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 Symmetry *
recover_symmetry_in_original_cell(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)
{
Symmetry *symmetry, *t_sym;
double inv_tmat[3][3], tmp_mat[3][3];
VecDBL *pure_trans, *lattice_trans;
symmetry = NULL;
t_sym = NULL;
pure_trans = NULL;
lattice_trans = NULL;
mat_cast_matrix_3i_to_3d(tmp_mat, t_mat);
mat_inverse_matrix_d3(inv_tmat, tmp_mat, 0);
if ((lattice_trans = get_lattice_translations(frame, inv_tmat)) == NULL) {
return NULL;
}
if ((pure_trans = remove_overlapping_lattice_points(lattice,
lattice_trans,
symprec)) == NULL) {
mat_free_VecDBL(lattice_trans);
lattice_trans = NULL;
return NULL;
}
if ((t_sym = get_symmetry_in_original_cell(t_mat,
inv_tmat,
lattice,
prim_sym,
symprec)) == NULL) {
mat_free_VecDBL(pure_trans);
pure_trans = NULL;
mat_free_VecDBL(lattice_trans);
lattice_trans = NULL;
return NULL;
}
if (pure_trans->size == multiplicity) {
symmetry = copy_symmetry_upon_lattice_points(pure_trans, t_sym);
}
mat_free_VecDBL(lattice_trans);
lattice_trans = NULL;
mat_free_VecDBL(pure_trans);
pure_trans = NULL;
sym_free_symmetry(t_sym);
t_sym = NULL;
return symmetry;
}
static Symmetry * recover_operations_original(SPGCONST Symmetry *symmetry,
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];
Symmetry *symmetry_orig, *sym_tmp;
debug_print("recover_operations_original:\n");
multi = pure_trans->size;
sym_tmp = sym_alloc_symmetry(symmetry->size);
symmetry_orig = sym_alloc_symmetry(symmetry->size * multi);
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 < symmetry->size; i++) {
mat_copy_matrix_i3(sym_tmp->rot[i], symmetry->rot[i]);
mat_copy_vector_d3(sym_tmp->trans[i], symmetry->trans[i]);
}
for(i = 0; i < symmetry->size; i++) {
mat_cast_matrix_3i_to_3d(drot, sym_tmp->rot[i]);
mat_get_similar_matrix_d3(drot, drot, trans_mat, 0);
mat_cast_matrix_3d_to_3i(sym_tmp->rot[i], drot);
mat_multiply_matrix_vector_d3(sym_tmp->trans[i],
trans_mat_inv,
sym_tmp->trans[i]);
}
for(i = 0; i < symmetry->size; i++) {
for(j = 0; j < multi; j++) {
mat_copy_matrix_i3(symmetry_orig->rot[i * multi + j], sym_tmp->rot[i]);
for (k = 0; k < 3; k++) {
symmetry_orig->trans[i * multi + j][k] =
sym_tmp->trans[i][k] + pure_trans->vec[j][k];
}
}
}
sym_free_symmetry(sym_tmp);
return symmetry_orig;
}
static PointSymmetry
transform_pointsymmetry(SPGCONST PointSymmetry * lat_sym_orig,
SPGCONST double new_lattice[3][3],
SPGCONST double original_lattice[3][3])
{
int i, size;
double trans_mat[3][3], inv_mat[3][3], drot[3][3];
PointSymmetry lat_sym_new;
lat_sym_new.size = 0;
mat_inverse_matrix_d3(inv_mat, original_lattice, 0);
mat_multiply_matrix_d3(trans_mat, inv_mat, new_lattice);
size = 0;
for (i = 0; i < lat_sym_orig->size; i++) {
mat_cast_matrix_3i_to_3d(drot, lat_sym_orig->rot[i]);
mat_get_similar_matrix_d3(drot, drot, trans_mat, 0);
/* new_lattice may have lower point symmetry than original_lattice.*/
/* The operations that have non-integer elements are not counted. */
if (mat_is_int_matrix(drot, mat_Dabs(mat_get_determinant_d3(trans_mat)) / 10)) {
mat_cast_matrix_3d_to_3i(lat_sym_new.rot[size], drot);
if (abs(mat_get_determinant_i3(lat_sym_new.rot[size])) != 1) {
warning_print("spglib: A point symmetry operation is not unimodular.");
warning_print("(line %d, %s).\n", __LINE__, __FILE__);
goto err;
}
size++;
}
}
#ifdef SPGWARNING
if (! (lat_sym_orig->size == size)) {
warning_print("spglib: Some of point symmetry operations were dropped.");
warning_print("(line %d, %s).\n", __LINE__, __FILE__);
}
#endif
lat_sym_new.size = size;
return lat_sym_new;
err:
return lat_sym_new;
}
static Symmetry * get_conventional_symmetry(SPGCONST double transform_mat[3][3],
const Centering centering,
const Symmetry *primitive_sym)
{
int i, j, k, multi, size;
double tmp_trans;
double tmp_matrix_d3[3][3], shift[4][3];
double symmetry_rot_d3[3][3], primitive_sym_rot_d3[3][3];
Symmetry *symmetry;
size = primitive_sym->size;
if (centering == FACE) {
symmetry = sym_alloc_symmetry(size * 4);
}
else {
if (centering) {
symmetry = sym_alloc_symmetry(size * 2);
} else {
symmetry = sym_alloc_symmetry(size);
}
}
for (i = 0; i < size; i++) {
mat_cast_matrix_3i_to_3d(primitive_sym_rot_d3, primitive_sym->rot[i]);
/* C*S*C^-1: recover conventional cell symmetry operation */
mat_get_similar_matrix_d3(symmetry_rot_d3,
primitive_sym_rot_d3,
transform_mat,
0);
mat_cast_matrix_3d_to_3i(symmetry->rot[i], symmetry_rot_d3);
/* translation in conventional cell: C = B^-1*P */
mat_inverse_matrix_d3(tmp_matrix_d3,
transform_mat,
0);
mat_multiply_matrix_vector_d3(symmetry->trans[i],
tmp_matrix_d3,
primitive_sym->trans[i]);
}
multi = 1;
if (centering) {
if (! (centering == FACE)) {
for (i = 0; i < 3; i++) {
shift[0][i] = 0.5;
}
if (centering == A_FACE) {
shift[0][0] = 0;
}
if (centering == B_FACE) {
shift[0][1] = 0;
}
if (centering == C_FACE) {
shift[0][2] = 0;
}
multi = 2;
}
if (centering == FACE) {
shift[0][0] = 0;
shift[0][1] = 0.5;
shift[0][2] = 0.5;
shift[1][0] = 0.5;
shift[1][1] = 0;
shift[1][2] = 0.5;
shift[2][0] = 0.5;
shift[2][1] = 0.5;
shift[2][2] = 0;
multi = 4;
}
for (i = 0; i < multi - 1; i++) {
for (j = 0; j < size; j++) {
mat_copy_matrix_i3(symmetry->rot[(i+1) * size + j],
symmetry->rot[j]);
for (k = 0; k < 3; k++) {
tmp_trans = symmetry->trans[j][k] + shift[i][k];
symmetry->trans[(i+1) * size + j][k] = tmp_trans;
}
}
}
}
/* Reduce translations into -0 < trans < 1.0 */
for (i = 0; i < multi; i++) {
for (j = 0; j < size; j++) {
for (k = 0; k < 3; k++) {
tmp_trans = symmetry->trans[i * size + j][k];
tmp_trans -= mat_Nint(tmp_trans);
if (tmp_trans < 0) {
tmp_trans += 1.0;
}
symmetry->trans[i * size + j][k] = tmp_trans;
}
}
}
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 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 0 if failed */
static int get_primitive_lattice_vectors(double prim_lattice[3][3],
const VecDBL * vectors,
SPGCONST Cell * cell,
const double symprec)
{
int i, j, k, size;
double initial_volume, volume;
double relative_lattice[3][3], min_vectors[3][3], tmp_lattice[3][3];
double inv_mat_dbl[3][3];
int inv_mat_int[3][3];
debug_print("get_primitive_lattice_vectors:\n");
size = vectors->size;
initial_volume = mat_Dabs(mat_get_determinant_d3(cell->lattice));
/* check volumes of all possible lattices, find smallest volume */
for (i = 0; i < size; i++) {
for (j = i + 1; j < size; j++) {
for (k = j + 1; k < size; k++) {
mat_multiply_matrix_vector_d3(tmp_lattice[0],
cell->lattice,
vectors->vec[i]);
mat_multiply_matrix_vector_d3(tmp_lattice[1],
cell->lattice,
vectors->vec[j]);
mat_multiply_matrix_vector_d3(tmp_lattice[2],
cell->lattice,
vectors->vec[k]);
volume = mat_Dabs(mat_get_determinant_d3(tmp_lattice));
if (volume > symprec) {
if (mat_Nint(initial_volume / volume) == size-2) {
mat_copy_vector_d3(min_vectors[0], vectors->vec[i]);
mat_copy_vector_d3(min_vectors[1], vectors->vec[j]);
mat_copy_vector_d3(min_vectors[2], vectors->vec[k]);
goto ret;
}
}
}
}
}
/* Not found */
warning_print("spglib: Primitive lattice vectors cound not be found ");
warning_print("(line %d, %s).\n", __LINE__, __FILE__);
return 0;
/* Found */
ret:
for (i = 0; i < 3; i++) {
for (j = 0; j < 3; j++) {
relative_lattice[j][i] = min_vectors[i][j];
}
}
mat_inverse_matrix_d3(inv_mat_dbl, relative_lattice, 0);
mat_cast_matrix_3d_to_3i(inv_mat_int, inv_mat_dbl);
if (abs(mat_get_determinant_i3(inv_mat_int)) == size-2) {
mat_cast_matrix_3i_to_3d(inv_mat_dbl, inv_mat_int);
mat_inverse_matrix_d3(relative_lattice, inv_mat_dbl, 0);
} else {
warning_print("spglib: Primitive lattice cleaning is incomplete ");
warning_print("(line %d, %s).\n", __LINE__, __FILE__);
}
mat_multiply_matrix_d3(prim_lattice, cell->lattice, relative_lattice);
return 1;
}
/* Return NULL if failed */
static Symmetry * get_conventional_symmetry(SPGCONST double transform_mat[3][3],
const Centering centering,
const Symmetry *primitive_sym)
{
int i, j, k, multi, size;
double inv_tmat[3][3], shift[4][3];
double symmetry_rot_d3[3][3], primitive_sym_rot_d3[3][3];
Symmetry *symmetry;
symmetry = NULL;
size = primitive_sym->size;
switch (centering) {
case FACE:
if ((symmetry = sym_alloc_symmetry(size * 4)) == NULL) {
return NULL;
}
break;
case R_CENTER:
if ((symmetry = sym_alloc_symmetry(size * 3)) == NULL) {
return NULL;
}
break;
case BODY:
case A_FACE:
case B_FACE:
case C_FACE:
if ((symmetry = sym_alloc_symmetry(size * 2)) == NULL) {
return NULL;
}
break;
default:
if ((symmetry = sym_alloc_symmetry(size)) == NULL) {
return NULL;
}
break;
}
for (i = 0; i < size; i++) {
mat_cast_matrix_3i_to_3d(primitive_sym_rot_d3, primitive_sym->rot[i]);
/* C*S*C^-1: recover conventional cell symmetry operation */
mat_get_similar_matrix_d3(symmetry_rot_d3,
primitive_sym_rot_d3,
transform_mat,
0);
mat_cast_matrix_3d_to_3i(symmetry->rot[i], symmetry_rot_d3);
/* translation in conventional cell: C = B^-1*P */
mat_inverse_matrix_d3(inv_tmat, transform_mat, 0);
mat_multiply_matrix_vector_d3(symmetry->trans[i],
inv_tmat,
primitive_sym->trans[i]);
}
multi = 1;
if (centering != PRIMITIVE) {
if (centering != FACE && centering != R_CENTER) {
for (i = 0; i < 3; i++) { shift[0][i] = 0.5; } /* BASE */
if (centering == A_FACE) { shift[0][0] = 0; }
if (centering == B_FACE) { shift[0][1] = 0; }
if (centering == C_FACE) { shift[0][2] = 0; }
multi = 2;
}
if (centering == R_CENTER) {
shift[0][0] = 2. / 3;
shift[0][1] = 1. / 3;
shift[0][2] = 1. / 3;
shift[1][0] = 1. / 3;
shift[1][1] = 2. / 3;
shift[1][2] = 2. / 3;
multi = 3;
}
if (centering == FACE) {
shift[0][0] = 0;
shift[0][1] = 0.5;
shift[0][2] = 0.5;
shift[1][0] = 0.5;
shift[1][1] = 0;
shift[1][2] = 0.5;
shift[2][0] = 0.5;
shift[2][1] = 0.5;
shift[2][2] = 0;
multi = 4;
}
for (i = 0; i < multi - 1; i++) {
for (j = 0; j < size; j++) {
mat_copy_matrix_i3(symmetry->rot[(i+1) * size + j],
symmetry->rot[j]);
for (k = 0; k < 3; k++) {
symmetry->trans[(i+1) * size + j][k] =
symmetry->trans[j][k] + shift[i][k];
}
}
}
}
for (i = 0; i < multi; i++) {
for (j = 0; j < size; j++) {
for (k = 0; k < 3; k++) {
symmetry->trans[i * size + j][k] =
mat_Dmod1(symmetry->trans[i * size + j][k]);
}
}
}
return symmetry;
}
