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=-1;
int indices_wyc[2];
int rot[3][3];
double trans[3], orbit[3];
VecDBL *pos_rot;
pos_rot = mat_alloc_VecDBL(conv_sym->size);
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;
}
/* Acta Cryst. (2002). A58, 60-65 */
static void get_exact_location(double position[3],
SPGCONST Symmetry * conv_sym,
SPGCONST double bravais_lattice[3][3],
const double symprec)
{
int i, j, k, num_sum;
double sum_rot[3][3];
double pos[3], sum_trans[3];
debug_print("get_exact_location\n");
num_sum = 0;
for (i = 0; i < 3; i++) {
sum_trans[i] = 0.0;
for (j = 0; j < 3; j++) {
sum_rot[i][j] = 0;
}
}
for (i = 0; i < conv_sym->size; i++) {
mat_multiply_matrix_vector_id3(pos,
conv_sym->rot[i],
position);
for (j = 0; j < 3; j++) {
pos[j] += conv_sym->trans[i][j];
}
if (cel_is_overlap(pos,
position,
bravais_lattice,
symprec)) {
for (j = 0; j < 3; j++) {
sum_trans[j] += conv_sym->trans[i][j] -
mat_Nint(pos[j] - position[j]);
for (k = 0; k < 3; k++) {
sum_rot[j][k] += conv_sym->rot[i][j][k];
}
}
num_sum++;
}
}
for (i = 0; i < 3; i++) {
sum_trans[i] /= num_sum;
for (j = 0; j < 3; j++) {
sum_rot[i][j] /= num_sum;
}
}
/* (sum_rot|sum_trans) is the special-position operator. */
/* Elements of sum_rot can be fractional values. */
mat_multiply_matrix_vector_d3(position,
sum_rot,
position);
for (i = 0; i < 3; i++) {
position[i] += sum_trans[i];
}
}
static VecDBL * reduce_lattice_points(SPGCONST double lattice[3][3],
const VecDBL *lattice_trans,
const double symprec)
{
int i, j, is_found, num_pure_trans;
VecDBL *pure_trans, *t;
num_pure_trans = 0;
t = mat_alloc_VecDBL(lattice_trans->size);
for (i = 0; i < lattice_trans->size; i++) {
is_found = 0;
for (j = 0; j < num_pure_trans; 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_pure_trans], lattice_trans->vec[i]);
num_pure_trans++;
}
}
pure_trans = mat_alloc_VecDBL(num_pure_trans);
for (i = 0; i < num_pure_trans; i++) {
mat_copy_vector_d3(pure_trans->vec[i], t->vec[i]);
}
mat_free_VecDBL(t);
return pure_trans;
}
/* Return 0 if failed */
static int get_overlap_table(int **overlap_table,
SPGCONST Cell *primitive_cell,
const VecDBL * position,
const int *types,
const double symprec)
{
int i, j, attempt, num_overlap, ratio, cell_size;
double trim_tolerance;
cell_size = position->size;
ratio = cell_size / primitive_cell->size;
trim_tolerance = symprec;
for (attempt = 0; attempt < 100; attempt++) {
/* Each value of -1 has to be overwritten by 0 or positive numbers. */
for (i = 0; i < cell_size; i++) {
for (j = 0; j < cell_size; j++) {
overlap_table[i][j] = -1;
}
}
for (i = 0; i < cell_size; i++) {
num_overlap = 0;
for (j = 0; j < cell_size; j++) {
if (types[i] == types[j]) {
if (cel_is_overlap(position->vec[i],
position->vec[j],
primitive_cell->lattice,
trim_tolerance)) {
overlap_table[i][num_overlap] = j;
num_overlap++;
}
}
}
}
if (check_overlap_table(overlap_table, cell_size, ratio)) {
goto found;
}
if (num_overlap < ratio) {
trim_tolerance *= INCREASE_RATE;
warning_print("spglib: Increase tolerance to %f ", trim_tolerance);
} else {
trim_tolerance *= REDUCE_RATE;
warning_print("spglib: Reduce tolerance to %f ", trim_tolerance);
}
warning_print("(line %d, %s).\n", __LINE__, __FILE__);
}
warning_print("spglib: Could not trim cell into primitive ");
warning_print("(line %d, %s).\n", __LINE__, __FILE__);
return 0;
found:
return 1;
}
/* Return 0 if failed */
static int set_equivalent_atoms(int * equiv_atoms,
SPGCONST Symmetry *symmetry,
SPGCONST Cell * cell,
const double symprec)
{
int i, j, k, is_found;
double pos[3];
int *mapping_table;
mapping_table = NULL;
if ((mapping_table = get_mapping_table(symmetry, cell, symprec)) == NULL) {
return 0;
}
for (i = 0; i < cell->size; i++) {
if (mapping_table[i] != i) {
continue;
}
is_found = 0;
for (j = 0; j < symmetry->size; j++) {
mat_multiply_matrix_vector_id3(pos,
symmetry->rot[j],
cell->position[i]);
for (k = 0; k < 3; k++) {
pos[k] += symmetry->trans[j][k];
}
for (k = 0; k < cell->size; k++) {
if (cel_is_overlap(pos, cell->position[k], cell->lattice, symprec)) {
if (mapping_table[k] < i) {
equiv_atoms[i] = equiv_atoms[mapping_table[k]];
is_found = 1;
break;
}
}
}
if (is_found) {
break;
}
}
if (!is_found) {
equiv_atoms[i] = i;
}
}
for (i = 0; i < cell->size; i++) {
if (mapping_table[i] == i) {
continue;
}
equiv_atoms[i] = equiv_atoms[mapping_table[i]];
}
free(mapping_table);
mapping_table = NULL;
return 1;
}
int cel_is_overlap_with_same_type(const double a[3],
const double b[3],
const int type_a,
const int type_b,
SPGCONST double lattice[3][3],
const double symprec)
{
if (type_a == type_b) {
return cel_is_overlap(a, b, lattice, symprec);
} else {
return 0;
}
}
/* 0: No overlap of atoms was found. */
int cel_any_overlap(const Cell * cell,
const double symprec) {
int i, j;
for (i = 0; i < cell->size; i++) {
for (j = i + 1; j < cell->size; j++) {
if (cel_is_overlap(cell->position[i],
cell->position[j],
cell->lattice,
symprec)) {
return 1;
}
}
}
return 0;
}
/* Return NULL if failed */
static int * get_mapping_table(SPGCONST Symmetry *symmetry,
SPGCONST Cell * cell,
const double symprec)
{
int i, j, k, is_found;
double pos[3];
int *mapping_table;
SPGCONST int I[3][3] = {{ 1, 0, 0},
{ 0, 1, 0},
{ 0, 0, 1}};
mapping_table = NULL;
if ((mapping_table = (int*) malloc(sizeof(int) * cell->size)) == NULL) {
warning_print("spglib: Memory could not be allocated.");
return NULL;
}
for (i = 0; i < cell->size; i++) {
is_found = 0;
for (j = 0; j < symmetry->size; j++) {
if (mat_check_identity_matrix_i3(symmetry->rot[j], I)) {
for (k = 0; k < 3; k++) {
pos[k] = cell->position[i][k] + symmetry->trans[j][k];
}
for (k = 0; k < cell->size; k++) {
if (cel_is_overlap(pos, cell->position[k], cell->lattice, symprec)) {
if (k < i) {
mapping_table[i] = mapping_table[k];
is_found = 1;
break;
}
}
}
}
if (is_found) {
break;
}
}
if (!is_found) {
mapping_table[i] = i;
}
}
return mapping_table;
}
static int search_equivalent_atom(const int atom_index,
SPGCONST Cell * cell,
const Symmetry *symmetry,
const double symprec)
{
int i, j;
double pos_rot[3];
for (i = 0; i < symmetry->size; i++) {
mat_multiply_matrix_vector_id3(pos_rot,
symmetry->rot[i],
cell->position[atom_index]);
for (j = 0; j < 3; j++) {
pos_rot[j] += symmetry->trans[i][j];
}
for (j = 0; j < atom_index; j++) {
if (cel_is_overlap(cell->position[j], pos_rot, cell->lattice, symprec)) {
return j;
}
}
}
return atom_index;
}
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_symmetrized_positions\n");
indep_atoms = (int*) malloc(sizeof(int) * bravais->size);
positions = mat_alloc_VecDBL(bravais->size);
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++) {
pos[l] -= mat_Nint(pos[l]);
}
mat_copy_vector_d3(positions->vec[i], pos);
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;
return positions;
}
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 int * get_overlap_table(const VecDBL * position,
const int cell_size,
const int * cell_types,
const Cell * trimmed_cell,
const double symprec)
{
int i, j, attempt, num_overlap, ratio;
double trim_tolerance;
int *overlap_table;
trim_tolerance = symprec;
ratio = cell_size / trimmed_cell->size;
if ((overlap_table = (int*)malloc(sizeof(int) * cell_size)) == NULL) {
return NULL;
}
for (attempt = 0; attempt < NUM_ATTEMPT; attempt++) {
for (i = 0; i < cell_size; i++) {
overlap_table[i] = i;
for (j = 0; j < cell_size; j++) {
if (cell_types[i] == cell_types[j]) {
if (cel_is_overlap(position->vec[i],
position->vec[j],
trimmed_cell->lattice,
trim_tolerance)) {
if (overlap_table[j] == j) {
overlap_table[i] = j;
break;
}
}
}
}
}
for (i = 0; i < cell_size; i++) {
if (overlap_table[i] != i) {
continue;
}
num_overlap = 0;
for (j = 0; j < cell_size; j++) {
if (i == overlap_table[j]) {
num_overlap++;
}
}
if (num_overlap == ratio) {
continue;
}
if (num_overlap < ratio) {
trim_tolerance *= INCREASE_RATE;
warning_print("spglib: Increase tolerance to %f ", trim_tolerance);
warning_print("(line %d, %s).\n", __LINE__, __FILE__);
goto cont;
}
if (num_overlap > ratio) {
trim_tolerance *= REDUCE_RATE;
warning_print("spglib: Reduce tolerance to %f ", trim_tolerance);
warning_print("(%d) ", attempt);
warning_print("(line %d, %s).\n", __LINE__, __FILE__);
goto cont;
}
}
goto found;
cont:
;
}
warning_print("spglib: Could not trim cell well ");
warning_print("(line %d, %s).\n", __LINE__, __FILE__);
free(overlap_table);
overlap_table = NULL;
found:
return overlap_table;
}
static int get_overlap_table( int **overlap_table,
const int cell_size,
SPGCONST Cell *primitive,
const VecDBL * position,
const double symprec )
{
int i, j, is_found, attempt, count, ratio;
int count_error=0, old_count_error=0;
double trim_tolerance, tol_adjust;
ratio = cell_size / primitive->size;
trim_tolerance = symprec;
tol_adjust = trim_tolerance/2.0;
is_found = 0;
/* Break when is_found */
for ( attempt = 0; attempt < 1000; attempt++ ) {
is_found = 1;
debug_print("Trim attempt %d: tolerance=%f\n",attempt+1,trim_tolerance);
/* Each value of -1 has to be overwritten by 0 or positive numbers. */
for (i = 0; i < cell_size; i++) {
for (j = 0; j < cell_size; j++) {
overlap_table[i][j] = -1;
}
}
for (i = 0; i < cell_size; i++) {
count = 0;
for (j = 0; j < cell_size; j++) {
if ( cel_is_overlap( position->vec[i], position->vec[j],
primitive->lattice, trim_tolerance ) ) {
overlap_table[i][count] = j;
count++;
}
}
/* Adjust tolerance to avoid too much and too few overlaps */
if (count != ratio) { /* check overlapping number */
count_error = count - ratio;
/* Initialize count error if needed: */
if (old_count_error == 0) {
old_count_error = count - ratio;
}
/* Adjust the tolerance adjustment if needed */
if ( ( old_count_error > 0 && count_error < 0 ) ||
( old_count_error < 0 && count_error > 0 ) ||
trim_tolerance - tol_adjust <= 0 ) {
tol_adjust /= 2.0;
}
old_count_error = count_error;
debug_print("Bad tolerance: count=%d ratio=%d tol_adjust=%f\n",
count,ratio,tol_adjust);
if ( count_error > 0 ) { trim_tolerance -= tol_adjust; }
else { trim_tolerance += tol_adjust; }
is_found = 0;
break;
}
}
if ( is_found ) { break; }
}
if ( ! is_found ) {
warning_print("spglib: Could not trim cell into primitive ");
warning_print("(line %d, %s).\n", __LINE__, __FILE__);
goto err;
}
return 1;
err:
return 0;
}
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;
}
/* Acta Cryst. (2002). A58, 60-65 */
static int set_exact_location(double position[3],
const Symmetry * conv_sym,
SPGCONST double bravais_lattice[3][3],
const double symprec)
{
int i, j, k, num_sum, multi, num_pure_trans;
double sum_rot[3][3];
double pos[3], sum_trans[3];
debug_print("get_exact_location\n");
num_sum = 0;
for (i = 0; i < 3; i++) {
sum_trans[i] = 0.0;
for (j = 0; j < 3; j++) {
sum_rot[i][j] = 0;
}
}
num_pure_trans = 0;
for (i = 0; i < conv_sym->size; i++) {
if (mat_check_identity_matrix_i3(identity, conv_sym->rot[i])) {
num_pure_trans++;
for (j = 0; j < 3; j++) {
pos[j] = position[j];
}
} else {
mat_multiply_matrix_vector_id3(pos,
conv_sym->rot[i],
position);
}
for (j = 0; j < 3; j++) {
pos[j] += conv_sym->trans[i][j];
}
if (cel_is_overlap(pos,
position,
bravais_lattice,
symprec)) {
for (j = 0; j < 3; j++) {
for (k = 0; k < 3; k++) {
sum_rot[j][k] += conv_sym->rot[i][j][k];
}
sum_trans[j] +=
conv_sym->trans[i][j] - mat_Nint(pos[j] - position[j]);
}
num_sum++;
}
}
for (i = 0; i < 3; i++) {
sum_trans[i] /= num_sum;
for (j = 0; j < 3; j++) {
sum_rot[i][j] /= num_sum;
}
}
/* (sum_rot|sum_trans) is the special-position operator. */
/* Elements of sum_rot can be fractional values. */
mat_multiply_matrix_vector_d3(position,
sum_rot,
position);
for (i = 0; i < 3; i++) {
position[i] += sum_trans[i];
}
multi = conv_sym->size / num_pure_trans / num_sum;
if (multi * num_sum * num_pure_trans == conv_sym->size) {
return multi;
} else {
return 0;
}
}
