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;
}
/* Reference can be found in International table A. */
static int get_Delaunay_reduction( double red_lattice[3][3],
SPGCONST double lattice[3][3],
const double symprec )
{
int i, j;
double volume;
double basis[4][3];
get_exteneded_basis(basis, lattice);
while (1) {
if (get_Delaunay_reduction_basis(basis, symprec)) {
break;
}
}
get_Delaunay_shortest_vectors( basis, symprec );
for ( i = 0; i < 3; i++ ) {
for ( j = 0; j < 3; j++ ) {
red_lattice[i][j] = basis[j][i];
}
}
volume = mat_get_determinant_d3( red_lattice );
if ( mat_Dabs( volume ) < symprec ) {
warning_print("spglib: Minimum lattice has no volume (line %d, %s).\n", __LINE__, __FILE__);
goto err;
}
if ( volume < 0 ) {
/* Flip axes */
for (i = 0; i < 3; i++) {
for ( j = 0; j < 3; j++ ) {
red_lattice[i][j] = -red_lattice[i][j];
}
}
}
#ifdef DEBUG
debug_print("Delaunay reduction:\n");
debug_print_matrix_d3(red_lattice);
double metric[3][3];
mat_get_metric( metric, red_lattice );
debug_print("It's metric tensor.\n");
debug_print_matrix_d3( metric );
#endif
return 1;
err:
return 0;
}
static void get_conventional_lattice(double lattice[3][3],
SPGCONST Spacegroup *spacegroup)
{
int i, j;
double metric[3][3];
Pointgroup pointgroup;
pointgroup = ptg_get_pointgroup(spacegroup->pointgroup_number);
for (i = 0; i < 3; i++) {
for (j = 0; j < 3; j++) {
lattice[i][j] = 0;
}
}
mat_get_metric(metric, spacegroup->bravais_lattice);
debug_print("bravais lattice\n");
debug_print_matrix_d3(spacegroup->bravais_lattice);
debug_print("%s\n", spacegroup->setting);
switch (pointgroup.holohedry) {
case TRICLI:
set_tricli(lattice, metric);
break;
case MONOCLI: /* b-axis is the unique axis. */
set_monocli(lattice, metric);
break;
case ORTHO:
set_ortho(lattice, metric);
break;
case TETRA:
set_tetra(lattice, metric);
break;
case TRIGO:
if (spacegroup->setting[0] == 'R') {
set_rhomb(lattice, metric);
} else {
set_trigo(lattice, metric);
}
break;
case HEXA:
set_trigo(lattice, metric);
break;
case CUBIC:
set_cubic(lattice, metric);
break;
case HOLOHEDRY_NONE:
break;
}
}
static int get_conventional_lattice(double lattice[3][3],
const Holohedry holohedry,
SPGCONST double bravais_lattice[3][3])
{
int i, j;
double metric[3][3];
for (i = 0; i < 3; i++) {
for (j = 0; j < 3; j++) {
lattice[i][j] = 0;
}
}
mat_get_metric(metric, bravais_lattice);
switch (holohedry) {
case TRICLI:
mat_copy_matrix_d3(lattice, bravais_lattice);
break;
case MONOCLI: /* b-axis is the unique axis. */
set_monocli(lattice, metric);
break;
case ORTHO:
set_ortho(lattice, metric);
break;
case TETRA:
set_tetra(lattice, metric);
break;
case RHOMB:
set_rhomb(lattice, metric);
break;
case TRIGO:
set_trigo(lattice, metric);
break;
case HEXA:
set_trigo(lattice, metric);
break;
case CUBIC:
set_cubic(lattice, metric);
break;
case NONE:
break;
}
return 1;
}
static void set_rhomb(double lattice[3][3],
SPGCONST double metric[3][3])
{
double a, b, c, angle, ahex, chex;
a = sqrt(metric[0][0]);
b = sqrt(metric[1][1]);
c = sqrt(metric[2][2]);
angle = acos((metric[0][1] / a / b +
metric[0][2] / a / c +
metric[1][2] / b / c) / 3);
/* Reference, http://cst-www.nrl.navy.mil/lattice/struk/rgr.html */
ahex = 2 * (a+b+c)/3 * sin(angle / 2);
chex = (a+b+c)/3 * sqrt(3 * (1 + 2 * cos(angle))) ;
lattice[0][0] = ahex / 2;
lattice[1][0] = -ahex / (2 * sqrt(3));
lattice[2][0] = chex / 3;
lattice[1][1] = ahex / sqrt(3);
lattice[2][1] = chex / 3;
lattice[0][2] = -ahex / 2;
lattice[1][2] = -ahex / (2 * sqrt(3));
lattice[2][2] = chex / 3;
#ifdef DEBUG
debug_print("Rhombo lattice: %f %f %f %f %f %f\n", a, b, c,
acos(metric[0][1] / a / b) / 3.14 * 180,
acos(metric[0][2] / a / c) / 3.14 * 180,
acos(metric[1][2] / b / c) / 3.14 * 180);
double dmetric[3][3];
mat_get_metric(dmetric, lattice);
a = sqrt(dmetric[0][0]);
b = sqrt(dmetric[1][1]);
c = sqrt(dmetric[2][2]);
debug_print("Rhombo lattice symmetrized: %f %f %f %f %f %f\n",
a, b, c,
acos(dmetric[0][1] / a / b) / 3.14 * 180,
acos(dmetric[0][2] / a / c) / 3.14 * 180,
acos(dmetric[1][2] / b / c) / 3.14 * 180);
#endif
}
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;
}