int kpt_get_stabilized_reciprocal_mesh(int grid_address[][3],
int map[],
const int mesh[3],
const int is_shift[3],
const int is_time_reversal,
const MatINT * rotations,
const int num_q,
SPGCONST double qpoints[][3])
{
int num_ir;
MatINT *rot_reciprocal, *rot_reciprocal_q;
double tolerance;
rot_reciprocal = NULL;
rot_reciprocal_q = NULL;
rot_reciprocal = get_point_group_reciprocal(rotations, is_time_reversal);
tolerance = 0.01 / (mesh[0] + mesh[1] + mesh[2]);
rot_reciprocal_q = get_point_group_reciprocal_with_q(rot_reciprocal,
tolerance,
num_q,
qpoints);
num_ir = get_ir_reciprocal_mesh(grid_address,
map,
mesh,
is_shift,
rot_reciprocal_q);
mat_free_MatINT(rot_reciprocal_q);
rot_reciprocal_q = NULL;
mat_free_MatINT(rot_reciprocal);
rot_reciprocal = NULL;
return num_ir;
}
/*---------*/
static int get_ir_reciprocal_mesh(int grid_address[][3],
int map[],
const int mesh[3],
const int is_shift[3],
const int is_time_reversal,
SPGCONST double lattice[3][3],
SPGCONST double position[][3],
const int types[],
const int num_atom,
const double symprec)
{
SpglibDataset *dataset;
int num_ir, i;
MatINT *rotations;
dataset = get_dataset(lattice,
position,
types,
num_atom,
symprec);
rotations = mat_alloc_MatINT(dataset->n_operations);
for (i = 0; i < dataset->n_operations; i++) {
mat_copy_matrix_i3(rotations->mat[i], dataset->rotations[i]);
}
num_ir = kpt_get_irreducible_reciprocal_mesh(grid_address,
map,
mesh,
is_shift,
is_time_reversal,
rotations);
mat_free_MatINT(rotations);
spg_free_dataset(dataset);
return num_ir;
}
static int get_stabilized_reciprocal_mesh(int grid_address[][3],
int map[],
const int mesh[3],
const int is_shift[3],
const int is_time_reversal,
const int num_rot,
SPGCONST int rotations[][3][3],
const int num_q,
SPGCONST double qpoints[][3])
{
MatINT *rot_real;
int i, num_ir;
rot_real = mat_alloc_MatINT(num_rot);
for (i = 0; i < num_rot; i++) {
mat_copy_matrix_i3(rot_real->mat[i], rotations[i]);
}
num_ir = kpt_get_stabilized_reciprocal_mesh(grid_address,
map,
mesh,
is_shift,
is_time_reversal,
rot_real,
num_q,
qpoints);
mat_free_MatINT(rot_real);
return num_ir;
}
int spg_get_triplets_reciprocal_mesh_at_q( int weights[],
int grid_points[][3],
int third_q[],
const int grid_point,
const int mesh[3],
const int is_time_reversal,
SPGCONST double lattice[3][3],
const int num_rot,
SPGCONST int rotations[][3][3],
const double symprec )
{
MatINT *rot_real;
int i, num_ir;
rot_real = mat_alloc_MatINT( num_rot );
for ( i = 0; i < num_rot; i++ ) {
mat_copy_matrix_i3( rot_real->mat[i], rotations[i] );
}
num_ir = kpt_get_ir_triplets_at_q( weights,
grid_points,
third_q,
grid_point,
mesh,
is_time_reversal,
lattice,
rot_real,
symprec );
mat_free_MatINT( rot_real );
return num_ir;
}
/* Each value of 'map' correspnds to the index of grid_point. */
int kpt_get_irreducible_reciprocal_mesh(int grid_points[][3],
int map[],
const int mesh[3],
const int is_shift[3],
const int is_time_reversal,
const Symmetry * symmetry)
{
int i;
PointSymmetry point_symmetry;
MatINT *rotations;
rotations = mat_alloc_MatINT(symmetry->size);
for (i = 0; i < symmetry->size; i++) {
mat_copy_matrix_i3(rotations->mat[i], symmetry->rot[i]);
}
point_symmetry = get_point_group_reciprocal(rotations,
is_time_reversal);
mat_free_MatINT(rotations);
#ifdef _OPENMP
return get_ir_reciprocal_mesh_openmp(grid_points,
map,
mesh,
is_shift,
&point_symmetry);
#else
return get_ir_reciprocal_mesh(grid_points,
map,
mesh,
is_shift,
&point_symmetry);
#endif
}
static int get_triplets_reciprocal_mesh_at_q(int map_triplets[],
int map_q[],
int grid_address[][3],
const int grid_point,
const int mesh[3],
const int is_time_reversal,
const int num_rot,
SPGCONST int rotations[][3][3])
{
MatINT *rot_real;
int i, num_ir;
rot_real = mat_alloc_MatINT(num_rot);
for (i = 0; i < num_rot; i++) {
mat_copy_matrix_i3(rot_real->mat[i], rotations[i]);
}
num_ir = tpk_get_ir_triplets_at_q(map_triplets,
map_q,
grid_address,
grid_point,
mesh,
is_time_reversal,
rot_real);
mat_free_MatINT(rot_real);
return num_ir;
}
int spg_get_BZ_grid_points_by_rotations(int rot_grid_points[],
const int address_orig[3],
const int num_rot,
SPGCONST int rot_reciprocal[][3][3],
const int mesh[3],
const int is_shift[3],
const int bz_map[])
{
int i;
MatINT *rot;
rot = NULL;
if ((rot = mat_alloc_MatINT(num_rot)) == NULL) {
return 0;
}
for (i = 0; i < num_rot; i++) {
mat_copy_matrix_i3(rot->mat[i], rot_reciprocal[i]);
}
kpt_get_BZ_grid_points_by_rotations(rot_grid_points,
address_orig,
rot,
mesh,
is_shift,
bz_map);
mat_free_MatINT(rot);
return 1;
}
/* Each value of 'map' correspnds to the index of grid_point. */
int kpt_get_irreducible_reciprocal_mesh(int grid_address[][3],
int map[],
const int mesh[3],
const int is_shift[3],
const int is_time_reversal,
const MatINT *rotations)
{
int num_ir;
MatINT *rot_reciprocal;
rot_reciprocal = get_point_group_reciprocal(rotations, is_time_reversal);
#ifdef _OPENMP
num_ir = get_ir_reciprocal_mesh_openmp(grid_address,
map,
mesh,
is_shift,
rot_reciprocal);
#else
num_ir = get_ir_reciprocal_mesh(grid_address,
map,
mesh,
is_shift,
rot_reciprocal);
#endif
mat_free_MatINT(rot_reciprocal);
return num_ir;
}
static int extract_triplets_reciprocal_mesh_at_q(int triplets_at_q[][3],
int weight_triplets_at_q[],
const int fixed_grid_number,
const int num_triplets,
SPGCONST int triplets[][3],
const int mesh[3],
const int is_time_reversal,
const int num_rot,
SPGCONST int rotations[][3][3])
{
MatINT *rot_real;
int i, num_ir;
rot_real = mat_alloc_MatINT(num_rot);
for (i = 0; i < num_rot; i++) {
mat_copy_matrix_i3(rot_real->mat[i], rotations[i]);
}
num_ir = kpt_extract_triplets_reciprocal_mesh_at_q(triplets_at_q,
weight_triplets_at_q,
fixed_grid_number,
num_triplets,
triplets,
mesh,
is_time_reversal,
rot_real);
mat_free_MatINT(rot_real);
return num_ir;
}
static int get_operation_supercell( int rot[][3][3],
double trans[][3],
const int num_sym,
const VecDBL * pure_trans,
SPGCONST Cell *cell,
SPGCONST Cell *primitive )
{
int i, j, k, multi;
double inv_prim_lat[3][3], drot[3][3], trans_mat[3][3], trans_mat_inv[3][3];
MatINT *rot_prim;
VecDBL *trans_prim;
rot_prim = mat_alloc_MatINT( num_sym );
trans_prim = mat_alloc_VecDBL( num_sym );
multi = pure_trans->size;
debug_print("get_operation_supercell\n");
mat_inverse_matrix_d3( inv_prim_lat, primitive->lattice, 0 );
mat_multiply_matrix_d3( trans_mat, inv_prim_lat, cell->lattice );
mat_inverse_matrix_d3( trans_mat_inv, trans_mat, 0 );
for( i = 0; i < num_sym; i++) {
/* Translations */
mat_multiply_matrix_vector_d3( trans[i], trans_mat_inv, trans[i] );
/* Rotations */
mat_cast_matrix_3i_to_3d( drot, rot[i] );
mat_get_similar_matrix_d3( drot, drot, trans_mat, 0 );
mat_cast_matrix_3d_to_3i( rot[i], drot );
}
for( i = 0; i < num_sym; i++ ) {
mat_copy_matrix_i3( rot_prim->mat[i], rot[i] );
for( j = 0; j < 3; j++ )
trans_prim->vec[i][j] = trans[i][j];
}
/* Rotations and translations are copied with the set of */
/* pure translations. */
for( i = 0; i < num_sym; i++ ) {
for( j = 0; j < multi; j++ ) {
mat_copy_matrix_i3( rot[ i * multi + j ], rot_prim->mat[i] );
for ( k = 0; k < 3; k++ ) {
trans[i * multi + j][k] =
mat_Dmod1( trans_prim->vec[i][k] + pure_trans->vec[j][k] );
}
}
}
mat_free_MatINT( rot_prim );
mat_free_VecDBL( trans_prim );
/* return number of symmetry operation of supercell */
return num_sym * multi;
}
static MatINT *get_point_group_reciprocal(const MatINT * rotations,
const int is_time_reversal)
{
int i, j, num_rot;
MatINT *rot_reciprocal, *rot_return;
int *unique_rot;
SPGCONST int inversion[3][3] = {
{-1, 0, 0 },
{ 0,-1, 0 },
{ 0, 0,-1 }
};
if (is_time_reversal) {
rot_reciprocal = mat_alloc_MatINT(rotations->size * 2);
} else {
rot_reciprocal = mat_alloc_MatINT(rotations->size);
}
unique_rot = (int*)malloc(sizeof(int) * rot_reciprocal->size);
for (i = 0; i < rot_reciprocal->size; i++) {
unique_rot[i] = -1;
}
for (i = 0; i < rotations->size; i++) {
mat_transpose_matrix_i3(rot_reciprocal->mat[i], rotations->mat[i]);
if (is_time_reversal) {
mat_multiply_matrix_i3(rot_reciprocal->mat[rotations->size+i],
inversion,
rot_reciprocal->mat[i]);
}
}
num_rot = 0;
for (i = 0; i < rot_reciprocal->size; i++) {
for (j = 0; j < num_rot; j++) {
if (mat_check_identity_matrix_i3(rot_reciprocal->mat[unique_rot[j]],
rot_reciprocal->mat[i])) {
goto escape;
}
}
unique_rot[num_rot] = i;
num_rot++;
escape:
;
}
rot_return = mat_alloc_MatINT(num_rot);
for (i = 0; i < num_rot; i++) {
mat_copy_matrix_i3(rot_return->mat[i], rot_reciprocal->mat[unique_rot[i]]); }
free(unique_rot);
mat_free_MatINT(rot_reciprocal);
return rot_return;
}
static Symmetry * get_primitive_db_symmetry(SPGCONST double t_mat[3][3],
const Symmetry *conv_sym,
const double symprec)
{
int i, j, num_op;
double inv_mat[3][3], tmp_mat[3][3];
MatINT *r_prim;
VecDBL *t_prim;
Symmetry *prim_sym;
r_prim = mat_alloc_MatINT(conv_sym->size);
t_prim = mat_alloc_VecDBL(conv_sym->size);
mat_inverse_matrix_d3(inv_mat, t_mat, symprec);
num_op = 0;
for (i = 0; i < conv_sym->size; i++) {
for (j = 0; j < i; j++) {
if (mat_check_identity_matrix_i3(conv_sym->rot[i],
conv_sym->rot[j])) {
goto pass;
}
}
/* R' = T*R*T^-1 */
mat_multiply_matrix_di3(tmp_mat, t_mat, conv_sym->rot[i]);
mat_multiply_matrix_d3(tmp_mat, tmp_mat, inv_mat);
mat_cast_matrix_3d_to_3i(r_prim->mat[ num_op ], tmp_mat);
/* t' = T*t */
mat_multiply_matrix_vector_d3(t_prim->vec[ num_op ],
t_mat,
conv_sym->trans[ i ]);
num_op++;
pass:
;
}
prim_sym = sym_alloc_symmetry(num_op);
for (i = 0; i < num_op; i++) {
mat_copy_matrix_i3(prim_sym->rot[i], r_prim->mat[i]);
for (j = 0; j < 3; j++) {
prim_sym->trans[i][j] = t_prim->vec[i][j] - mat_Nint(t_prim->vec[i][j]);
}
}
mat_free_MatINT(r_prim);
mat_free_VecDBL(t_prim);
return prim_sym;
}
SpglibTriplets * spg_get_triplets_reciprocal_mesh( const int mesh[3],
const int is_time_reversal,
SPGCONST double lattice[3][3],
const int num_rot,
SPGCONST int rotations[][3][3],
const double symprec )
{
int i, j, num_grid;
MatINT *rot_real;
Triplets *tps;
SpglibTriplets *spg_triplets;
num_grid = mesh[0] * mesh[1] * mesh[2];
rot_real = mat_alloc_MatINT( num_rot );
for ( i = 0; i < num_rot; i++ ) {
mat_copy_matrix_i3( rot_real->mat[i], rotations[i] );
}
tps = kpt_get_triplets_reciprocal_mesh( mesh,
is_time_reversal,
lattice,
rot_real,
symprec );
mat_free_MatINT( rot_real );
spg_triplets = (SpglibTriplets*) malloc( sizeof( SpglibTriplets ) );
spg_triplets->size = tps->size;
spg_triplets->triplets = (int (*)[3]) malloc( sizeof(int[3]) * tps->size );
spg_triplets->weights = (int*) malloc( sizeof(int) * tps->size );
spg_triplets->mesh_points = (int (*)[3]) malloc( sizeof(int[3]) * num_grid );
for ( i = 0; i < 3; i++ ) {
spg_triplets->mesh[i] = tps->mesh[i];
}
for ( i = 0; i < num_grid; i++ ) {
for ( j = 0; j < 3; j++ ) {
spg_triplets->mesh_points[i][j] = tps->mesh_points[i][j];
}
}
for ( i = 0; i < tps->size; i++ ) {
for ( j = 0; j < 3; j++ ) {
spg_triplets->triplets[i][j] = tps->triplets[i][j];
}
spg_triplets->weights[i] = tps->weights[i];
}
kpt_free_triplets( tps );
return spg_triplets;
}
/* num_q is the number of the qpoints. */
static PointSymmetry get_point_group_reciprocal(const MatINT * rotations,
const int is_time_reversal)
{
int i, j, num_pt = 0;
MatINT *rot_reciprocal;
PointSymmetry point_symmetry;
SPGCONST int inversion[3][3] = {
{-1, 0, 0 },
{ 0,-1, 0 },
{ 0, 0,-1 }
};
if (is_time_reversal) {
rot_reciprocal = mat_alloc_MatINT(rotations->size * 2);
} else {
rot_reciprocal = mat_alloc_MatINT(rotations->size);
}
for (i = 0; i < rotations->size; i++) {
mat_transpose_matrix_i3(rot_reciprocal->mat[i], rotations->mat[i]);
if (is_time_reversal) {
mat_multiply_matrix_i3(rot_reciprocal->mat[rotations->size+i],
inversion,
rot_reciprocal->mat[i]);
}
}
for (i = 0; i < rot_reciprocal->size; i++) {
for (j = 0; j < num_pt; j++) {
if (mat_check_identity_matrix_i3(point_symmetry.rot[j],
rot_reciprocal->mat[i])) {
goto escape;
}
}
mat_copy_matrix_i3(point_symmetry.rot[num_pt],
rot_reciprocal->mat[i]);
num_pt++;
escape:
;
}
point_symmetry.size = num_pt;
mat_free_MatINT(rot_reciprocal);
return point_symmetry;
}
static Symmetry * reduce_operation(SPGCONST Cell * cell,
SPGCONST Symmetry * symmetry,
const double symprec)
{
int i, j, num_sym;
Symmetry * sym_reduced;
PointSymmetry point_symmetry;
MatINT *rot;
VecDBL *trans;
debug_print("reduce_operation:\n");
point_symmetry = get_lattice_symmetry(cell, symprec);
rot = mat_alloc_MatINT(symmetry->size);
trans = mat_alloc_VecDBL(symmetry->size);
num_sym = 0;
for (i = 0; i < point_symmetry.size; i++) {
for (j = 0; j < symmetry->size; j++) {
if (mat_check_identity_matrix_i3(point_symmetry.rot[i],
symmetry->rot[j])) {
if (is_overlap_all_atoms(symmetry->trans[j],
symmetry->rot[j],
cell,
symprec,
0)) {
mat_copy_matrix_i3(rot->mat[num_sym], symmetry->rot[j]);
mat_copy_vector_d3(trans->vec[num_sym], symmetry->trans[j]);
num_sym++;
}
}
}
}
sym_reduced = sym_alloc_symmetry(num_sym);
for (i = 0; i < num_sym; i++) {
mat_copy_matrix_i3(sym_reduced->rot[i], rot->mat[i]);
mat_copy_vector_d3(sym_reduced->trans[i], trans->vec[i]);
}
mat_free_MatINT(rot);
mat_free_VecDBL(trans);
debug_print(" num_sym %d -> %d\n", symmetry->size, num_sym);
return sym_reduced;
}
void spg_get_grid_points_by_rotations(int rot_grid_points[],
const int address_orig[3],
const int num_rot,
SPGCONST int rot_reciprocal[][3][3],
const int mesh[3],
const int is_shift[3])
{
int i;
MatINT *rot;
rot = mat_alloc_MatINT(num_rot);
for (i = 0; i < num_rot; i++) {
mat_copy_matrix_i3(rot->mat[i], rot_reciprocal[i]);
}
kpt_get_grid_points_by_rotations(rot_grid_points,
address_orig,
rot,
mesh,
is_shift);
mat_free_MatINT(rot);
}
int kpt_get_ir_triplets_at_q(int map_triplets[],
int map_q[],
int grid_address[][3],
const int grid_point,
const int mesh[3],
const int is_time_reversal,
const MatINT * rotations)
{
int num_ir;
MatINT *rot_reciprocal;
rot_reciprocal = get_point_group_reciprocal(rotations, is_time_reversal);
num_ir = get_ir_triplets_at_q(map_triplets,
map_q,
grid_address,
grid_point,
mesh,
rot_reciprocal);
mat_free_MatINT(rot_reciprocal);
return num_ir;
}
int kpt_get_irreducible_kpoints(int map[],
SPGCONST double kpoints[][3],
const int num_kpoint,
const Symmetry * symmetry,
const int is_time_reversal,
const double symprec)
{
int i;
PointSymmetry point_symmetry;
MatINT *rotations;
rotations = mat_alloc_MatINT(symmetry->size);
for (i = 0; i < symmetry->size; i++) {
mat_copy_matrix_i3(rotations->mat[i], symmetry->rot[i]);
}
point_symmetry = get_point_group_reciprocal(rotations,
is_time_reversal);
mat_free_MatINT(rotations);
return get_ir_kpoints(map, kpoints, num_kpoint, &point_symmetry, symprec);
}
Symmetry * sym_get_operation( SPGCONST Cell *cell,
const double symprec ) {
int i, j, num_sym;
MatINT *rot;
VecDBL *trans;
Symmetry *symmetry;
rot = mat_alloc_MatINT( cell->size * 48 );
trans = mat_alloc_VecDBL( cell->size * 48 );
num_sym = get_operation( rot->mat, trans->vec, cell, symprec );
#ifdef DEBUG
debug_print("*** get_symmetry (found symmetry operations) *** \n");
debug_print("Lattice \n");
debug_print_matrix_d3(cell->lattice);
for ( i = 0; i < num_sym; i++ ) {
debug_print("--- %d ---\n", i + 1);
debug_print_matrix_i3(rot->mat[i]);
debug_print("%f %f %f\n",
trans->vec[i][0], trans->vec[i][1], trans->vec[i][2]);
}
#endif
symmetry = sym_alloc_symmetry( num_sym );
for ( i = 0; i < num_sym; i++ ) {
mat_copy_matrix_i3(symmetry->rot[i], rot->mat[i]);
for (j = 0; j < 3; j++)
symmetry->trans[i][j] = trans->vec[i][j];
}
mat_free_MatINT( rot );
mat_free_VecDBL( trans );
return symmetry;
}
/* Return NULL if failed */
static MatINT *get_point_group_reciprocal(const MatINT * rotations,
const int is_time_reversal)
{
int i, j, num_rot;
MatINT *rot_reciprocal, *rot_return;
int *unique_rot;
SPGCONST int inversion[3][3] = {
{-1, 0, 0 },
{ 0,-1, 0 },
{ 0, 0,-1 }
};
rot_reciprocal = NULL;
rot_return = NULL;
unique_rot = NULL;
if (is_time_reversal) {
if ((rot_reciprocal = mat_alloc_MatINT(rotations->size * 2)) == NULL) {
return NULL;
}
} else {
if ((rot_reciprocal = mat_alloc_MatINT(rotations->size)) == NULL) {
return NULL;
}
}
if ((unique_rot = (int*)malloc(sizeof(int) * rot_reciprocal->size)) == NULL) {
warning_print("spglib: Memory of unique_rot could not be allocated.");
mat_free_MatINT(rot_reciprocal);
return NULL;
}
for (i = 0; i < rot_reciprocal->size; i++) {
unique_rot[i] = -1;
}
for (i = 0; i < rotations->size; i++) {
mat_transpose_matrix_i3(rot_reciprocal->mat[i], rotations->mat[i]);
if (is_time_reversal) {
mat_multiply_matrix_i3(rot_reciprocal->mat[rotations->size+i],
inversion,
rot_reciprocal->mat[i]);
}
}
num_rot = 0;
for (i = 0; i < rot_reciprocal->size; i++) {
for (j = 0; j < num_rot; j++) {
if (mat_check_identity_matrix_i3(rot_reciprocal->mat[unique_rot[j]],
rot_reciprocal->mat[i])) {
goto escape;
}
}
unique_rot[num_rot] = i;
num_rot++;
escape:
;
}
if ((rot_return = mat_alloc_MatINT(num_rot)) != NULL) {
for (i = 0; i < num_rot; i++) {
mat_copy_matrix_i3(rot_return->mat[i], rot_reciprocal->mat[unique_rot[i]]);
}
}
free(unique_rot);
unique_rot = NULL;
mat_free_MatINT(rot_reciprocal);
rot_reciprocal = NULL;
return rot_return;
}
/* Return NULL if failed */
static Symmetry * reduce_operation(SPGCONST Cell * primitive,
SPGCONST Symmetry * symmetry,
const double symprec,
const double angle_symprec)
{
int i, j, num_sym;
Symmetry * sym_reduced;
PointSymmetry point_symmetry;
MatINT *rot;
VecDBL *trans;
debug_print("reduce_operation:\n");
sym_reduced = NULL;
rot = NULL;
trans = NULL;
point_symmetry = get_lattice_symmetry(primitive->lattice,
symprec,
angle_symprec);
if (point_symmetry.size == 0) {
return NULL;
}
if ((rot = mat_alloc_MatINT(symmetry->size)) == NULL) {
return NULL;
}
if ((trans = mat_alloc_VecDBL(symmetry->size)) == NULL) {
mat_free_MatINT(rot);
rot = NULL;
return NULL;
}
num_sym = 0;
for (i = 0; i < point_symmetry.size; i++) {
for (j = 0; j < symmetry->size; j++) {
if (mat_check_identity_matrix_i3(point_symmetry.rot[i],
symmetry->rot[j])) {
if (is_overlap_all_atoms(symmetry->trans[j],
symmetry->rot[j],
primitive,
symprec,
0)) {
mat_copy_matrix_i3(rot->mat[num_sym], symmetry->rot[j]);
mat_copy_vector_d3(trans->vec[num_sym], symmetry->trans[j]);
num_sym++;
}
}
}
}
if ((sym_reduced = sym_alloc_symmetry(num_sym)) != NULL) {
for (i = 0; i < num_sym; i++) {
mat_copy_matrix_i3(sym_reduced->rot[i], rot->mat[i]);
mat_copy_vector_d3(sym_reduced->trans[i], trans->vec[i]);
}
}
mat_free_MatINT(rot);
rot = NULL;
mat_free_VecDBL(trans);
trans = NULL;
return sym_reduced;
}
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;
}
static Symmetry * get_collinear_operations(SPGCONST Symmetry *sym_nonspin,
SPGCONST Cell *cell,
const double spins[],
const double symprec)
{
Symmetry *symmetry;
int i, j, k, sign, is_found, num_sym;
double pos[3];
MatINT * rot;
VecDBL * trans;
rot = mat_alloc_MatINT(sym_nonspin->size);
trans = mat_alloc_VecDBL(sym_nonspin->size);
num_sym = 0;
for (i = 0; i < sym_nonspin->size; i++) {
sign = 0; /* Set sign as undetermined */
is_found = 1;
for (j = 0; j < cell->size; j++) {
mat_multiply_matrix_vector_id3(pos, sym_nonspin->rot[i], cell->position[j]);
for (k = 0; k < 3; k++) {
pos[k] += sym_nonspin->trans[i][k];
}
for (k = 0; k < cell->size; k++) {
if (cel_is_overlap(cell->position[k],
pos,
cell->lattice,
symprec)) {
if (sign == 0) {
if (mat_Dabs(spins[j] - spins[k]) < symprec) {
sign = 1;
break;
}
if (mat_Dabs(spins[j] + spins[k]) < symprec) {
sign = -1;
break;
}
is_found = 0;
break;
} else {
if (mat_Dabs(spins[j] - spins[k] * sign) < symprec) {
break;
} else {
is_found = 0;
break;
}
}
}
}
if (! is_found) {
break;
}
}
if (is_found) {
mat_copy_matrix_i3(rot->mat[num_sym], sym_nonspin->rot[i]);
mat_copy_vector_d3(trans->vec[num_sym], sym_nonspin->trans[i]);
num_sym++;
}
}
symmetry = sym_alloc_symmetry(num_sym);
for (i = 0; i < num_sym; i++) {
mat_copy_matrix_i3(symmetry->rot[i], rot->mat[ i ]);
mat_copy_vector_d3(symmetry->trans[i], trans->vec[ i ]);
}
mat_free_MatINT(rot);
mat_free_VecDBL(trans);
return symmetry;
}
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;
}
