static PointSymmetry get_lattice_symmetry( SPGCONST Cell *cell,
const double symprec )
{
int i, j, k, num_sym;
int axes[3][3];
double lattice[3][3], min_lattice[3][3];
double metric[3][3], cell_metric[3][3];
PointSymmetry lattice_sym;
if ( ! lat_smallest_lattice_vector( min_lattice,
cell->lattice,
symprec ) ) {
goto err;
}
mat_get_metric( cell_metric, min_lattice );
num_sym = 0;
for ( i = 0; i < 26; i++ ) {
for ( j = 0; j < 26; j++ ) {
for ( k = 0; k < 26; k++ ) {
set_axes( axes, i, j, k );
if ( ! ( ( mat_get_determinant_i3( axes ) == 1 ) ||
( mat_get_determinant_i3( axes ) == -1 ) ) ) {
continue;
}
mat_multiply_matrix_di3( lattice, min_lattice, axes );
mat_get_metric( metric, lattice );
if ( mat_check_identity_matrix_d3( metric,
cell_metric,
symprec ) ) {
mat_copy_matrix_i3( lattice_sym.rot[num_sym], axes );
num_sym++;
}
if ( num_sym > 48 ) {
warning_print("spglib: Too many lattice symmetries was found.\n");
warning_print(" Tolerance may be too large ");
warning_print("(line %d, %s).\n", __LINE__, __FILE__);
goto err;
}
}
}
}
lattice_sym.size = num_sym;
return transform_pointsymmetry( &lattice_sym,
cell->lattice,
min_lattice );
err:
lattice_sym.size = 0;
return lattice_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 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;
}
/* Return NULL if failed */
static Symmetry *
get_symmetry_in_original_cell(SPGCONST int t_mat[3][3],
SPGCONST double inv_tmat[3][3],
SPGCONST double lattice[3][3],
SPGCONST Symmetry *prim_sym,
const double symprec)
{
int i, size_sym_orig;
double tmp_rot_d[3][3], tmp_lat_d[3][3], tmp_lat_i[3][3], tmp_mat[3][3];
int tmp_rot_i[3][3];
Symmetry *t_sym, *t_red_sym;
t_sym = NULL;
t_red_sym = NULL;
if ((t_sym = sym_alloc_symmetry(prim_sym->size)) == NULL) {
return NULL;
}
/* transform symmetry operations of primitive cell to those of original */
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);
/* In spglib, symmetry of supercell is defined by the set of symmetry */
/* operations that are searched among supercell lattice point group */
/* operations. The supercell lattice may be made by breaking the */
/* unit cell lattice symmetry. In this case, a part of symmetry */
/* operations is discarded. */
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++;
}
}
/* Broken symmetry due to supercell multiplicity */
if (size_sym_orig != prim_sym->size) {
if ((t_red_sym = sym_alloc_symmetry(size_sym_orig)) == NULL) {
sym_free_symmetry(t_sym);
t_sym = NULL;
return NULL;
}
for (i = 0; i < size_sym_orig; i++) {
mat_copy_matrix_i3(t_red_sym->rot[i], t_sym->rot[i]);
mat_copy_vector_d3(t_red_sym->trans[i], t_sym->trans[i]);
}
sym_free_symmetry(t_sym);
t_sym = NULL;
t_sym = t_red_sym;
t_red_sym = NULL;
}
return t_sym;
}
