/* Copyright (C) 2012 Atsushi Togo */
/* All rights reserved. */

/* This file is part of spglib. */

/* Redistribution and use in source and binary forms, with or without */
/* modification, are permitted provided that the following conditions */
/* are met: */

/* * Redistributions of source code must retain the above copyright */
/*   notice, this list of conditions and the following disclaimer. */

/* * Redistributions in binary form must reproduce the above copyright */
/*   notice, this list of conditions and the following disclaimer in */
/*   the documentation and/or other materials provided with the */
/*   distribution. */

/* * Neither the name of the spglib project nor the names of its */
/*   contributors may be used to endorse or promote products derived */
/*   from this software without specific prior written permission. */

/* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS */
/* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT */
/* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS */
/* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE */
/* COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, */
/* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, */
/* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; */
/* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER */
/* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT */
/* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN */
/* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE */
/* POSSIBILITY OF SUCH DAMAGE. */

#include "spin.h"

#include <stdio.h>
#include <stdlib.h>

#include "cell.h"
#include "debug.h"
#include "mathfunc.h"
#include "primitive.h"
#include "symmetry.h"

static Symmetry *get_operations(int *spin_flips, const Symmetry *sym_nonspin,
                                const Cell *cell, const double *tensors,
                                const int tensor_rank, const int is_magnetic,
                                const double symprec);
static int set_equivalent_atoms(int *equiv_atoms, const Symmetry *symmetry,
                                const Cell *cell, const double symprec);
static int *get_mapping_table(const Symmetry *symmetry, const Cell *cell,
                              const double symprec);
static int check_spin(const double spin_j, const double spin_k, const int sign,
                      const double symprec);
static int check_vector(const int j, const int k, const double *spins,
                        SPGCONST int rot[3][3], SPGCONST double lattice[3][3],
                        const int is_magnetic, const double symprec);

/* Return NULL if failed */
Symmetry *spn_get_operations_with_site_tensors(
    int equiv_atoms[], double prim_lattice[3][3], int *spin_flips,
    const Symmetry *sym_nonspin, const Cell *cell, const double *tensors,
    const int tensor_rank, const int is_magnetic, const double symprec,
    const double angle_tolerance) {
    int i, num_pure_trans, multi;
    Symmetry *symmetry;
    VecDBL *pure_trans;
    int identity[3][3] = {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}};

    symmetry = NULL;
    pure_trans = NULL;

    if ((symmetry = get_operations(spin_flips, sym_nonspin, cell, tensors,
                                   tensor_rank, is_magnetic, symprec)) ==
        NULL) {
        return NULL;
    }

    if ((set_equivalent_atoms(equiv_atoms, symmetry, cell, symprec)) == 0) {
        sym_free_symmetry(symmetry);
        symmetry = NULL;
    }

    num_pure_trans = 0;
    for (i = 0; i < symmetry->size; i++) {
        if (mat_check_identity_matrix_i3(identity, symmetry->rot[i])) {
            num_pure_trans++;
        }
    }

    if ((pure_trans = mat_alloc_VecDBL(num_pure_trans)) == NULL) {
        return NULL;
    }

    num_pure_trans = 0;
    for (i = 0; i < symmetry->size; i++) {
        if (mat_check_identity_matrix_i3(identity, symmetry->rot[i])) {
            mat_copy_vector_d3(pure_trans->vec[num_pure_trans],
                               symmetry->trans[i]);
            num_pure_trans++;
        }
    }

    multi = prm_get_primitive_lattice_vectors(prim_lattice, cell, pure_trans,
                                              symprec, angle_tolerance);

    /* By definition, change of number of pure translations would */
    /* not be allowed. */
    if (multi != num_pure_trans) {
        return NULL;
    }

    mat_free_VecDBL(pure_trans);
    pure_trans = NULL;

    return symmetry;
}

/* Return NULL if failed */
/* spin_flips can be NULL if tensor_rank != 0. */
static Symmetry *get_operations(int *spin_flips, const Symmetry *sym_nonspin,
                                const Cell *cell, const double *tensors,
                                const int tensor_rank, const int is_magnetic,
                                const double symprec) {
    Symmetry *symmetry;
    int i, j, k, sign, num_sym, is_found;
    double pos[3];
    MatINT *rotations;
    VecDBL *trans;

    rotations = mat_alloc_MatINT(sym_nonspin->size);
    trans = mat_alloc_VecDBL(sym_nonspin->size);
    num_sym = 0;

    is_found = 0;

    for (i = 0; i < sym_nonspin->size; i++) {
        /* Set sign as undetermined (used for collinear spin case (rank = 0) */
        sign = 0;
        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_with_same_type(
                        cell->position[k], pos, cell->types[k], cell->types[j],
                        cell->lattice, symprec)) {
                    if (tensor_rank == 0) {
                        if (is_magnetic) {
                            sign = check_spin(tensors[j], tensors[k], sign,
                                              symprec);
                            is_found = abs(sign);
                        } else {
                            if (mat_Dabs(tensors[j] - tensors[k]) < symprec) {
                                is_found = 1;
                            } else {
                                is_found = 0;
                            }
                        }
                    }
                    if (tensor_rank == 1) {
                        is_found =
                            check_vector(j, k, tensors, sym_nonspin->rot[i],
                                         cell->lattice, is_magnetic, symprec);
                    }
                    /* Break because cel_is_overlap_with_same_type == true */
                    /* for only one atom. */
                    break;
                }
            }
            if (!is_found) {
                break;
            }
        }
        if (is_found) {
            mat_copy_matrix_i3(rotations->mat[num_sym], sym_nonspin->rot[i]);
            mat_copy_vector_d3(trans->vec[num_sym], sym_nonspin->trans[i]);
            if ((tensor_rank == 0) && (is_magnetic)) {
                spin_flips[num_sym] = sign;
            }
            num_sym++;
        }
    }

    symmetry = sym_alloc_symmetry(num_sym);
    for (i = 0; i < num_sym; i++) {
        mat_copy_matrix_i3(symmetry->rot[i], rotations->mat[i]);
        mat_copy_vector_d3(symmetry->trans[i], trans->vec[i]);
    }

    mat_free_MatINT(rotations);
    rotations = NULL;
    mat_free_VecDBL(trans);
    trans = NULL;

    return symmetry;
}

/* Return 0 if failed */
static int set_equivalent_atoms(int *equiv_atoms, const Symmetry *symmetry,
                                const 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_with_same_type(
                        pos, cell->position[k], cell->types[i], cell->types[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;
}

/* Return NULL if failed */
static int *get_mapping_table(const Symmetry *symmetry, const 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_with_same_type(
                            pos, cell->position[k], cell->types[i],
                            cell->types[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 check_spin(const double spin_j, const double spin_k, const int sign,
                      const double symprec) {
    if (sign == 0) {
        if (mat_Dabs(spin_j - spin_k) < symprec) {
            return 1;
        }
        if (mat_Dabs(spin_j + spin_k) < symprec) {
            return -1;
        }
        return 0;
    } else {
        if (mat_Dabs(spin_j - spin_k * sign) < symprec) {
            return sign;
        } else {
            return 0;
        }
    }
}

/* Work in Cartesian coordinates. */
static int check_vector(const int j, const int k, const double *vectors,
                        SPGCONST int rot[3][3], SPGCONST double lattice[3][3],
                        const int is_magnetic, const double symprec) {
    int i, detR;
    double vec_j[3], vec_jp[3], diff[3];
    double inv_lat[3][3], rot_cart[3][3];

    /* is_magnetic: Non-collinear magnetic moment m' = |detR|Rm */
    /* !is_magnetic: Usual vector: v' = Rv */

    mat_inverse_matrix_d3(inv_lat, lattice, 0);
    mat_multiply_matrix_id3(rot_cart, rot, inv_lat);
    mat_multiply_matrix_d3(rot_cart, lattice, rot_cart);

    for (i = 0; i < 3; i++) {
        vec_j[i] = vectors[j * 3 + i];
    }

    /* v_j' = R v_j */
    mat_multiply_matrix_vector_d3(vec_jp, rot_cart, vec_j);

    if (is_magnetic) {
        detR = mat_get_determinant_i3(rot);
        for (i = 0; i < 3; i++) {
            diff[i] = mat_Dabs(detR * vec_jp[i] - vectors[k * 3 + i]);
        }
    } else {
        for (i = 0; i < 3; i++) {
            diff[i] = mat_Dabs(vec_jp[i] - vectors[k * 3 + i]);
        }
    }

    if (diff[0] < symprec && diff[1] < symprec && diff[2] < symprec) {
        return 1;
    } else {
        return 0;
    }
}
