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], metric_orig[3][3];
PointSymmetry lattice_sym;
debug_print("get_lattice_symmetry:\n");
if (! lat_smallest_lattice_vector(min_lattice,
cell->lattice,
symprec)) {
goto err;
}
mat_get_metric(metric_orig, 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 (is_identity_metric(metric, metric_orig, 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 * 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;
}
static PointSymmetry get_lattice_symmetry(SPGCONST double cell_lattice[3][3],
const double symprec,
const double angle_symprec)
{
int i, j, k, attempt, num_sym;
double angle_tol;
int axes[3][3];
double lattice[3][3], min_lattice[3][3];
double metric[3][3], metric_orig[3][3];
PointSymmetry lattice_sym;
debug_print("get_lattice_symmetry:\n");
lattice_sym.size = 0;
if (! del_delaunay_reduce(min_lattice, cell_lattice, symprec)) {
goto err;
}
mat_get_metric(metric_orig, min_lattice);
angle_tol = angle_symprec;
for (attempt = 0; attempt < 100; attempt++) {
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 (is_identity_metric(metric, metric_orig, symprec, angle_tol)) {
if (num_sym > 47) {
angle_tol *= ANGLE_REDUCE_RATE;
warning_print("spglib: Too many lattice symmetries was found.\n");
warning_print(" Reduce angle tolerance to %f", angle_tol);
warning_print(" (line %d, %s).\n", __LINE__, __FILE__);
goto next_attempt;
}
mat_copy_matrix_i3(lattice_sym.rot[num_sym], axes);
num_sym++;
}
}
}
}
if (num_sym < 49 || angle_tol < 0) {
lattice_sym.size = num_sym;
return transform_pointsymmetry(&lattice_sym, cell_lattice, min_lattice);
}
next_attempt:
;
}
err:
debug_print("get_lattice_symmetry failed.\n");
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;
}
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 *
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;
}
/* Return 0 if failed */
static int search_hall_number(double origin_shift[3],
double conv_lattice[3][3],
const int candidates[],
const int num_candidates,
SPGCONST double primitive_lattice[3][3],
SPGCONST Symmetry * symmetry,
const double symprec)
{
int i, hall_number;
Centering centering;
Pointgroup pointgroup;
Symmetry * conv_symmetry;
int int_transform_mat[3][3];
double correction_mat[3][3], transform_mat[3][3];
debug_print("search_hall_number:\n");
hall_number = 0;
conv_symmetry = NULL;
pointgroup = ptg_get_transformation_matrix(int_transform_mat,
symmetry->rot,
symmetry->size);
if (pointgroup.number == 0) {
goto err;
}
mat_multiply_matrix_di3(conv_lattice, primitive_lattice, int_transform_mat);
if (pointgroup.laue == LAUE1) {
if (! change_basis_tricli(int_transform_mat,
conv_lattice,
primitive_lattice,
symprec)) {
goto err;
}
}
if (pointgroup.laue == LAUE2M) {
if (! change_basis_monocli(int_transform_mat,
conv_lattice,
primitive_lattice,
symprec)) {
goto err;
}
}
if ((centering = get_centering(correction_mat,
int_transform_mat,
pointgroup.laue)) == CENTERING_ERROR) {
goto err;
}
mat_multiply_matrix_id3(transform_mat, int_transform_mat, correction_mat);
mat_multiply_matrix_d3(conv_lattice, primitive_lattice, transform_mat);
if ((conv_symmetry = get_initial_conventional_symmetry(centering,
transform_mat,
symmetry)) == NULL) {
goto err;
}
for (i = 0; i < num_candidates; i++) {
if (match_hall_symbol_db(origin_shift,
conv_lattice, /* <-- modified only matched */
candidates[i],
pointgroup.number,
pointgroup.holohedry,
centering,
conv_symmetry,
symprec)) {
hall_number = candidates[i];
break;
}
}
sym_free_symmetry(conv_symmetry);
conv_symmetry = NULL;
return hall_number;
err:
return 0;
}
