double2[3];
int *map_q, *ir_addresses, *weight_q;
double tolerance;
double stabilizer_q[1][3];
PointSymmetry pointgroup_q;
tolerance = 0.1 / (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 */
address_to_grid(grid_double0, grid_point, mesh, is_shift); /* q */
for (i = 0; i < 3; i++) {
stabilizer_q[0][i] = (double)grid_double0[i] / mesh_double[i];
}
pointgroup_q = get_point_group_reciprocal_with_q(pointgroup,
tolerance,
1,
stabilizer_q);
map_q = (int*) malloc(sizeof(int) * num_grid);
#ifdef _OPENMP
num_ir_q = get_ir_reciprocal_mesh_openmp(grid_points,
map_q,
mesh,
is_shift,
&pointgroup_q);
#else
num_ir_q = get_ir_reciprocal_mesh(grid_points,
map_q,
mesh,
is_shift,
&pointgroup_q);
#endif
ir_addresses = (int*) malloc(sizeof(int) * num_ir_q);
weight_q = (int*) malloc(sizeof(int) * num_grid);
num_ir_q = 0;
for (i = 0; i < num_grid; i++) {
if (map_q[i] == i) {
ir_addresses[num_ir_q] = i;
num_ir_q++;
}
weight_q[i] = 0;
third_q[i] = -1;
weights[i] = 0;
}
for (i = 0; i < num_grid; i++) {
weight_q[map_q[i]]++;
}
#pragma omp parallel for private(j, grid_double1, grid_double2)
for (i = 0; i < num_ir_q; i++) {
address_to_grid(grid_double1, ir_addresses[i], mesh, is_shift); /* q' */
for (j = 0; j < 3; j++) { /* q'' */
grid_double2[j] = - grid_double0[j] - grid_double1[j];
}
get_vector_modulo(grid_double2, mesh_double);
third_q[ir_addresses[i]] = grid_to_address(grid_double2, mesh, is_shift);
}
num_ir_triplets = 0;
for (i = 0; i < num_ir_q; i++) {
ir_address = ir_addresses[i];
q_2 = third_q[ir_address];
if (weights[map_q[q_2]]) {
weights[map_q[q_2]] += weight_q[ir_address];
} else {
weights[ir_address] = weight_q[ir_address];
num_ir_triplets++;
}
}
free(map_q);
map_q = NULL;
free(weight_q);
weight_q = NULL;
free(ir_addresses);
ir_addresses = NULL;
return num_ir_triplets;
}
static void set_grid_triplets_at_q(int triplets[][3],
const int q_grid_point,
SPGCONST int grid_points[][3],
const int third_q[],
const int weights[],
const int mesh[3])
{
const int is_shift[3] = {0, 0, 0};
int i, j, k, num_edge, edge_pos, num_ir;
int grid_double[3][3], ex_mesh[3], ex_mesh_double[3];
for (i = 0; i < 3; i++) {
ex_mesh[i] = mesh[i] + (mesh[i] % 2 == 0);
ex_mesh_double[i] = ex_mesh[i] * 2;
}
for (i = 0; i < 3; i++) {
grid_double[0][i] = grid_points[q_grid_point][i] * 2;
}
num_ir = 0;
for (i = 0; i < mesh[0] * mesh[1] * mesh[2]; i++) {
if (weights[i] < 1) {
continue;
}
for (j = 0; j < 3; j++) {
grid_double[1][j] = grid_points[i][j] * 2;
grid_double[2][j] = grid_points[third_q[i]][j] * 2;
}
for (j = 0; j < 3; j++) {
num_edge = 0;
edge_pos = -1;
for (k = 0; k < 3; k++) {
if (abs(grid_double[k][j]) == mesh[j]) {
num_edge++;
edge_pos = k;
}
}
if (num_edge == 1) {
grid_double[edge_pos][j] = 0;
for (k = 0; k < 3; k++) {
if (k != edge_pos) {
grid_double[edge_pos][j] -= grid_double[k][j];
}
}
}
if (num_edge == 2) {
grid_double[edge_pos][j] = -grid_double[edge_pos][j];
}
}
for (j = 0; j < 3; j++) {
get_vector_modulo(grid_double[j], ex_mesh_double);
triplets[num_ir][j] = grid_to_address(grid_double[j], ex_mesh, is_shift);
}
num_ir++;
}
}
static int grid_to_address(const int grid_double[3],
const int mesh[3],
const int is_shift[3])
{
int i, grid[3];
for (i = 0; i < 3; i++) {
if (grid_double[i] % 2 == 0 && (! is_shift[i]) ) {
grid[i] = grid_double[i] / 2;
} else {
if (grid_double[i] % 2 != 0 && is_shift[i]) {
grid[i] = (grid_double[i] - 1) / 2;
} else {
return -1;
}
}
}
#ifndef GRID_ORDER_XYZ
return grid[2] * mesh[0] * mesh[1] + grid[1] * mesh[0] + grid[0];
#else
return grid[0] * mesh[1] * mesh[2] + grid[1] * mesh[2] + grid[2];
#endif
}
static void address_to_grid(int grid_double[3],
const int address,
const int mesh[3],
const int is_shift[3])
{
int i;
int grid[3];
#ifndef GRID_ORDER_XYZ
grid[2] = address / (mesh[0] * mesh[1]);
grid[1] = (address - grid[2] * mesh[0] * mesh[1]) / mesh[0];
grid[0] = address % mesh[0];
#else
grid[0] = address / (mesh[1] * mesh[2]);
grid[1] = (address - grid[0] * mesh[1] * mesh[2]) / mesh[2];
grid[2] = address % mesh[2];
#endif
for (i = 0; i < 3; i++) {
grid_double[i] = grid[i] * 2 + is_shift[i];
}
}
static void get_grid_points(int grid[3],
const int grid_double[3],
const int mesh[3])
{
int i;
for (i = 0; i < 3; i++) {
if (grid_double[i] % 2 == 0) {
grid[i] = grid_double[i] / 2;
} else {
grid[i] = (grid_double[i] - 1) / 2;
}
#ifndef GRID_BOUNDARY_AS_NEGATIVE
grid[i] = grid[i] - mesh[i] * (grid[i] > mesh[i] / 2);
#else
grid[i] = grid[i] - mesh[i] * (grid[i] >= mesh[i] / 2);
#endif
}
}
static void get_vector_modulo(int v[3], const int m[3])
{
int i;
for (i = 0; i < 3; i++) {
v[i] = v[i] % m[i];
if (v[i] < 0)
v[i] += m[i];
}
}
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;
}
static int get_ir_reciprocal_mesh(int grid_address[][3],
int map[],
const int mesh[3],
const int is_shift[3],
SPGCONST PointSymmetry * point_symmetry)
{
/* In the following loop, mesh is doubled. */
/* Even and odd mesh numbers correspond to */
/* is_shift[i] = 0 and 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 grid_double[3], grid_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++) {
grid_double[0] = k * 2 + is_shift[0];
grid_double[1] = j * 2 + is_shift[1];
grid_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++) {
grid_double[0] = i * 2 + is_shift[0];
grid_double[1] = j * 2 + is_shift[1];
grid_double[2] = k * 2 + is_shift[2];
#endif
grid_point = get_grid_point(grid_double, mesh);
get_grid_address(grid_address[grid_point], grid_double, mesh);
for (l = 0; l < point_symmetry->size; l++) {
mat_multiply_matrix_vector_i3(grid_rot,
point_symmetry->rot[l], grid_double);
get_vector_modulo(grid_rot, mesh_double);
grid_point_rot = get_grid_point(grid_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],
SPGCONST PointSymmetry * point_symmetry)
{
int i, j, k, l, grid_point, grid_point_rot, num_ir;
int grid_double[3], grid_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, grid_double, grid_rot)
for (i = 0; i < mesh[2]; i++) {
for (j = 0; j < mesh[1]; j++) {
for (k = 0; k < mesh[0]; k++) {
grid_double[0] = k * 2 + is_shift[0];
grid_double[1] = j * 2 + is_shift[1];
grid_double[2] = i * 2 + is_shift[2];
#else
#pragma omp parallel for private(j, k, l, grid_point, grid_point_rot, grid_double, grid_rot)
for (i = 0; i < mesh[0]; i++) {
for (j = 0; j < mesh[1]; j++) {
for (k = 0; k < mesh[2]; k++) {
grid_double[0] = i * 2 + is_shift[0];
grid_double[1] = j * 2 + is_shift[1];
grid_double[2] = k * 2 + is_shift[2];
#endif
grid_point = get_grid_point(grid_double, mesh);
map[grid_point] = grid_point;
get_grid_address(grid_address[grid_point], grid_double, mesh);
for (l = 0; l < point_symmetry->size; l++) {
mat_multiply_matrix_vector_i3(grid_rot,
point_symmetry->rot[l], grid_double);
get_vector_modulo(grid_rot, mesh_double);
grid_point_rot = get_grid_point(grid_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 - 1)] */
static int relocate_BZ_grid_address(int bz_grid_address[][3],
int bz_map[],
int grid_address[][3],
const int mesh[3],
SPGCONST double rec_lattice[3][3],
const int is_shift[3])
{
double tolerance, min_distance;
double vector[3], distance[27];
int bzmesh[3], bzmesh_double[3], address_double[3];
int i, j, k, min_index, boundary_gp, total_num_gp, bzgp, gp;
tolerance = get_tolerance_for_BZ_reduction(rec_lattice);
for (i = 0; i < 3; i++) {
bzmesh[i] = mesh[i] * 2 - 1;
bzmesh_double[i] = bzmesh[i] * 2;
}
for (i = 0; i < bzmesh[0] * bzmesh[1] * bzmesh[2]; i++) {
bz_map[i] = -1;
}
boundary_gp = 0;
total_num_gp = mesh[0] * mesh[1] * mesh[2];
for (i = 0; i < total_num_gp; i++) {
for (j = 0; j < 27; j++) {
for (k = 0; k < 3; k++) {
address_double[k] =
(grid_address[i][k] + search_space[j][k] * mesh[k]) * 2 + is_shift[k];
}
mat_multiply_matrix_vector_di3(vector, rec_lattice, address_double);
distance[j] = mat_norm_squared_d3(vector);
}
min_distance = distance[0];
min_index = 0;
for (j = 1; j < 27; j++) {
if (distance[j] + tolerance < min_distance) {
min_distance = distance[j];
min_index = j;
}
}
for (j = 0; j < 27; j++) {
if (distance[j] < min_distance + tolerance) {
if (j == min_index) {
gp = i;
} else {
gp = boundary_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];
address_double[k] = bz_grid_address[gp][k] * 2 + is_shift[k];
if (address_double[k] < 0) {
address_double[k] += bzmesh_double[k];
}
}
bzgp = get_grid_point(address_double, bzmesh);
bz_map[bzgp] = gp;
if (j != min_index) {
boundary_gp++;
}
}
}
}
return boundary_gp + total_num_gp;
}
static double get_tolerance_for_BZ_reduction(SPGCONST double rec_lattice[3][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];
}
}
tolerance = length[0];
for (i = 1; i < 3; i++) {
if (tolerance > length[i]) {
tolerance = length[i];
}
}
tolerance /= 100;
return tolerance;
}
static int get_ir_triplets_at_q(int weights[],
int grid_address[][3],
int third_q[],
const int grid_point,
const int mesh[3],
SPGCONST PointSymmetry * pointgroup)
{
int i, j, num_grid, q_2, num_ir_q, num_ir_triplets, ir_grid_point;
int mesh_double[3], is_shift[3];
int grid_double0[3], grid_double1[3], grid_double2[3];
int *map_q, *ir_grid_points, *weight_q;
double tolerance;
double stabilizer_q[1][3];
PointSymmetry pointgroup_q;
tolerance = 0.1 / (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 */
grid_point_to_grid_double(grid_double0, grid_point, mesh, is_shift); /* q */
for (i = 0; i < 3; i++) {
stabilizer_q[0][i] =
(double)grid_double0[i] / mesh_double[i] - (grid_double0[i] > mesh[i]);
}
pointgroup_q = get_point_group_reciprocal_with_q(pointgroup,
tolerance,
1,
stabilizer_q);
map_q = (int*) malloc(sizeof(int) * num_grid);
#ifdef _OPENMP
num_ir_q = get_ir_reciprocal_mesh_openmp(grid_address,
map_q,
mesh,
is_shift,
&pointgroup_q);
#else
num_ir_q = get_ir_reciprocal_mesh(grid_address,
map_q,
mesh,
is_shift,
&pointgroup_q);
#endif
ir_grid_points = (int*) malloc(sizeof(int) * num_ir_q);
weight_q = (int*) malloc(sizeof(int) * num_grid);
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++;
}
weight_q[i] = 0;
third_q[i] = -1;
weights[i] = 0;
}
for (i = 0; i < num_grid; i++) {
weight_q[map_q[i]]++;
}
#pragma omp parallel for private(j, grid_double1, grid_double2)
for (i = 0; i < num_ir_q; i++) {
grid_point_to_grid_double(grid_double1, ir_grid_points[i], mesh, is_shift); /* q' */
for (j = 0; j < 3; j++) { /* q'' */
grid_double2[j] = - grid_double0[j] - grid_double1[j];
}
get_vector_modulo(grid_double2, mesh_double);
third_q[ir_grid_points[i]] = get_grid_point(grid_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[ir_grid_point];
if (weights[map_q[q_2]]) {
weights[map_q[q_2]] += weight_q[ir_grid_point];
} else {
weights[ir_grid_point] = weight_q[ir_grid_point];
num_ir_triplets++;
}
}
free(map_q);
map_q = NULL;
free(weight_q);
weight_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 weights[],
const int mesh[3])
{
int i, j, k, num_ir;
int address[3][3], address_double[3], bzmesh[3], bzmesh_double[3];
int *ir_grid_points;
for (i = 0; i < 3; i++) {
bzmesh[i] = mesh[i] * 2 - 1;
bzmesh_double[i] = bzmesh[i] * 2;
}
num_ir = 0;
ir_grid_points = (int*) malloc(sizeof(int) * mesh[0] * mesh[1] * mesh[2]);
for (i = 0; i < mesh[0] * mesh[1] * mesh[2]; i++) {
if (weights[i] > 0) {
ir_grid_points[num_ir] = i;
num_ir++;
}
}
#pragma omp parallel for private(j, k, address, address_double)
for (i = 0; i < num_ir; i++) {
for (j = 0; j < 3; j++) {
address[0][j] = bz_grid_address[grid_point][j];
address[1][j] = bz_grid_address[ir_grid_points[i]][j];
address[2][j] = - address[0][j] - address[1][j];
}
get_third_q_of_triplets_at_q(address,
bz_map,
mesh,
bzmesh,
bzmesh_double);
for (j = 0; j < 3; j++) {
for (k = 0; k < 3; k++) {
address_double[k] = address[j][k] * 2;
if (address_double[k] < 0) {
address_double[k] += bzmesh_double[k];
}
}
triplets[i][j] = bz_map[get_grid_point(address_double, bzmesh)];
}
}
free(ir_grid_points);
return num_ir;
}
static void get_third_q_of_triplets_at_q(int address[3][3],
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[27], address_double[3];
get_vector_modulo(address[2], mesh);
for (i = 0; i < 3; i++) {
delta_g[i] = 0;
for (j = 0; j < 3; j++) {
delta_g[i] += address[j][i];
}
delta_g[i] /= mesh[i];
}
for (i = 0; i < 27; i++) {
for (j = 0; j < 3; j++) {
address_double[j] = (address[2][j] + search_space[i][j] * mesh[j]) * 2;
}
if (abs(address_double[0] > bzmesh[0]) ||
abs(address_double[1] > bzmesh[1]) ||
abs(address_double[2] > bzmesh[2]) ||
abs(address_double[0] < -bzmesh[0]) ||
abs(address_double[1] < -bzmesh[1]) ||
abs(address_double[2] < -bzmesh[2])) { /* outside extended zone */
bzgp[i] = -1;
continue;
}
for (j = 0; j < 3; j++) {
if (address_double[j] < 0) {
address_double[j] += bzmesh_double[j];
}
}
bzgp[i] = bz_map[get_grid_point(address_double, bzmesh)];
}
for (i = 0; i < 27; i++) {
if (bzgp[i] != -1) {
goto escape;
}
}
printf("******* Warning *******\n");
printf(" No third-q was found.\n");
printf("******* Warning *******\n");
escape:
smallest_g = 4;
smallest_index = 0;
for (i = 0; i < 27; 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++) {
address[2][i] += search_space[smallest_index][i] * mesh[i];
}
}
