mirror of https://github.com/phonopy/phonopy.git
702 lines
19 KiB
C
702 lines
19 KiB
C
/* primitive.c */
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/* Copyright (C) 2008 Atsushi Togo */
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#include <stdio.h>
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#include <stdlib.h>
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#include "cell.h"
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#include "lattice.h"
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#include "mathfunc.h"
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#include "primitive.h"
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#include "symmetry.h"
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#include "debug.h"
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#define INCREASE_RATE 2.0
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#define REDUCE_RATE 0.95
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static double current_tolerance;
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static Primitive get_primitive_and_pure_translation(SPGCONST Cell * cell,
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const double symprec);
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static Cell * get_primitive_with_mapping_table(int * mapping_table,
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SPGCONST Cell * cell,
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const double symprec);
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static int set_primitive_positions(Cell * primitive_cell,
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const VecDBL * position,
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const Cell * cell,
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int * const * table);
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static VecDBL * get_positions_primitive(SPGCONST Cell * cell,
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SPGCONST double prim_lat[3][3]);
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static int get_overlap_table(int ** table,
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const int cell_size,
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SPGCONST Cell *primitive_cell,
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const VecDBL * position,
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const double symprec);
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static int check_overlap_table(SPGCONST int **overlap_table,
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const int cell_size,
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const int ratio);
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static void free_overlap_table(int ** table, const int size);
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static int ** allocate_overlap_table(const int size);
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static Cell * get_cell_with_smallest_lattice(SPGCONST Cell * cell,
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const double symprec);
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static Cell * get_primitive(int * mapping_table,
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SPGCONST Cell * cell,
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const VecDBL * pure_trans,
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const double symprec);
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static int trim_cell(Cell * primitive_cell,
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int * mapping_table,
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SPGCONST Cell * cell,
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const double symprec);
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static int get_primitive_lattice_vectors_iterative(double prim_lattice[3][3],
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SPGCONST Cell * cell,
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const VecDBL * pure_trans,
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const double symprec);
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static int get_primitive_lattice_vectors(double prim_lattice[3][3],
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const VecDBL * vectors,
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SPGCONST Cell * cell,
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const double symprec);
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static VecDBL * get_translation_candidates(const VecDBL * pure_trans);
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static void set_current_tolerance(const double tolerance);
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Cell * prm_get_primitive(SPGCONST Cell * cell,
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const double symprec)
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{
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int *mapping_table;
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Cell *primitive_cell;
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mapping_table = (int*) malloc(sizeof(int) * cell->size);
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primitive_cell = prm_get_primitive_with_mapping_table(mapping_table,
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cell,
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symprec);
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free(mapping_table);
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return primitive_cell;
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}
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Primitive prm_get_primitive_and_pure_translations(SPGCONST Cell * cell,
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const double symprec)
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{
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return get_primitive_and_pure_translation(cell, symprec);
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}
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Cell * prm_get_primitive_with_mapping_table(int * mapping_table,
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SPGCONST Cell * cell,
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const double symprec)
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{
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return get_primitive_with_mapping_table(mapping_table,
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cell,
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symprec);
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}
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double prm_get_current_tolerance(void)
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{
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debug_print("prm_get_current_tolerance %f\n", current_tolerance);
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return current_tolerance;
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}
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/* If primitive could not be found, primitive->size = 0 is returned. */
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/* If cell is already primitive cell, */
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/* primitive cell with smallest lattice is returned. */
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static Primitive get_primitive_and_pure_translation(SPGCONST Cell * cell,
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const double symprec)
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{
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int attempt, is_found = 0;
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double tolerance;
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int *mapping_table;
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Primitive primitive;
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tolerance = symprec;
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for (attempt = 0; attempt < 100; attempt++) {
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primitive.pure_trans = sym_get_pure_translation(cell, tolerance);
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if (primitive.pure_trans->size == 0) {
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mat_free_VecDBL(primitive.pure_trans);
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continue;
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}
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if (primitive.pure_trans->size == 1) {
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primitive.cell = get_cell_with_smallest_lattice(cell, tolerance);
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} else {
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mapping_table = (int*) malloc(sizeof(int) * cell->size);
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primitive.cell = get_primitive(mapping_table,
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cell,
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primitive.pure_trans,
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tolerance);
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free(mapping_table);
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}
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if (primitive.cell->size > 0) {
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is_found = 1;
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break;
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}
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cel_free_cell(primitive.cell);
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mat_free_VecDBL(primitive.pure_trans);
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tolerance *= REDUCE_RATE;
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warning_print("spglib: Reduce tolerance to %f ", tolerance);
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warning_print("(line %d, %s).\n", __LINE__, __FILE__);
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}
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if (! is_found) {
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primitive.cell = cel_alloc_cell(0);
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primitive.pure_trans = mat_alloc_VecDBL(0);
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}
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return primitive;
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}
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/* If cell is already primitive cell, */
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/* primitive cell with smallest lattice is returned. */
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static Cell * get_primitive_with_mapping_table(int * mapping_table,
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SPGCONST Cell * cell,
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const double symprec)
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{
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int i, attempt;
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double tolerance;
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Cell *primitive_cell;
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VecDBL *pure_trans;
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tolerance = symprec;
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for (attempt = 0; attempt < 100; attempt++) {
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pure_trans = sym_get_pure_translation(cell, tolerance);
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if (pure_trans->size == 1) {
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primitive_cell = get_cell_with_smallest_lattice(cell, symprec);
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for (i = 0; i < cell->size; i++) {
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mapping_table[i] = i;
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}
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goto ret;
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}
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if (pure_trans->size > 1) {
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primitive_cell = get_primitive(mapping_table, cell, pure_trans, tolerance);
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if (primitive_cell->size > 0) {
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goto ret;
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}
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cel_free_cell(primitive_cell);
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}
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tolerance *= REDUCE_RATE;
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warning_print("spglib: Tolerance is reduced to %f at attempt %d\n", tolerance, attempt);
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warning_print("(line %d, %s).\n", __LINE__, __FILE__);
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mat_free_VecDBL(pure_trans);
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}
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/* not found: I hope this will not happen. */
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warning_print("spglib: Primitive cell could not be found ");
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warning_print("(line %d, %s).\n", __LINE__, __FILE__);
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return cel_alloc_cell(0);
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ret:
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mat_free_VecDBL(pure_trans);
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set_current_tolerance(tolerance);
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return primitive_cell;
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}
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static void set_current_tolerance(const double tolerance)
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{
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current_tolerance = tolerance;
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}
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static Cell * get_cell_with_smallest_lattice(SPGCONST Cell * cell,
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const double symprec)
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{
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int i, j;
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double min_lat[3][3], trans_mat[3][3], inv_lat[3][3];
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Cell * smallest_cell;
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debug_print("get_cell_with_smallest_lattice:\n");
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if (lat_smallest_lattice_vector(min_lat,
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cell->lattice,
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symprec)) {
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mat_inverse_matrix_d3(inv_lat, min_lat, 0);
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mat_multiply_matrix_d3(trans_mat, inv_lat, cell->lattice);
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smallest_cell = cel_alloc_cell(cell->size);
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mat_copy_matrix_d3(smallest_cell->lattice, min_lat);
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for (i = 0; i < cell->size; i++) {
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smallest_cell->types[i] = cell->types[i];
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mat_multiply_matrix_vector_d3(smallest_cell->position[i],
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trans_mat, cell->position[i]);
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for (j = 0; j < 3; j++) {
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cell->position[i][j] -= mat_Nint(cell->position[i][j]);
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}
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}
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} else {
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smallest_cell = cel_alloc_cell(0);
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}
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return smallest_cell;
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}
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/* If primitive could not be found, primitive->size = 0 is returned. */
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static Cell * get_primitive(int * mapping_table,
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SPGCONST Cell * cell,
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const VecDBL * pure_trans,
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const double symprec)
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{
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int multi;
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double prim_lattice[3][3];
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Cell * primitive_cell;
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debug_print("get_primitive:\n");
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/* Primitive lattice vectors are searched. */
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/* To be consistent, sometimes tolerance is decreased iteratively. */
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/* The descreased tolerance is stored in 'static double tolerance'. */
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multi = get_primitive_lattice_vectors_iterative(prim_lattice,
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cell,
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pure_trans,
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symprec);
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if (! multi) {
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goto not_found;
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}
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primitive_cell = cel_alloc_cell(cell->size / multi);
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if (! lat_smallest_lattice_vector(primitive_cell->lattice,
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prim_lattice,
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symprec)) {
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cel_free_cell(primitive_cell);
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goto not_found;
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}
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/* Fit atoms into new primitive cell */
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if (! trim_cell(primitive_cell, mapping_table, cell, symprec)) {
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cel_free_cell(primitive_cell);
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goto not_found;
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}
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/* found */
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return primitive_cell;
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not_found:
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primitive_cell = cel_alloc_cell(0);
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warning_print("spglib: Primitive cell could not be found ");
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warning_print("(line %d, %s).\n", __LINE__, __FILE__);
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return primitive_cell;
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}
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static int trim_cell(Cell * primitive_cell,
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int * mapping_table,
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SPGCONST Cell * cell,
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const double symprec)
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{
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int i, index_prim_atom;
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VecDBL * position;
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int **overlap_table;
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overlap_table = allocate_overlap_table(cell->size);
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/* Get reduced positions of atoms in original cell with respect to */
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/* primitive lattice */
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position = get_positions_primitive(cell, primitive_cell->lattice);
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/* Create overlapping table */
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if (! get_overlap_table(overlap_table,
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cell->size,
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primitive_cell,
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position,
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symprec)) {goto err;}
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/* Create original cell to primitive cell mapping table */
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index_prim_atom = 0;
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for (i = 0; i < cell->size; i++) {
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if (overlap_table[i][0] == i) {
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mapping_table[i] = index_prim_atom;
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index_prim_atom++;
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} else {
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mapping_table[i] = mapping_table[overlap_table[i][0]];
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}
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}
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/* Copy positions. Positions of overlapped atoms are averaged. */
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if (! set_primitive_positions(primitive_cell,
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position,
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cell,
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overlap_table)) {goto err;}
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mat_free_VecDBL(position);
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free_overlap_table(overlap_table, cell->size);
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return 1;
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err:
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mat_free_VecDBL(position);
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free_overlap_table(overlap_table, cell->size);
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return 0;
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}
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static int set_primitive_positions(Cell * primitive_cell,
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const VecDBL * position,
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const Cell * cell,
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int * const * table)
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{
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int i, j, k, ratio, index_prim_atom;
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int *is_equivalent;
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is_equivalent = (int*)malloc(cell->size * sizeof(int));
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for (i = 0; i < cell->size; i++) {
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is_equivalent[i] = 0;
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}
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ratio = cell->size / primitive_cell->size;
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/* Copy positions. Positions of overlapped atoms are averaged. */
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index_prim_atom = 0;
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for (i = 0; i < cell->size; i++) {
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if (! is_equivalent[i]) {
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primitive_cell->types[index_prim_atom] = cell->types[i];
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for (j = 0; j < 3; j++) {
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primitive_cell->position[index_prim_atom][j] = 0;
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}
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for (j = 0; j < ratio; j++) { /* Loop for averaging positions */
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is_equivalent[table[i][j]] = 1;
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for (k = 0; k < 3; k++) {
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/* boundary treatment */
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/* One is at right and one is at left or vice versa. */
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if (mat_Dabs(position->vec[table[i][0]][k] -
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position->vec[table[i][j]][k]) > 0.5) {
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if (position->vec[table[i][j]][k] < 0) {
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primitive_cell->position[index_prim_atom][k] =
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primitive_cell->position[index_prim_atom][k] +
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position->vec[table[i][j]][k] + 1;
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} else {
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primitive_cell->position[index_prim_atom][k] =
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primitive_cell->position[index_prim_atom][k] +
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position->vec[table[i][j]][k] - 1;
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}
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} else {
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primitive_cell->position[index_prim_atom][k] =
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primitive_cell->position[index_prim_atom][k] +
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position->vec[table[i][j]][k];
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}
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}
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}
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for (j = 0; j < 3; j++) { /* take average and reduce */
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primitive_cell->position[index_prim_atom][j] =
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primitive_cell->position[index_prim_atom][j] / ratio;
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primitive_cell->position[index_prim_atom][j] =
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primitive_cell->position[index_prim_atom][j] -
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mat_Nint(primitive_cell->position[index_prim_atom][j]);
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}
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index_prim_atom++;
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}
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}
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free(is_equivalent);
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is_equivalent = NULL;
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if (! (index_prim_atom == primitive_cell->size)) {
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warning_print("spglib: Atomic positions of primitive cell could not be determined ");
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warning_print("(line %d, %s).\n", __LINE__, __FILE__);
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goto err;
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}
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return 1;
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err:
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return 0;
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}
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static VecDBL * get_positions_primitive(SPGCONST Cell * cell,
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SPGCONST double prim_lat[3][3])
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{
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int i, j;
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double tmp_matrix[3][3], axis_inv[3][3];
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VecDBL * position;
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position = mat_alloc_VecDBL(cell->size);
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mat_inverse_matrix_d3(tmp_matrix, prim_lat, 0);
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mat_multiply_matrix_d3(axis_inv, tmp_matrix, cell->lattice);
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/* Send atoms into the primitive cell */
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for (i = 0; i < cell->size; i++) {
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mat_multiply_matrix_vector_d3(position->vec[i],
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axis_inv, cell->position[i]);
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for (j = 0; j < 3; j++) {
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position->vec[i][j] -= mat_Nint(position->vec[i][j]);
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}
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}
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return position;
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}
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/* If overlap_table is correctly obtained, */
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/* shape of overlap_table will be (cell->size, cell->size / primitive->size). */
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static int get_overlap_table(int **overlap_table,
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const int cell_size,
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SPGCONST Cell *primitive_cell,
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const VecDBL * position,
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const double symprec)
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{
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int i, j, attempt, num_overlap, ratio;
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double trim_tolerance;
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ratio = cell_size / primitive_cell->size;
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trim_tolerance = symprec;
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for (attempt = 0; attempt < 100; attempt++) {
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/* Each value of -1 has to be overwritten by 0 or positive numbers. */
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for (i = 0; i < cell_size; i++) {
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for (j = 0; j < cell_size; j++) {
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overlap_table[i][j] = -1;
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}
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}
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for (i = 0; i < cell_size; i++) {
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num_overlap = 0;
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for (j = 0; j < cell_size; j++) {
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if (cel_is_overlap(position->vec[i],
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position->vec[j],
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primitive_cell->lattice,
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trim_tolerance)) {
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overlap_table[i][num_overlap] = j;
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num_overlap++;
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}
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}
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}
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if (check_overlap_table(overlap_table, cell_size, ratio)) {
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goto found;
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}
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if (num_overlap < ratio) {
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trim_tolerance *= INCREASE_RATE;
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warning_print("spglib: Increase tolerance to %f ", trim_tolerance);
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} else {
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trim_tolerance *= REDUCE_RATE;
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warning_print("spglib: Reduce tolerance to %f ", trim_tolerance);
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}
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warning_print("(line %d, %s).\n", __LINE__, __FILE__);
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}
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warning_print("spglib: Could not trim cell into primitive ");
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warning_print("(line %d, %s).\n", __LINE__, __FILE__);
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return 0;
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found:
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return 1;
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}
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static int check_overlap_table(SPGCONST int **overlap_table,
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const int cell_size,
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const int ratio) {
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int i, j, index_compared, all_ok;
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all_ok = 1;
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for (i = 0; i < cell_size; i++) {
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index_compared = overlap_table[i][0];
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for (j = 0; j < cell_size; j++) {
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if (! (overlap_table[i][j] == overlap_table[index_compared][j])) {
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all_ok = 0;
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break;
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}
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if (j < ratio) {
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if (overlap_table[i][j] == -1) {
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all_ok = 0;
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break;
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}
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} else {
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if (overlap_table[i][j] > -1) {
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all_ok = 0;
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break;
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}
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}
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}
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if (! all_ok) {
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break;
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}
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}
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return all_ok;
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}
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static void free_overlap_table(int **table, const int size)
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{
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int i;
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for (i = 0; i < size; i++) {
|
|
free(table[i]);
|
|
table[i] = NULL;
|
|
}
|
|
free(table);
|
|
table = NULL;
|
|
}
|
|
|
|
static int ** allocate_overlap_table(const int size)
|
|
{
|
|
int i;
|
|
int **table = (int**)malloc(size * sizeof(int*));
|
|
for (i = 0; i < size; i++) {
|
|
table[i] = (int*)malloc(size * sizeof(int));
|
|
}
|
|
return table;
|
|
}
|
|
|
|
|
|
static int get_primitive_lattice_vectors_iterative(double prim_lattice[3][3],
|
|
SPGCONST Cell * cell,
|
|
const VecDBL * pure_trans,
|
|
const double symprec)
|
|
{
|
|
int i, multi, attempt;
|
|
double tolerance;
|
|
VecDBL * vectors, * pure_trans_reduced, *tmp_vec;
|
|
|
|
tolerance = symprec;
|
|
pure_trans_reduced = mat_alloc_VecDBL(pure_trans->size);
|
|
for (i = 0; i < pure_trans->size; i++) {
|
|
mat_copy_vector_d3(pure_trans_reduced->vec[i], pure_trans->vec[i]);
|
|
}
|
|
|
|
for (attempt = 0; attempt < 100; attempt++) {
|
|
multi = pure_trans_reduced->size;
|
|
vectors = get_translation_candidates(pure_trans_reduced);
|
|
|
|
/* Lattice of primitive cell is found among pure translation vectors */
|
|
if (get_primitive_lattice_vectors(prim_lattice,
|
|
vectors,
|
|
cell,
|
|
tolerance)) {
|
|
|
|
mat_free_VecDBL(vectors);
|
|
mat_free_VecDBL(pure_trans_reduced);
|
|
|
|
goto found;
|
|
} else {
|
|
|
|
tmp_vec = mat_alloc_VecDBL(multi);
|
|
for (i = 0; i < multi; i++) {
|
|
mat_copy_vector_d3(tmp_vec->vec[i], pure_trans_reduced->vec[i]);
|
|
}
|
|
mat_free_VecDBL(pure_trans_reduced);
|
|
pure_trans_reduced = sym_reduce_pure_translation(cell,
|
|
tmp_vec,
|
|
tolerance);
|
|
warning_print("Tolerance is reduced to %f (%d), size = %d\n",
|
|
tolerance, attempt, pure_trans_reduced->size);
|
|
|
|
mat_free_VecDBL(tmp_vec);
|
|
mat_free_VecDBL(vectors);
|
|
|
|
tolerance *= REDUCE_RATE;
|
|
}
|
|
}
|
|
|
|
/* Not found */
|
|
return 0;
|
|
|
|
found:
|
|
#ifdef SPGWARNING
|
|
if (attempt > 0) {
|
|
printf("spglib: Tolerance to find primitive lattice vectors was changed to %f\n", tolerance);
|
|
}
|
|
#endif
|
|
return multi;
|
|
}
|
|
|
|
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;
|
|
}
|
|
|
|
static VecDBL * get_translation_candidates(const VecDBL * pure_trans)
|
|
{
|
|
int i, j, multi;
|
|
VecDBL * vectors;
|
|
|
|
multi = pure_trans->size;
|
|
vectors = mat_alloc_VecDBL(multi+2);
|
|
|
|
/* store pure translations in original cell */
|
|
/* as trial primitive lattice vectors */
|
|
for (i = 0; i < multi - 1; i++) {
|
|
mat_copy_vector_d3(vectors->vec[i], pure_trans->vec[i + 1]);
|
|
}
|
|
|
|
/* store lattice translations of original cell */
|
|
/* as trial primitive lattice vectors */
|
|
for (i = 0; i < 3; i++) {
|
|
for (j = 0; j < 3; j++) {
|
|
if (i == j) {
|
|
vectors->vec[i+multi-1][j] = 1;
|
|
} else {
|
|
vectors->vec[i+multi-1][j] = 0;
|
|
}
|
|
}
|
|
}
|
|
|
|
return vectors;
|
|
}
|
|
|