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;
}
/* Only the atoms corresponding to those in primitive are returned. */
static Cell * get_bravais_exact_positions_and_lattice(int * wyckoffs,
int * equiv_atoms,
SPGCONST Spacegroup *spacegroup,
SPGCONST Cell * primitive,
const double symprec)
{
int i;
Symmetry *conv_sym;
Cell *bravais;
VecDBL *exact_positions;
/* Positions of primitive atoms are represented wrt Bravais lattice */
bravais = get_conventional_primitive(spacegroup, primitive);
/* Symmetries in database (wrt Bravais lattice) */
conv_sym = get_db_symmetry(spacegroup->hall_number);
/* Lattice vectors are set. */
get_conventional_lattice(bravais->lattice,
spacegroup->holohedry,
spacegroup->bravais_lattice);
/* Symmetrize atomic positions of conventional unit cell */
exact_positions = ssm_get_exact_positions(wyckoffs,
equiv_atoms,
bravais,
conv_sym,
spacegroup->hall_number,
symprec);
sym_free_symmetry(conv_sym);
if (exact_positions->size > 0) {
for (i = 0; i < bravais->size; i++) {
mat_copy_vector_d3(bravais->position[i], exact_positions->vec[i]);
}
} else {
cel_free_cell(bravais);
bravais = cel_alloc_cell(0);
}
mat_free_VecDBL(exact_positions);
return bravais;
}
int spg_find_primitive( double lattice[3][3],
double position[][3],
int types[],
const int num_atom,
const double symprec )
{
int i, j, num_prim_atom=0;
int *mapping_table;
Cell *cell, *primitive;
VecDBL *pure_trans;
cell = cel_alloc_cell( num_atom );
cel_set_cell( cell, lattice, position, types );
pure_trans = sym_get_pure_translation( cell, symprec );
/* find primitive cell */
if ( pure_trans->size > 1 ) {
mapping_table = (int*) malloc( sizeof(int) * cell->size );
primitive = prm_get_primitive( mapping_table, cell, pure_trans, symprec );
free( mapping_table );
mapping_table = NULL;
num_prim_atom = primitive->size;
if ( num_prim_atom < num_atom && num_prim_atom > 0 ) {
mat_copy_matrix_d3( lattice, primitive->lattice );
for ( i = 0; i < primitive->size; i++ ) {
types[i] = primitive->types[i];
for (j=0; j<3; j++) {
position[i][j] = primitive->position[i][j];
}
}
}
cel_free_cell( primitive );
} else {
num_prim_atom = 0;
}
mat_free_VecDBL( pure_trans );
cel_free_cell( cell );
return num_prim_atom;
}
static Symmetry *
get_space_group_operations(SPGCONST PointSymmetry *lattice_sym,
SPGCONST Cell *cell,
const double symprec)
{
int i, j, num_sym, total_num_sym;
VecDBL **trans;
Symmetry *symmetry;
debug_print("get_space_group_operations:\n");
trans = (VecDBL**) malloc(sizeof(VecDBL*) * lattice_sym->size);
total_num_sym = 0;
for (i = 0; i < lattice_sym->size; i++) {
trans[i] = get_translation(lattice_sym->rot[i], cell, symprec, 0);
total_num_sym += trans[i]->size;
}
symmetry = sym_alloc_symmetry(total_num_sym);
num_sym = 0;
for (i = 0; i < lattice_sym->size; i++) {
for (j = 0; j < trans[i]->size; j++) {
mat_copy_vector_d3(symmetry->trans[num_sym + j], trans[i]->vec[j]);
mat_copy_matrix_i3(symmetry->rot[num_sym + j], lattice_sym->rot[i]);
}
num_sym += trans[i]->size;
}
for (i = 0; i < lattice_sym->size; i++) {
mat_free_VecDBL(trans[i]);
}
free(trans);
trans = NULL;
return symmetry;
}
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;
}
/* was not a primitive cell. */
static int get_operation( int rot[][3][3],
double trans[][3],
SPGCONST Cell *cell,
const double symprec )
{
int num_sym;
int multi;
int *mapping_table;
PointSymmetry lattice_sym;
Cell *primitive;
VecDBL *pure_trans;
pure_trans = sym_get_pure_translation(cell, symprec);
multi = pure_trans->size;
/* Lattice symmetry for input cell*/
lattice_sym = get_lattice_symmetry( cell, symprec );
if ( lattice_sym.size == 0 ) {
goto err;
}
/* Obtain primitive cell */
if( multi > 1 ) {
mapping_table = (int*) malloc( sizeof(int) * cell->size );
primitive = prm_get_primitive( mapping_table, cell, pure_trans, symprec );
free( mapping_table );
mapping_table = NULL;
if ( primitive->size < 1 ) { goto err; }
lattice_sym = transform_pointsymmetry( &lattice_sym,
primitive->lattice,
cell->lattice );
if ( lattice_sym.size == 0 ) { goto err; }
} else {
primitive = cell;
}
/* Symmetry operation search for primitive cell */
num_sym = get_space_group_operation( rot, trans, &lattice_sym,
primitive, symprec );
/* Recover symmetry operation for the input structure (overwritten) */
if( multi > 1 ) {
num_sym = get_operation_supercell( rot,
trans,
num_sym,
pure_trans,
cell,
primitive );
cel_free_cell( primitive );
if ( num_sym == 0 ) { goto err; }
}
mat_free_VecDBL( pure_trans );
return num_sym;
err:
mat_free_VecDBL( pure_trans );
return 0;
}
/* Return NULL if failed */
static Primitive * get_primitive(SPGCONST Cell * cell, const double symprec)
{
int i, attempt, is_found = 0;
double tolerance;
Primitive *primitive;
VecDBL * pure_trans;
debug_print("get_primitive (tolerance = %f):\n", symprec);
primitive = NULL;
pure_trans = NULL;
if ((primitive = prm_alloc_primitive(cell->size)) == NULL) {
return NULL;
}
tolerance = symprec;
for (attempt = 0; attempt < 100; attempt++) {
if ((pure_trans = sym_get_pure_translation(cell, tolerance)) == NULL) {
printf("***** hoge ******\n");
goto cont;
}
if (pure_trans->size == 1) {
if ((primitive->cell = get_cell_with_smallest_lattice(cell, tolerance))
== NULL) {
mat_free_VecDBL(pure_trans);
goto cont;
}
for (i = 0; i < cell->size; i++) {
primitive->mapping_table[i] = i;
}
} else {
if ((primitive->cell = get_primitive_cell(primitive->mapping_table,
cell,
pure_trans,
tolerance)) == NULL) {
mat_free_VecDBL(pure_trans);
goto cont;
}
}
is_found = 1;
break;
cont:
tolerance *= REDUCE_RATE;
warning_print("spglib: Reduce tolerance to %f ", tolerance);
warning_print("(line %d, %s).\n", __LINE__, __FILE__);
}
mat_free_VecDBL(pure_trans);
if (is_found) {
primitive->tolerance = tolerance;
} else {
prm_free_primitive(primitive);
}
return primitive;
}
static Symmetry * reduce_symmetry_in_frame(const int frame[3],
SPGCONST Symmetry *prim_sym,
SPGCONST int t_mat[3][3],
SPGCONST double lattice[3][3],
const int multiplicity,
const double symprec)
{
int i, j, k, l, num_trans, size_sym_orig;
Symmetry *symmetry, *t_sym;
double inv_tmat[3][3], tmp_mat[3][3], tmp_rot_d[3][3], tmp_lat_d[3][3], tmp_lat_i[3][3];
int tmp_rot_i[3][3];
VecDBL *pure_trans, *lattice_trans;
mat_cast_matrix_3i_to_3d(tmp_mat, t_mat);
mat_inverse_matrix_d3(inv_tmat, tmp_mat, symprec);
/* transformed lattice points */
lattice_trans = mat_alloc_VecDBL(frame[0]*frame[1]*frame[2]);
num_trans = 0;
for (i = 0; i < frame[0]; i++) {
for (j = 0; j < frame[1]; j++) {
for (k = 0; k < frame[2]; k++) {
lattice_trans->vec[num_trans][0] = i;
lattice_trans->vec[num_trans][1] = j;
lattice_trans->vec[num_trans][2] = k;
mat_multiply_matrix_vector_d3(lattice_trans->vec[num_trans],
inv_tmat,
lattice_trans->vec[num_trans]);
for (l = 0; l < 3; l++) {
/* t' = T^-1*t */
lattice_trans->vec[num_trans][l] = \
mat_Dmod1(lattice_trans->vec[num_trans][l]);
}
num_trans++;
}
}
}
/* transformed symmetry operations of primitive cell */
t_sym = sym_alloc_symmetry(prim_sym->size);
size_sym_orig = 0;
for (i = 0; i < prim_sym->size; i++) {
/* R' = T^-1*R*T */
mat_multiply_matrix_di3(tmp_mat, inv_tmat, prim_sym->rot[i]);
mat_multiply_matrix_di3(tmp_rot_d, tmp_mat, t_mat);
mat_cast_matrix_3d_to_3i(tmp_rot_i, tmp_rot_d);
mat_multiply_matrix_di3(tmp_lat_i, lattice, tmp_rot_i);
mat_multiply_matrix_d3(tmp_lat_d, lattice, tmp_rot_d);
if (mat_check_identity_matrix_d3(tmp_lat_i, tmp_lat_d, symprec)) {
mat_copy_matrix_i3(t_sym->rot[size_sym_orig], tmp_rot_i);
/* t' = T^-1*t */
mat_multiply_matrix_vector_d3(t_sym->trans[size_sym_orig],
inv_tmat, prim_sym->trans[i]);
size_sym_orig++;
}
}
/* reduce lattice points */
pure_trans = reduce_lattice_points(lattice,
lattice_trans,
symprec);
if (! (pure_trans->size == multiplicity)) {
symmetry = sym_alloc_symmetry(0);
goto ret;
}
/* copy symmetry operations upon lattice points */
symmetry = sym_alloc_symmetry(pure_trans->size * size_sym_orig);
for (i = 0; i < pure_trans->size; i++) {
for (j = 0; j < size_sym_orig; j++) {
mat_copy_matrix_i3(symmetry->rot[size_sym_orig * i + j],
t_sym->rot[j]);
mat_copy_vector_d3(symmetry->trans[size_sym_orig * i + j],
t_sym->trans[j]);
for (k = 0; k < 3; k++) {
symmetry->trans[size_sym_orig * i + j][k] += pure_trans->vec[i][k];
symmetry->trans[size_sym_orig * i + j][k] = \
mat_Dmod1(symmetry->trans[size_sym_orig * i + j][k]);
}
}
}
ret:
mat_free_VecDBL(lattice_trans);
mat_free_VecDBL(pure_trans);
sym_free_symmetry(t_sym);
return symmetry;
}
static Symmetry * get_primitive_db_symmetry(SPGCONST double t_mat[3][3],
const Symmetry *conv_sym)
{
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 = NULL;
t_prim = NULL;
prim_sym = NULL;
if ((r_prim = mat_alloc_MatINT(conv_sym->size)) == NULL) {
return NULL;
}
if ((t_prim = mat_alloc_VecDBL(conv_sym->size)) == NULL) {
mat_free_MatINT(r_prim);
r_prim = NULL;
return NULL;
}
mat_inverse_matrix_d3(inv_mat, t_mat, 0);
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:
;
}
if ((prim_sym = sym_alloc_symmetry(num_op)) == NULL) {
goto ret;
}
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] = mat_Dmod1(t_prim->vec[i][j]);
}
}
ret:
mat_free_MatINT(r_prim);
r_prim = NULL;
mat_free_VecDBL(t_prim);
t_prim = NULL;
return prim_sym;
}
static Symmetry * reduce_symmetry_in_frame( const int frame[3],
SPGCONST Symmetry *prim_sym,
SPGCONST int t_mat[3][3],
SPGCONST double lattice[3][3],
const double symprec )
{
int i, j, k, l, n, num_op, is_found;
Symmetry *symmetry, *t_sym;
double inv_mat[3][3], tmp_mat[3][3];
VecDBL *t, *lattice_trans;
mat_cast_matrix_3i_to_3d( tmp_mat, t_mat );
mat_inverse_matrix_d3( inv_mat, tmp_mat, symprec );
/* transformed lattice points */
lattice_trans = mat_alloc_VecDBL( frame[0]*frame[1]*frame[2] );
n = 0;
for ( i = 0; i < frame[0]; i++ ) {
for ( j = 0; j < frame[1]; j++ ) {
for ( k = 0; k < frame[2]; k++ ) {
lattice_trans->vec[n][0] = i;
lattice_trans->vec[n][1] = j;
lattice_trans->vec[n][2] = k;
mat_multiply_matrix_vector_d3( lattice_trans->vec[n],
inv_mat,
lattice_trans->vec[n] );
for ( l = 0; l < 3; l++ ) {
/* t' = T^-1*t */
lattice_trans->vec[n][l] = mat_Dmod1( lattice_trans->vec[n][l] );
}
n++;
}
}
}
/* transformed symmetry operations of primitive cell */
t_sym = sym_alloc_symmetry( prim_sym->size );
for ( i = 0; i < prim_sym->size; i++ ) {
/* R' = T^-1*R*T */
mat_multiply_matrix_di3( tmp_mat, inv_mat, prim_sym->rot[i] );
mat_multiply_matrix_di3( tmp_mat, tmp_mat, t_mat );
mat_cast_matrix_3d_to_3i( t_sym->rot[i], tmp_mat );
/* t' = T^-1*t */
mat_multiply_matrix_vector_d3( t_sym->trans[i], inv_mat, prim_sym->trans[ i ] );
}
/* reduce lattice points */
num_op = 0;
t = mat_alloc_VecDBL( lattice_trans->size );
for ( i = 0; i < lattice_trans->size; i++ ) {
is_found = 0;
for ( j = 0; j < num_op; j++ ) {
if ( cel_is_overlap( lattice_trans->vec[i], t->vec[j], lattice, symprec ) ) {
is_found = 1;
break;
}
}
if ( ! is_found ) {
mat_copy_vector_d3( t->vec[num_op], lattice_trans->vec[i] );
num_op++;
}
}
/* copy symmetry operations upon lattice points */
symmetry = sym_alloc_symmetry( num_op * t_sym->size );
for ( i = 0; i < num_op; i++ ) {
for ( j = 0; j < t_sym->size; j++ ) {
mat_copy_matrix_i3( symmetry->rot[ t_sym->size * i + j ], t_sym->rot[j] );
mat_copy_vector_d3( symmetry->trans[ t_sym->size * i + j ], t_sym->trans[j] );
for ( k = 0; k < 3; k++ ) {
symmetry->trans[ t_sym->size * i + j ][k] += t->vec[i][k];
symmetry->trans[ t_sym->size * i + j ][k] = \
mat_Dmod1( symmetry->trans[ t_sym->size * i + j ][k] );
}
}
}
mat_free_VecDBL( t );
sym_free_symmetry( t_sym );
return symmetry;
}
/* 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;
}
/* was not a primitive cell. */
static Symmetry * get_operations(SPGCONST Cell *cell,
const double symprec)
{
int i, j, attempt;
double tolerance;
PointSymmetry lattice_sym;
Symmetry *symmetry, *symmetry_orig, *symmetry_reduced;
Primitive primitive;
debug_print("get_operations:\n");
symmetry_orig = NULL;
lattice_sym = get_lattice_symmetry(cell, symprec);
if (lattice_sym.size == 0) {
debug_print("get_lattice_symmetry failed.\n");
goto end;
}
primitive = prm_get_primitive_and_pure_translations(cell, symprec);
if (primitive.cell->size == 0) {
goto deallocate_and_end;
}
lattice_sym = transform_pointsymmetry(&lattice_sym,
primitive.cell->lattice,
cell->lattice);
if (lattice_sym.size == 0) {
goto deallocate_and_end;
}
symmetry = get_space_group_operations(&lattice_sym,
primitive.cell,
symprec);
if (symmetry->size > 48) {
tolerance = symprec;
for (attempt = 0; attempt < 100; attempt++) {
tolerance *= REDUCE_RATE;
warning_print("spglib: number of symmetry operations for primitive cell > 48 was found. (line %d, %s).\n", __LINE__, __FILE__);
warning_print("tolerance is reduced to %f\n", tolerance);
symmetry_reduced = reduce_operation(primitive.cell,
symmetry,
tolerance);
sym_free_symmetry(symmetry);
symmetry = symmetry_reduced;
if (symmetry_reduced->size > 48) {
;
} else {
break;
}
}
}
symmetry_orig = recover_operations_original(symmetry,
primitive.pure_trans,
cell,
primitive.cell);
sym_free_symmetry(symmetry);
for (i = 0; i < symmetry_orig->size; i++) {
for (j = 0; j < 3; j++) {
symmetry_orig->trans[i][j] -= mat_Nint(symmetry_orig->trans[i][j]);
}
}
deallocate_and_end:
cel_free_cell(primitive.cell);
mat_free_VecDBL(primitive.pure_trans);
end:
if (! symmetry_orig) {
symmetry_orig = sym_alloc_symmetry(0);
}
return symmetry_orig;
}
SpglibDataset * spg_get_dataset( SPGCONST double lattice[3][3],
SPGCONST double position[][3],
const int types[],
const int num_atom,
const double symprec )
{
int i, j;
int *mapping_table, *wyckoffs, *equiv_atoms, *equiv_atoms_prim;
Spacegroup spacegroup;
SpglibDataset *dataset;
Cell *cell, *primitive;
double inv_mat[3][3];
Symmetry *symmetry;
VecDBL *pure_trans;
dataset = (SpglibDataset*) malloc( sizeof( SpglibDataset ) );
cell = cel_alloc_cell( num_atom );
cel_set_cell( cell, lattice, position, types );
pure_trans = sym_get_pure_translation( cell, symprec );
mapping_table = (int*) malloc( sizeof(int) * cell->size );
primitive = prm_get_primitive( mapping_table, cell, pure_trans, symprec );
mat_free_VecDBL( pure_trans );
spacegroup = spa_get_spacegroup_with_primitive( primitive, symprec );
/* Spacegroup type, transformation matrix, origin shift */
if ( spacegroup.number > 0 ) {
dataset->spacegroup_number = spacegroup.number;
strcpy( dataset->international_symbol, spacegroup.international_short);
strcpy( dataset->hall_symbol, spacegroup.hall_symbol);
mat_inverse_matrix_d3( inv_mat, lattice, symprec );
mat_multiply_matrix_d3( dataset->transformation_matrix,
inv_mat,
spacegroup.bravais_lattice );
mat_copy_vector_d3( dataset->origin_shift, spacegroup.origin_shift );
}
/* Wyckoff positions */
wyckoffs = (int*) malloc( sizeof(int) * primitive->size );
equiv_atoms_prim = (int*) malloc( sizeof(int) * primitive->size );
for ( i = 0; i < primitive->size; i++ ) {
wyckoffs[i] = -1;
equiv_atoms_prim[i] = -1;
}
ref_get_Wyckoff_positions( wyckoffs,
equiv_atoms_prim,
primitive,
&spacegroup,
symprec );
dataset->n_atoms = cell->size;
dataset->wyckoffs = (int*) malloc( sizeof(int) * cell->size );
for ( i = 0; i < cell->size; i++ ) {
dataset->wyckoffs[i] = wyckoffs[ mapping_table[i] ];
}
free( wyckoffs );
wyckoffs = NULL;
dataset->equivalent_atoms = (int*) malloc( sizeof(int) * cell->size );
equiv_atoms = (int*) malloc( sizeof(int) * primitive->size );
for ( i = 0; i < primitive->size; i++ ) {
for ( j = 0; j < cell->size; j++ ) {
if ( mapping_table[j] == equiv_atoms_prim[i] ) {
equiv_atoms[i] = j;
break;
}
}
}
for ( i = 0; i < cell->size; i++ ) {
dataset->equivalent_atoms[i] = equiv_atoms[ mapping_table[i] ];
}
free( equiv_atoms );
equiv_atoms = NULL;
free( equiv_atoms_prim );
equiv_atoms_prim = NULL;
free( mapping_table );
mapping_table = NULL;
/* Symmetry operations */
symmetry = ref_get_refined_symmetry_operations( cell,
primitive->lattice,
&spacegroup,
symprec );
cel_free_cell( cell );
cel_free_cell( primitive );
dataset->rotations = (int (*)[3][3]) malloc(sizeof(int[3][3]) * symmetry->size );
dataset->translations = (double (*)[3]) malloc(sizeof(double[3]) * symmetry->size );
dataset->n_operations = symmetry->size;
for ( i = 0; i < symmetry->size; i++ ) {
mat_copy_matrix_i3( dataset->rotations[i], symmetry->rot[i] );
mat_copy_vector_d3( dataset->translations[i], symmetry->trans[i] );
}
sym_free_symmetry( symmetry );
return dataset;
}
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;
}
/* Return NULL if failed */
static VecDBL * get_exact_positions(int * wyckoffs,
int * equiv_atoms,
SPGCONST Cell * bravais,
SPGCONST Symmetry * conv_sym,
const int hall_number,
const double symprec)
{
int i, j, k, l, num_indep_atoms;
double pos[3];
int *indep_atoms;
VecDBL *positions;
debug_print("get_exact_positions\n");
indep_atoms = NULL;
positions = NULL;
if ((indep_atoms = (int*) malloc(sizeof(int) * bravais->size)) == NULL) {
warning_print("spglib: Memory could not be allocated ");
return NULL;
}
if ((positions = mat_alloc_VecDBL(bravais->size)) == NULL) {
free(indep_atoms);
indep_atoms = NULL;
return NULL;
}
num_indep_atoms = 0;
for (i = 0; i < bravais->size; i++) {
/* Check if atom_i overlap to an atom already set at the exact position. */
for (j = 0; j < num_indep_atoms; j++) {
for (k = 0; k < conv_sym->size; k++) {
mat_multiply_matrix_vector_id3(pos,
conv_sym->rot[k],
positions->vec[indep_atoms[j]]);
for (l = 0; l < 3; l++) {
pos[l] += conv_sym->trans[k][l];
}
if (cel_is_overlap(pos,
bravais->position[i],
bravais->lattice,
symprec)) {
/* Equivalent atom was found. */
for (l = 0; l < 3; l++) {
positions->vec[i][l] = mat_Dmod1(pos[l]);
}
wyckoffs[i] = wyckoffs[indep_atoms[j]];
equiv_atoms[i] = indep_atoms[j];
goto escape;
}
}
}
/* No equivalent atom was found. */
indep_atoms[num_indep_atoms] = i;
num_indep_atoms++;
mat_copy_vector_d3(positions->vec[i], bravais->position[i]);
get_exact_location(positions->vec[i],
conv_sym,
bravais->lattice,
symprec);
wyckoffs[i] = get_Wyckoff_notation(positions->vec[i],
conv_sym,
bravais->lattice,
hall_number,
symprec);
equiv_atoms[i] = i;
escape:
;
}
free(indep_atoms);
indep_atoms = NULL;
for (i = 0; i < bravais->size; i++) {
if (wyckoffs[i] == -1) {
mat_free_VecDBL(positions);
positions = NULL;
break;
}
}
return positions;
}
/* Return -1 if failed */
static int get_Wyckoff_notation(double position[3],
SPGCONST Symmetry * conv_sym,
SPGCONST double bravais_lattice[3][3],
const int hall_number,
const double symprec)
{
int i, j, k, l, at_orbit, num_sitesym, wyckoff_letter;
int indices_wyc[2];
int rot[3][3];
double trans[3], orbit[3];
VecDBL *pos_rot;
debug_print("get_Wyckoff_notation\n");
wyckoff_letter = -1;
pos_rot = NULL;
if ((pos_rot = mat_alloc_VecDBL(conv_sym->size)) == NULL) {
return -1;
}
for (i = 0; i < conv_sym->size; i++) {
mat_multiply_matrix_vector_id3(pos_rot->vec[i], conv_sym->rot[i], position);
for (j = 0; j < 3; j++) {
pos_rot->vec[i][j] += conv_sym->trans[i][j];
}
}
ssmdb_get_wyckoff_indices(indices_wyc, hall_number);
for (i = 0; i < indices_wyc[1]; i++) {
num_sitesym = ssmdb_get_coordinate(rot, trans, i + indices_wyc[0]);
for (j = 0; j < pos_rot->size; j++) {
at_orbit = 0;
for (k = 0; k < pos_rot->size; k++) {
if (cel_is_overlap(pos_rot->vec[j],
pos_rot->vec[k],
bravais_lattice,
symprec)) {
mat_multiply_matrix_vector_id3(orbit, rot, pos_rot->vec[k]);
for (l = 0; l < 3; l++) {
orbit[l] += trans[l];
}
if (cel_is_overlap(pos_rot->vec[k],
orbit,
bravais_lattice,
symprec)) {
at_orbit++;
}
}
}
if (at_orbit == conv_sym->size / num_sitesym) {
/* Database is made reversed order, e.g., gfedcba. */
/* wyckoff is set 0 1 2 3 4... for a b c d e..., respectively. */
wyckoff_letter = indices_wyc[1] - i - 1;
goto end;
}
}
}
end:
mat_free_VecDBL(pos_rot);
return wyckoff_letter;
}
/* Return if failed */
VecDBL * ssm_get_exact_positions(int *wyckoffs,
int *equiv_atoms,
const Cell * conv_prim,
const Symmetry * conv_sym,
const int hall_number,
const double symprec)
{
int attempt, num_atoms;
double tolerance;
VecDBL *positions;
positions = NULL;
if ((positions = mat_alloc_VecDBL(conv_prim->size)) == NULL) {
return NULL;
}
tolerance = symprec;
for (attempt = 0; attempt < NUM_ATTEMPT; attempt++) {
num_atoms = get_exact_positions(positions,
equiv_atoms,
conv_prim,
conv_sym,
tolerance);
if (num_atoms == conv_prim->size) {
goto succeeded;
}
if (num_atoms > conv_prim->size || num_atoms == 0) {
tolerance *= INCREASE_RATE;
warning_print("spglib: Some site-symmetry is found broken. ");
warning_print("(%d != %d)\n", num_atoms, conv_prim->size);
warning_print(" Increase tolerance to %f", tolerance);
warning_print(" (%d)", attempt);
warning_print(" (line %d, %s).\n", __LINE__, __FILE__);
}
if (num_atoms < conv_prim->size && num_atoms) {
tolerance *= REDUCE_RATE;
warning_print("spglib: Some site-symmetry is found broken. ");
warning_print("(%d != %d)\n", num_atoms, conv_prim->size);
warning_print(" Reduce tolerance to %f", tolerance);
warning_print(" (%d)", attempt);
warning_print(" (line %d, %s).\n", __LINE__, __FILE__);
}
}
mat_free_VecDBL(positions);
positions = NULL;
return NULL;
succeeded:
if (! set_Wyckoffs_labels(wyckoffs,
positions,
equiv_atoms,
conv_prim,
conv_sym,
hall_number,
symprec)) {
mat_free_VecDBL(positions);
positions = NULL;
}
return positions;
}
/* Return NULL if failed */
static Symmetry *
get_space_group_operations(SPGCONST PointSymmetry *lattice_sym,
SPGCONST Cell *primitive,
const double symprec)
{
int i, j, num_sym, total_num_sym;
VecDBL **trans;
Symmetry *symmetry;
debug_print("get_space_group_operations (tolerance = %f):\n", symprec);
trans = NULL;
symmetry = NULL;
if ((trans = (VecDBL**) malloc(sizeof(VecDBL*) * lattice_sym->size))
== NULL) {
warning_print("spglib: Memory could not be allocated ");
return NULL;
}
for (i = 0; i < lattice_sym->size; i++) {
trans[i] = NULL;
}
total_num_sym = 0;
for (i = 0; i < lattice_sym->size; i++) {
if ((trans[i] = get_translation(lattice_sym->rot[i], primitive, symprec, 0))
!= NULL) {
debug_print(" match translation %d/%d; tolerance = %f\n",
i + 1, lattice_sym->size, symprec);
total_num_sym += trans[i]->size;
}
}
if ((symmetry = sym_alloc_symmetry(total_num_sym)) == NULL) {
goto ret;
}
num_sym = 0;
for (i = 0; i < lattice_sym->size; i++) {
if (trans[i] == NULL) {
continue;
}
for (j = 0; j < trans[i]->size; j++) {
mat_copy_vector_d3(symmetry->trans[num_sym + j], trans[i]->vec[j]);
mat_copy_matrix_i3(symmetry->rot[num_sym + j], lattice_sym->rot[i]);
}
num_sym += trans[i]->size;
}
ret:
for (i = 0; i < lattice_sym->size; i++) {
if (trans[i] != NULL) {
mat_free_VecDBL(trans[i]);
trans[i] = NULL;
}
}
free(trans);
trans = NULL;
return symmetry;
}
/* Return NULL if failed */
static Cell * trim_cell(int * mapping_table,
SPGCONST double trimmed_lattice[3][3],
const Cell * cell,
const double symprec)
{
int i, index_atom, ratio;
Cell *trimmed_cell;
VecDBL * position;
int *overlap_table;
position = NULL;
overlap_table = NULL;
trimmed_cell = NULL;
ratio = abs(mat_Nint(mat_get_determinant_d3(cell->lattice) /
mat_get_determinant_d3(trimmed_lattice)));
/* Check if cell->size is dividable by ratio */
if ((cell->size / ratio) * ratio != cell->size) {
return NULL;
}
if ((trimmed_cell = cel_alloc_cell(cell->size / ratio)) == NULL) {
return NULL;
}
if ((position = translate_atoms_in_trimmed_lattice(cell,
trimmed_lattice))
== NULL) {
cel_free_cell(trimmed_cell);
trimmed_cell = NULL;
goto err;
}
mat_copy_matrix_d3(trimmed_cell->lattice, trimmed_lattice);
if ((overlap_table = get_overlap_table(position,
cell->size,
cell->types,
trimmed_cell,
symprec)) == NULL) {
mat_free_VecDBL(position);
position = NULL;
cel_free_cell(trimmed_cell);
trimmed_cell = NULL;
goto err;
}
index_atom = 0;
for (i = 0; i < cell->size; i++) {
if (overlap_table[i] == i) {
mapping_table[i] = index_atom;
trimmed_cell->types[index_atom] = cell->types[i];
index_atom++;
} else {
mapping_table[i] = mapping_table[overlap_table[i]];
}
}
set_positions(trimmed_cell,
position,
mapping_table,
overlap_table);
mat_free_VecDBL(position);
position = NULL;
free(overlap_table);
return trimmed_cell;
err:
return NULL;
}
/* Return 0 if failed */
static int get_primitive_lattice_vectors_iterative(double prim_lattice[3][3],
SPGCONST Cell * cell,
const VecDBL * pure_trans,
const double symprec)
{
int i, multi, attempt;
double tolerance;
VecDBL * vectors, * pure_trans_reduced, *tmp_vec;
vectors = NULL;
pure_trans_reduced = NULL;
tmp_vec = NULL;
tolerance = symprec;
if ((pure_trans_reduced = mat_alloc_VecDBL(pure_trans->size)) == NULL) {
goto fail;
}
for (i = 0; i < pure_trans->size; i++) {
mat_copy_vector_d3(pure_trans_reduced->vec[i], pure_trans->vec[i]);
}
for (attempt = 0; attempt < 100; attempt++) {
multi = pure_trans_reduced->size;
if ((vectors = get_translation_candidates(pure_trans_reduced)) == NULL) {
mat_free_VecDBL(pure_trans_reduced);
goto fail;
}
/* Lattice of primitive cell is found among pure translation vectors */
if (get_primitive_lattice_vectors(prim_lattice,
vectors,
cell,
tolerance)) {
mat_free_VecDBL(vectors);
mat_free_VecDBL(pure_trans_reduced);
goto found;
} else {
if ((tmp_vec = mat_alloc_VecDBL(multi)) == NULL) {
mat_free_VecDBL(vectors);
mat_free_VecDBL(pure_trans_reduced);
goto fail;
}
for (i = 0; i < multi; i++) {
mat_copy_vector_d3(tmp_vec->vec[i], pure_trans_reduced->vec[i]);
}
mat_free_VecDBL(pure_trans_reduced);
pure_trans_reduced = sym_reduce_pure_translation(cell,
tmp_vec,
tolerance);
mat_free_VecDBL(tmp_vec);
mat_free_VecDBL(vectors);
if (pure_trans_reduced == NULL) {
goto fail;
}
warning_print("Tolerance is reduced to %f (%d), size = %d\n",
tolerance, attempt, pure_trans_reduced->size);
tolerance *= REDUCE_RATE;
}
}
mat_free_VecDBL(pure_trans_reduced);
fail:
return 0;
found:
return multi;
}
/* Return NULL if failed */
static Cell *
get_bravais_exact_positions_and_lattice(int * wyckoffs,
int * equiv_atoms,
SPGCONST Spacegroup *spacegroup,
SPGCONST Cell * primitive,
const double symprec)
{
int i;
int *wyckoffs_prim, *equiv_atoms_prim;
Symmetry *conv_sym;
Cell *bravais, *conv_prim;
VecDBL *exact_positions;
debug_print("get_bravais_exact_positions_and_lattice\n");
wyckoffs_prim = NULL;
equiv_atoms_prim = NULL;
conv_prim = NULL;
bravais = NULL;
conv_sym = NULL;
exact_positions = NULL;
/* Symmetrize atomic positions of conventional unit cell */
if ((wyckoffs_prim = (int*)malloc(sizeof(int) * primitive->size)) == NULL) {
warning_print("spglib: Memory could not be allocated ");
return NULL;
}
if ((equiv_atoms_prim = (int*)malloc(sizeof(int) * primitive->size)) == NULL) {
warning_print("spglib: Memory could not be allocated ");
free(wyckoffs_prim);
wyckoffs_prim = NULL;
return NULL;
}
for (i = 0; i < primitive->size; i++) {
wyckoffs_prim[i] = -1;
equiv_atoms_prim[i] = -1;
}
/* Positions of primitive atoms are represented wrt Bravais lattice */
if ((conv_prim = get_conventional_primitive(spacegroup, primitive)) == NULL) {
free(wyckoffs_prim);
wyckoffs_prim = NULL;
free(equiv_atoms_prim);
equiv_atoms_prim = NULL;
return NULL;
}
/* Symmetries in database (wrt Bravais lattice) */
if ((conv_sym = spgdb_get_spacegroup_operations(spacegroup->hall_number))
== NULL) {
goto err;
}
/* Lattice vectors are set. */
get_conventional_lattice(conv_prim->lattice, spacegroup);
if ((exact_positions = ssm_get_exact_positions(wyckoffs_prim,
equiv_atoms_prim,
conv_prim,
conv_sym,
spacegroup->hall_number,
symprec)) == NULL) {
sym_free_symmetry(conv_sym);
conv_sym = NULL;
goto err;
}
for (i = 0; i < conv_prim->size; i++) {
mat_copy_vector_d3(conv_prim->position[i], exact_positions->vec[i]);
}
bravais = expand_positions(wyckoffs,
equiv_atoms,
conv_prim,
conv_sym,
wyckoffs_prim,
equiv_atoms_prim);
mat_free_VecDBL(exact_positions);
exact_positions = NULL;
sym_free_symmetry(conv_sym);
conv_sym = NULL;
err:
free(wyckoffs_prim);
wyckoffs_prim = NULL;
free(equiv_atoms_prim);
equiv_atoms_prim = NULL;
cel_free_cell(conv_prim);
conv_prim = NULL;
return bravais;
}
