static int lauennn(int axes[3],
SPGCONST PointSymmetry * pointsym,
const int rot_order)
{
int i, count, axis;
int prop_rot[3][3];
for (i = 0; i < 3; i++) { axes[i] = -1; }
count = 0;
for (i = 0; i < pointsym->size; i++) {
get_proper_rotation(prop_rot, pointsym->rot[i]);
/* Search two- or four-fold rotation */
if ((mat_get_trace_i3(prop_rot) == -1 && rot_order == 2) ||
(mat_get_trace_i3(prop_rot) == 1 && rot_order == 4)) {
axis = get_rotation_axis(prop_rot);
if (! ((axis == axes[0]) ||
(axis == axes[1]) ||
(axis == axes[2]))) {
axes[count] = axis;
count++;
}
}
}
sort_axes(axes);
return 1;
}
static int lauennn( int axes[3],
const Symmetry * symmetry,
const int rot_order )
{
int i, count, axis, tmpval;
int prop_rot[3][3], t_mat[3][3];
for ( i = 0; i < 3; i++ ) { axes[i] = -1; }
count = 0;
for ( i = 0; i < symmetry->size; i++ ) {
get_proper_rotation( prop_rot, symmetry->rot[i] );
/* Search two- or four-fold rotation */
if ( ( mat_get_trace_i3( prop_rot ) == -1 && rot_order == 2) ||
( mat_get_trace_i3( prop_rot ) == 1 && rot_order == 4 ) ) {
axis = get_rotation_axis( prop_rot );
if ( ! ( ( axis == axes[0] ) ||
( axis == axes[1] ) ||
( axis == axes[2] ) ) ) {
axes[count] = axis;
count++;
}
}
}
get_transform_matrix( t_mat, axes );
if ( mat_get_determinant_i3( t_mat ) < 0 ) {
tmpval = axes[0];
axes[0] = axes[1];
axes[1] = tmpval;
}
return 1;
}
static int get_rotation_type(SPGCONST int rot[3][3])
{
int rot_type;
if (mat_get_determinant_i3(rot) == -1) {
switch (mat_get_trace_i3(rot)) {
case -2: /* -6 */
rot_type = 0;
break;
case -1: /* -4 */
rot_type = 1;
break;
case 0: /* -3 */
rot_type = 2;
break;
case 1: /* -2 */
rot_type = 3;
break;
case -3: /* -1 */
rot_type = 4;
break;
default:
rot_type = -1;
break;
}
} else {
switch (mat_get_trace_i3(rot)) {
case 3: /* 1 */
rot_type = 5;
break;
case -1: /* 2 */
rot_type = 6;
break;
case 0: /* 3 */
rot_type = 7;
break;
case 1: /* 4 */
rot_type = 8;
break;
case 2: /* 6 */
rot_type = 9;
break;
default:
rot_type = -1;
break;
}
}
return rot_type;
}
static int lauem3m(int axes[3],
SPGCONST PointSymmetry * pointsym)
{
int i, count, axis, tmpval;
int prop_rot[3][3];
for (i = 0; i < 3; i++) { axes[i] = -1; }
count = 0;
for (i = 0; i < pointsym->size; i++) {
get_proper_rotation(prop_rot, pointsym->rot[i]);
/* Search four-fold rotation */
if (! (mat_get_trace_i3(prop_rot) == 1)) {
continue;
}
axis = get_rotation_axis(prop_rot);
if (! ((axis == axes[0]) ||
(axis == axes[1]) ||
(axis == axes[2]))) {
axes[count] = axis;
count++;
}
}
sort_axes(axes);
return 1;
}
static int laue4m(int axes[3],
SPGCONST PointSymmetry * pointsym)
{
int i, num_ortho_axis, norm, min_norm, is_found, tmpval;
int axis_vec[3];
int prop_rot[3][3], t_mat[3][3];
int ortho_axes[NUM_ROT_AXES];
for (i = 0; i < pointsym->size; i++) {
get_proper_rotation(prop_rot, pointsym->rot[i]);
/* Search foud-fold rotation */
if ( mat_get_trace_i3(prop_rot) == 1) {
/* The first axis */
axes[2] = get_rotation_axis(prop_rot);
break;
}
}
/* The second axis */
num_ortho_axis = get_orthogonal_axis(ortho_axes, prop_rot, 4);
if (! num_ortho_axis) { goto err; }
min_norm = 8;
is_found = 0;
for (i = 0; i < num_ortho_axis; i++) {
norm = mat_norm_squared_i3(rot_axes[ortho_axes[i]]);
if (norm < min_norm) {
min_norm = norm;
axes[0] = ortho_axes[i];
is_found = 1;
}
}
if (! is_found) { goto err; }
/* The third axis */
mat_multiply_matrix_vector_i3(axis_vec, prop_rot, rot_axes[axes[0]]);
is_found = 0;
for (i = 0; i < NUM_ROT_AXES; i++) {
if (is_exist_axis(axis_vec, i)) {
is_found = 1;
axes[1] = i;
break;
}
}
if (! is_found) { goto err; }
set_transformation_matrix(t_mat, axes);
if (mat_get_determinant_i3(t_mat) < 0) {
tmpval = axes[0];
axes[0] = axes[1];
axes[1] = tmpval;
}
return 1;
err:
return 0;
}
static int laue3m(int axes[3],
SPGCONST PointSymmetry * pointsym)
{
int i, is_found, tmpval, axis;
int prop_rot[3][3], prop_rot2[3][3], t_mat[3][3];
int axis_vec[3];
for (i = 0; i < pointsym->size; i++) {
get_proper_rotation(prop_rot, pointsym->rot[i]);
/* Search three-fold rotation */
if (mat_get_trace_i3(prop_rot) == 0) {
/* The first axis */
axes[2] = get_rotation_axis(prop_rot);
debug_print("laue3m prop_rot\n");
debug_print_matrix_i3(prop_rot);
break;
}
}
is_found = 0;
for (i = 0; i < pointsym->size; i++) {
get_proper_rotation(prop_rot2, pointsym->rot[i]);
/* Search two-fold rotation */
if (! (mat_get_trace_i3(prop_rot2) == -1)) {
continue;
}
/* The second axis */
axis = get_rotation_axis(prop_rot2);
if (! (axis == axes[2])) {
axes[0] = axis;
is_found = 1;
break;
}
}
if (! is_found) { goto err; }
/* The third axis */
mat_multiply_matrix_vector_i3(axis_vec, prop_rot, rot_axes[axes[0]]);
is_found = 0;
for (i = 0; i < NUM_ROT_AXES; i++) {
is_found = is_exist_axis(axis_vec, i);
if (is_found == 1) {
axes[1] = i;
break;
}
if (is_found == -1) {
axes[1] = i + NUM_ROT_AXES;
break;
}
}
if (! is_found) { goto err; }
set_transformation_matrix(t_mat, axes);
if (mat_get_determinant_i3(t_mat) < 0) {
tmpval = axes[0];
axes[0] = axes[1];
axes[1] = tmpval;
}
return 1;
err:
return 0;
}
static int laue_one_axis(int axes[3],
SPGCONST PointSymmetry * pointsym,
const int rot_order)
{
int i, j, num_ortho_axis, det, is_found, tmpval;
int axis_vec[3], tmp_axes[3];
int prop_rot[3][3], t_mat[3][3];
int ortho_axes[NUM_ROT_AXES];
debug_print("laue_one_axis with rot_order %d\n", rot_order);
for (i = 0; i < pointsym->size; i++) {
get_proper_rotation(prop_rot, pointsym->rot[i]);
/* Search foud-fold rotation */
if (rot_order == 4) {
if (mat_get_trace_i3(prop_rot) == 1) {
/* The first axis */
axes[2] = get_rotation_axis(prop_rot);
break;
}
}
/* Search three-fold rotation */
if (rot_order == 3) {
if (mat_get_trace_i3(prop_rot) == 0) {
/* The first axis */
axes[2] = get_rotation_axis(prop_rot);
break;
}
}
}
/* Candidates of the second axis */
num_ortho_axis = get_orthogonal_axis(ortho_axes, prop_rot, rot_order);
if (! num_ortho_axis) { goto err; }
tmp_axes[1] = -1;
tmp_axes[2] = axes[2];
for (i = 0; i < num_ortho_axis; i++) {
is_found = 0;
tmp_axes[0] = ortho_axes[i];
mat_multiply_matrix_vector_i3(axis_vec,
prop_rot,
rot_axes[tmp_axes[0]]);
for (j = 0; j < num_ortho_axis; j++) {
is_found = is_exist_axis(axis_vec, ortho_axes[j]);
if (is_found == 1) {
tmp_axes[1] = ortho_axes[j];
break;
}
if (is_found == -1) {
tmp_axes[1] = ortho_axes[j] + NUM_ROT_AXES;
break;
}
}
if (!is_found) { continue; }
set_transformation_matrix(t_mat, tmp_axes);
det = abs(mat_get_determinant_i3(t_mat));
if (det < 4) { /* to avoid F-center choice det=4 */
axes[0] = tmp_axes[0];
axes[1] = tmp_axes[1];
goto end;
}
}
err: /* axes are not correctly found. */
warning_print("spglib: Secondary axis is not found.");
warning_print("(line %d, %s).\n", __LINE__, __FILE__);
return 0;
end:
set_transformation_matrix(t_mat, axes);
if (mat_get_determinant_i3(t_mat) < 0) {
tmpval = axes[0];
axes[0] = axes[1];
axes[1] = tmpval;
}
debug_print("axes[0] = %d\n", axes[0]);
debug_print("axes[1] = %d\n", axes[1]);
debug_print("axes[2] = %d\n", axes[2]);
return 1;
}
static int laue_one_axis( int axes[3],
const Symmetry * symmetry,
const int rot_order )
{
int i, j, num_ortho_axis, det, min_det, is_found, tmpval;
int axis_vec[3], tmp_axes[3];
int prop_rot[3][3], t_mat[3][3];
int ortho_axes[NUM_ROT_AXES];
for ( i = 0; i < symmetry->size; i++ ) {
get_proper_rotation( prop_rot, symmetry->rot[i] );
/* Search foud-fold rotation */
if ( rot_order == 4 ) {
if ( mat_get_trace_i3( prop_rot ) == 1 ) {
/* The first axis */
axes[2] = get_rotation_axis( prop_rot );
break;
}
}
/* Search three-fold rotation */
if ( rot_order == 3 ) {
if ( mat_get_trace_i3( prop_rot ) == 0 ) {
/* The first axis */
axes[2] = get_rotation_axis( prop_rot );
break;
}
}
}
/* Candidates of the second axis */
num_ortho_axis = get_orthogonal_axis( ortho_axes, prop_rot, rot_order );
if ( ! num_ortho_axis ) { goto err; }
tmp_axes[2] = axes[2];
min_det = 4;
is_found = 0;
for ( i = 0; i < num_ortho_axis; i++ ) {
tmp_axes[0] = ortho_axes[i];
mat_multiply_matrix_vector_i3( axis_vec, prop_rot,
rot_axes[tmp_axes[0]] );
for ( j = 0; j < num_ortho_axis; j++ ) {
is_found = is_exist_axis( axis_vec, ortho_axes[j] );
if ( is_found == 1 ) {
tmp_axes[1] = ortho_axes[j];
break;
}
if ( is_found == -1 ) {
tmp_axes[1] = ortho_axes[j] + NUM_ROT_AXES;
break;
}
}
get_transform_matrix( t_mat, tmp_axes );
det = mat_get_determinant_i3( t_mat );
if ( det < 0 ) { det = -det; }
if ( det < min_det ) {
min_det = det;
axes[0] = tmp_axes[0];
axes[1] = tmp_axes[1];
}
}
if ( ! is_found ) { goto err; }
get_transform_matrix( t_mat, axes );
if ( mat_get_determinant_i3( t_mat ) < 0 ) {
tmpval = axes[0];
axes[0] = axes[1];
axes[1] = tmpval;
}
return 1;
err:
return 0;
}
static int laue4mmm( int axes[3],
const Symmetry * symmetry )
{
int i, is_found, tmpval, axis;
int prop_rot[3][3], prop_rot2[3][3], t_mat[3][3];
int axis_vec[3];
for ( i = 0; i < symmetry->size; i++ ) {
get_proper_rotation( prop_rot, symmetry->rot[i] );
/* Search foud-fold rotation */
if ( mat_get_trace_i3( prop_rot ) == 1 ) {
/* The first axis */
axes[2] = get_rotation_axis( prop_rot );
break;
}
}
is_found = 0;
for ( i = 0; i < symmetry->size; i++ ) {
get_proper_rotation( prop_rot2, symmetry->rot[i] );
/* Search two-fold rotation */
if ( ! ( mat_get_trace_i3( prop_rot2 ) == -1 ) ) {
continue;
}
/* The second axis */
axis = get_rotation_axis( prop_rot2 );
if ( ! ( axis == axes[2] ) ) {
axes[0] = axis;
is_found = 1;
break;
}
}
if ( ! is_found ) { goto err; }
/* The third axis */
mat_multiply_matrix_vector_i3( axis_vec, prop_rot, rot_axes[axes[0]] );
is_found = 0;
for ( i = 0; i < NUM_ROT_AXES; i++ ) {
if ( is_exist_axis( axis_vec, i ) ) {
is_found = 1;
axes[1] = i;
break;
}
}
if ( ! is_found ) { goto err; }
get_transform_matrix( t_mat, axes );
if ( mat_get_determinant_i3( t_mat ) < 0 ) {
tmpval = axes[0];
axes[0] = axes[1];
axes[1] = tmpval;
}
return 1;
err:
return 0;
}
static int laue2m( int axes[3],
const Symmetry * symmetry )
{
int i, num_ortho_axis, norm, min_norm, is_found, tmpval;
int prop_rot[3][3], t_mat[3][3];
int ortho_axes[NUM_ROT_AXES];
for ( i = 0; i < symmetry->size; i++ ) {
get_proper_rotation( prop_rot, symmetry->rot[i] );
/* Search two-fold rotation */
if ( ! ( mat_get_trace_i3( prop_rot ) == -1 ) ) {
continue;
}
/* The first axis */
axes[1] = get_rotation_axis( prop_rot );
break;
}
/* The second axis */
num_ortho_axis = get_orthogonal_axis( ortho_axes, prop_rot, 2 );
if ( ! num_ortho_axis ) { goto err; }
min_norm = 8;
is_found = 0;
for ( i = 0; i < num_ortho_axis; i++ ) {
norm = mat_norm_squared_i3( rot_axes[ortho_axes[i]] );
if ( norm < min_norm ) {
min_norm = norm;
axes[0] = ortho_axes[i];
is_found = 1;
}
}
if ( ! is_found ) { goto err; }
/* The third axis */
min_norm = 8;
is_found = 0;
for ( i = 0; i < num_ortho_axis; i++ ) {
norm = mat_norm_squared_i3( rot_axes[ortho_axes[i]] );
if ( norm < min_norm && ( ! ( ortho_axes[i] == axes[0] ) ) ) {
min_norm = norm;
axes[2] = ortho_axes[i];
is_found = 1;
}
}
if ( ! is_found ) { goto err; }
get_transform_matrix( t_mat, axes );
if ( mat_get_determinant_i3( t_mat ) < 0 ) {
tmpval = axes[0];
axes[0] = axes[2];
axes[2] = tmpval;
}
return 1;
err:
return 0;
}
