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phonopy/c/spglib/hall_symbol.c

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/* Copyright (C) 2010 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 phonopy 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 <stdio.h>
#include "hall_symbol.h"
#include "spg_database.h"
#include "spacegroup.h"
#include "symmetry.h"
#include "mathfunc.h"
static int M_bcc[3][3] = {
{ 0, 1, 1 },
{ 1, 0, 1 },
{ 1, 1, 0 },
};
static int M_fcc[3][3] = {
{-1, 1, 1 },
{ 1,-1, 1 },
{ 1, 1,-1 },
};
static int M_ac[3][3] = {
{ 1, 0, 0 },
{ 0, 1, 1 },
{ 0,-1, 1 },
};
static int M_bc[3][3] = {
{ 1, 0, 1 },
{ 0, 1, 0 },
{-1, 0, 1 },
};
static int M_cc[3][3] = {
{ 1,-1, 0 },
{ 1, 1, 0 },
{ 0, 0, 1 },
};
static int M_rc[3][3] = {
{ 1, 0, 1 },
{-1, 1, 1 },
{ 0,-1, 1 },
};
static double M_bcc_inv[3][3] = {
{-0.5, 0.5, 0.5},
{ 0.5,-0.5, 0.5},
{ 0.5, 0.5,-0.5},
};
static double M_fcc_inv[3][3] = {
{ 0.0, 0.5, 0.5},
{ 0.5, 0.0, 0.5},
{ 0.5, 0.5, 0.0},
};
static double M_ac_inv[3][3] = {
{ 1.0, 0.0, 0.0},
{ 0.0, 0.5,-0.5},
{ 0.0, 0.5, 0.5},
};
static double M_bc_inv[3][3] = {
{ 0.5, 0.0,-0.5},
{ 0.0, 1.0, 0.0},
{ 0.5, 0.0, 0.5},
};
static double M_cc_inv[3][3] = {
{ 0.5, 0.5, 0.0},
{-0.5, 0.5, 0.0},
{ 0.0, 0.0, 1.0},
};
static double M_rc_inv[3][3] = {
{ 2./3,-1./3,-1./3},
{ 1./3, 1./3,-2./3},
{ 1./3, 1./3, 1./3},
};
/* See: R. W. Grosse-Kunstleve, Acta Cryst. (1999). A55, 383-395 */
/* */
/* S is the Smith normal form, S = U*M*V */
/* M = R - I, where R is virtical stack of generator rotation matrices */
/* and I is virtical stack of identity matrices. */
/* */
/* Origin shift is given by (V*S+*U)*dw where dw is translations */
/* corresponding to those obtained by symmetry finder and from */
/* International table. */
/* S+ is given by the operations of inversion of the diagonal elements */
/* and then transpose. */
static double tricli_VSpU[][3][9] =
{
{ /* 1 */
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 2 */
{ 0, 0, 0, -1.0/2, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, -1.0/2, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, -1.0/2, 0, 0, 0, },
},
};
static int tricli_generators[][3][9] =
{
{ /* 1 */
{ 1, 0, 0, 0, 1, 0, 0, 0, 1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 2 */
{ 1, 0, 0, 0, 1, 0, 0, 0, 1, },
{ -1, 0, 0, 0, -1, 0, 0, 0, -1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
};
static double monocli_VSpU[][3][9] =
{
{ /* 1 */
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, -1.0/2, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, -1.0/2, 0, 0, 0, 0, 0, 0, },
},
{ /* 2 */
{ -1.0/2, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, -1.0/2, 0, 0, 0, 0, 0, 0, },
},
{ /* 3 */
{ -1.0/2, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, -1.0/2, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 4 */
{ -1.0/2, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 5 */
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, -1.0/2, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 6 */
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, -1.0/2, 0, 0, 0, 0, 0, 0, },
},
{ /* 7 */
{ 0, 0, 0, -1.0/2, 0, 0, 0, 0, 0, },
{ 0, -1.0/2, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, -1.0/2, 0, 0, 0, 0, 0, 0, },
},
{ /* 8 */
{ -1.0/2, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, -1.0/2, 0, 0, 0, 0, },
{ 0, 0, -1.0/2, 0, 0, 0, 0, 0, 0, },
},
{ /* 9 */
{ -1.0/2, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, -1.0/2, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, -1.0/2, 0, 0, 0, },
},
};
static double monocli_A_VSpU[][3][9] =
{
{ /* 1 */
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, -1.0/2, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, -1.0/2, 0, 0, 0, 0, 0, 0, },
},
{ /* 2 */
{ -1.0/2, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, -1, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 3 */
{ -1.0/2, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, -1, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 4 */
{ -1.0/2, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 5 */
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, -1, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 6 */
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, -1, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 7 */
{ 0, 0, 0, -1.0/2, 0, 0, 0, 0, 0, },
{ 0, -1.0/2, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, -1.0/2, 0, 0, 0, 0, 0, 0, },
},
{ /* 8 */
{ -1.0/2, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, -1.0/2, 0, 0, 0, 0, },
{ 0, -1, 0, 0, 1.0/2, 0, 0, 0, 0, },
},
{ /* 9 */
{ -1.0/2, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, -1.0/2, 0, 0, 0, 0, },
{ 0, 1, 0, 0, -1.0/2, 0, 0, 0, 0, },
},
};
static double monocli_B_VSpU[][3][9] =
{
{ /* 1 */
{ -1, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, -1.0/2, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 2 */
{ -1.0/2, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, -1.0/2, 0, 0, 0, 0, 0, 0, },
},
{ /* 3 */
{ -1, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, -1.0/2, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 4 */
{ -1, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 5 */
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, -1.0/2, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 6 */
{ -1, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 7 */
{ 0, 0, 0, -1.0/2, 0, 0, 0, 0, 0, },
{ 0, -1.0/2, 0, 0, 0, 0, 0, 0, 0, },
{ -1, 0, 0, 1.0/2, 0, 0, 0, 0, 0, },
},
{ /* 8 */
{ -1.0/2, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, -1.0/2, 0, 0, 0, 0, },
{ 0, 0, -1.0/2, 0, 0, 0, 0, 0, 0, },
},
{ /* 9 */
{ 0, 0, 0, -1.0/2, 0, 0, 0, 0, 0, },
{ 0, -1.0/2, 0, 0, 0, 0, 0, 0, 0, },
{ 1, 0, 0, -1.0/2, 0, 0, 0, 0, 0, },
},
};
static double monocli_C_VSpU[][3][9] =
{
{ /* 1 */
{ -1, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, -1.0/2, 0, 0, 0, 0, 0, 0, },
},
{ /* 2 */
{ -1, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, -1.0/2, 0, 0, 0, 0, 0, 0, },
},
{ /* 3 */
{ -1.0/2, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, -1.0/2, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 4 */
{ -1, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 5 */
{ -1, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 6 */
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, -1.0/2, 0, 0, 0, 0, 0, 0, },
},
{ /* 7 */
{ 0, 0, 0, -1.0/2, 0, 0, 0, 0, 0, },
{ 1, 0, 0, -1.0/2, 0, 0, 0, 0, 0, },
{ 0, 0, -1.0/2, 0, 0, 0, 0, 0, 0, },
},
{ /* 8 */
{ 0, 0, 0, -1.0/2, 0, 0, 0, 0, 0, },
{ -1, 0, 0, 1.0/2, 0, 0, 0, 0, 0, },
{ 0, 0, -1.0/2, 0, 0, 0, 0, 0, 0, },
},
{ /* 9 */
{ -1.0/2, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, -1.0/2, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, -1.0/2, 0, 0, 0, },
},
};
static double monocli_I_VSpU[][3][9] =
{
{ /* 1 */
{ -1.0/2, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 1.0/2, -1, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 2 */
{ -1, 1.0/2, 0, 0, 0, 0, 0, 0, 0, },
{ 0, -1.0/2, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 3 */
{ -1, 0, 1.0/2, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, -1.0/2, 0, 0, 0, 0, 0, 0, },
},
{ /* 4 */
{ 0, 1, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 5 */
{ -1, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 6 */
{ -1, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 7 */
{ 0, 0, 0, -1.0/2, 0, 0, 0, 0, 0, },
{ 0, -1, 0, 1.0/2, 0, -1.0/2, 0, 0, 0, },
{ 0, 0, 0, 0, 0, -1.0/2, 0, 0, 0, },
},
{ /* 8 */
{ 0, 0, 0, -1.0/2, 0, 0, 0, 0, 0, },
{ 0, -1.0/2, 0, 0, 0, 0, 0, 0, 0, },
{ 1, -1.0/2, 0, -1.0/2, 0, 0, 0, 0, 0, },
},
{ /* 9 */
{ 0, 0, 0, -1.0/2, 0, 0, 0, 0, 0, },
{ 1, 0, -1.0/2, -1.0/2, 0, 0, 0, 0, 0, },
{ 0, 0, -1.0/2, 0, 0, 0, 0, 0, 0, },
},
};
static int monocli_generators[][3][9] =
{
{ /* 1 */
{ 1, 0, 0, 0, -1, 0, 0, 0, -1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 2 */
{ -1, 0, 0, 0, 1, 0, 0, 0, -1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 3 */
{ -1, 0, 0, 0, -1, 0, 0, 0, 1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 4 */
{ -1, 0, 0, 0, 1, 0, 0, 0, 1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 5 */
{ 1, 0, 0, 0, -1, 0, 0, 0, 1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 6 */
{ 1, 0, 0, 0, 1, 0, 0, 0, -1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 7 */
{ 1, 0, 0, 0, -1, 0, 0, 0, -1, },
{ -1, 0, 0, 0, -1, 0, 0, 0, -1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 8 */
{ -1, 0, 0, 0, 1, 0, 0, 0, -1, },
{ -1, 0, 0, 0, -1, 0, 0, 0, -1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 9 */
{ -1, 0, 0, 0, -1, 0, 0, 0, 1, },
{ -1, 0, 0, 0, -1, 0, 0, 0, -1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
};
static double ortho_VSpU[][3][9] =
{
{ /* 1 */
{ -1.0/2, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, -1.0/2, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, -1.0/2, 0, 0, 0, },
},
{ /* 2 */
{ -1.0/2, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, -1.0/2, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 3 */
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, -1.0/2, 0, 0, 0, 0, },
{ 0, 0, -1.0/2, 0, 0, 0, 0, 0, 0, },
},
{ /* 4 */
{ 0, 0, 0, -1.0/2, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, -1.0/2, 0, 0, 0, 0, 0, 0, },
},
{ /* 5 */
{ -1.0/2, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, -1.0/2, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, -1.0/2, 0, 0, 0, },
},
};
static double ortho_F_VSpU[][3][9] =
{
{ /* 1 */
{ 0, 1.0/2, 0, -1.0/4, -1.0/4, 0, 0, 0, 0, },
{ 0, -1.0/2, 0, -1.0/4, -1.0/4, 0, 0, 0, 0, },
{ 0, -1.0/2, 0, -1.0/4, 3.0/4, 0, 0, 0, 0, },
},
{ /* 2 */
{ 0, 1, 0, 0, -1, 0, 0, 0, 0, },
{ 0, 0, 0, 0, -1, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 3 */
{ 0, -1, 0, 0, 1, 0, 0, 0, 0, },
{ 0, 0, 0, 0, -1, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 4 */
{ 0, -1, 0, 0, 1, 0, 0, 0, 0, },
{ 0, 0, 0, 0, -1, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 5 */
{ 0, 1, 0, 0, 0, 0, 0, -1.0/2, 0, },
{ 0, 0, 0, 0, 0, 0, 0, -1.0/2, 0, },
{ 0, 0, 0, 0, 1, 0, 0, -1.0/2, 0, },
},
};
static double ortho_I_VSpU[][3][9] =
{
{ /* 1 */
{ 0, 0, 0, -1.0/2, 0, 0, 0, 0, 0, },
{ 1.0/2, -1.0/2, 0, -1.0/2, 0, 0, 0, 0, 0, },
{ -1.0/2, -1.0/2, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 2 */
{ -1.0/2, 0, 0, 0, 1.0/2, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ -1.0/2, 0, 0, 0, -1.0/2, 0, 0, 0, 0, },
},
{ /* 3 */
{ 0, 0, 0, -1.0/2, 0, 0, 0, 0, 0, },
{ 0, -1, 0, 1.0/2, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 4 */
{ -1.0/2, 0, 0, 0, 1.0/2, 0, 0, 0, 0, },
{ -1.0/2, 0, 0, 0, -1.0/2, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 5 */
{ 0, 0, 0, 0, 0, 0, -1.0/2, 0, 0, },
{ 0, 0, -1.0/2, 0, -1, 0, 1.0/2, 0, 0, },
{ 0, 0, -1.0/2, 0, 0, 0, 0, 0, 0, },
},
};
static double ortho_A_VSpU[][3][9] =
{
{ /* 1 */
{ -1.0/2, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, -1.0/2, 0, 0, 0, 0, },
{ 0, 1, 0, 0, -1.0/2, 0, 0, 0, 0, },
},
{ /* 2 */
{ -1.0/2, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, -1, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 3 */
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, -1.0/2, 0, 0, 0, 0, },
{ 0, -1, 0, 0, 1.0/2, 0, 0, 0, 0, },
},
{ /* 4 */
{ 0, 0, 0, -1.0/2, 0, 0, 0, 0, 0, },
{ 0, -1, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 5 */
{ -1.0/2, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, -1, 0, 0, 0, -1.0/2, 0, 0, 0, },
{ 0, 0, 0, 0, 0, -1.0/2, 0, 0, 0, },
},
};
static double ortho_B_VSpU[][3][9] =
{
{ /* 1 */
{ -1.0/2, 0, 0, -1.0/2, 0, 0, 0, 0, 0, },
{ 0, -1.0/2, 0, 0, 0, 0, 0, 0, 0, },
{ 1.0/2, 0, 0, -1.0/2, 0, 0, 0, 0, 0, },
},
{ /* 2 */
{ 0, 0, 0, -1, 0, 0, 0, 0, 0, },
{ 0, -1.0/2, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 3 */
{ 0, 0, 0, -1, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, -1.0/2, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 4 */
{ -1.0/2, 0, 0, -1.0/2, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ -1.0/2, 0, 0, 1.0/2, 0, 0, 0, 0, 0, },
},
{ /* 5 */
{ 0, 0, 0, 0, 0, 0, -1.0/2, 0, 0, },
{ 0, 0, 0, 0, -1.0/2, 0, 0, 0, 0, },
{ 0, 0, 0, -1, 0, 0, 1.0/2, 0, 0, },
},
};
static double ortho_C_VSpU[][3][9] =
{
{ /* 1 */
{ -1.0/2, 0, 0, 0, 0, 0, 0, 0, 0, },
{ -1.0/2, 0, 0, 1, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, -1.0/2, 0, 0, 0, },
},
{ /* 2 */
{ -1.0/2, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 1.0/2, 0, 0, -1, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 3 */
{ 0, 0, 0, -1, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, -1.0/2, 0, 0, 0, 0, 0, 0, },
},
{ /* 4 */
{ 0, 0, 0, -1, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, -1.0/2, 0, 0, 0, 0, 0, 0, },
},
{ /* 5 */
{ 0, 0, 0, 0, 0, 0, -1.0/2, 0, 0, },
{ 0, 0, 0, 1, 0, 0, -1.0/2, 0, 0, },
{ 0, 0, 0, 0, 0, -1.0/2, 0, 0, 0, },
},
};
static int ortho_generators[][3][9] =
{
{ /* 1 */
{ -1, 0, 0, 0, -1, 0, 0, 0, 1, },
{ 1, 0, 0, 0, -1, 0, 0, 0, -1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 2 */
{ -1, 0, 0, 0, -1, 0, 0, 0, 1, },
{ -1, 0, 0, 0, 1, 0, 0, 0, 1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 3 */
{ 1, 0, 0, 0, 1, 0, 0, 0, -1, },
{ 1, 0, 0, 0, -1, 0, 0, 0, -1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 4 */
{ 1, 0, 0, 0, 1, 0, 0, 0, -1, },
{ -1, 0, 0, 0, 1, 0, 0, 0, 1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 5 */
{ -1, 0, 0, 0, -1, 0, 0, 0, 1, },
{ 1, 0, 0, 0, -1, 0, 0, 0, -1, },
{ -1, 0, 0, 0, -1, 0, 0, 0, -1, },
},
};
static double tetra_VSpU[][3][9] =
{
{ /* 1 */
{ -1.0/2, 1.0/2, 0, 0, 0, 0, 0, 0, 0, },
{ -1.0/2, -1.0/2, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 2 */
{ -1, 0, 0, 0, 1.0/2, 0, 0, 0, 0, },
{ 0, 0, 0, 0, -1.0/2, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, -1.0/2, 0, 0, 0, },
},
{ /* 3 */
{ 0, 0, 0, -1.0/2, 0, 0, 0, 0, 0, },
{ -1, 0, 0, 1.0/2, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 4 */
{ -1.0/2, -1.0/2, 0, 0, 0, 0, 0, 0, 0, },
{ 1.0/2, -1.0/2, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, -1.0/2, 0, 0, 0, 0, 0, 0, },
},
{ /* 5 */
{ -1, 0, 0, 0, -1.0/2, 0, 0, 0, 0, },
{ 0, 0, 0, 0, -1.0/2, 0, 0, 0, 0, },
{ 0, 0, -1.0/2, 0, 0, 0, 0, 0, 0, },
},
{ /* 6 */
{ 0, 0, 0, -1.0/2, 0, 0, 0, 0, 0, },
{ 1, 0, 0, -1.0/2, 0, 0, 0, 0, 0, },
{ 0, 0, -1.0/2, 0, 0, 0, 0, 0, 0, },
},
{ /* 7 */
{ 0, 0, 0, -1.0/2, 0, 0, 0, 0, 0, },
{ -1, 0, 0, 1.0/2, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, -1.0/2, 0, 0, 0, },
},
{ /* 8 */
{ -1, 0, 0, 0, 1.0/2, 0, 0, 0, 0, },
{ 0, 0, 0, 0, -1.0/2, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, -1.0/2, 0, 0, 0, },
},
};
static double tetra_I_VSpU[][3][9] =
{
{ /* 1 */
{ -1, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, -1, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 2 */
{ 0, 0, 0, -1.0/2, 0, 0, 0, 0, 0, },
{ 1, 0, 0, -1.0/2, 0, 0, 0, 0, 0, },
{ 1, 0, -1, 0, 0, 0, 0, 0, 0, },
},
{ /* 3 */
{ -1, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ -1, 0, 0, 0, -1, 0, 0, 0, 0, },
},
{ /* 4 */
{ -3.0/4, 1.0/4, 1.0/4, 0, 0, 0, 0, 0, 0, },
{ -1.0/4, -1.0/4, -1.0/4, 0, 0, 0, 0, 0, 0, },
{ -1.0/2, 1.0/2, -1.0/2, 0, 0, 0, 0, 0, 0, },
},
{ /* 5 */
{ 0, 0, 0, -1.0/2, 0, 0, 0, 0, 0, },
{ -1, 0, 0, 1.0/2, 0, 0, 0, 0, 0, },
{ 1, 0, -1, -1, 0, 0, 0, 0, 0, },
},
{ /* 6 */
{ -3.0/4, 1.0/4, 0, 0, 1.0/4, 0, 0, 0, 0, },
{ -1.0/4, -1.0/4, 0, 0, -1.0/4, 0, 0, 0, 0, },
{ -1.0/2, 1.0/2, 0, 0, -1.0/2, 0, 0, 0, 0, },
},
{ /* 7 */
{ 0, 2, 0, -1.0/2, 0, -1, 0, 0, 0, },
{ 1, 0, 0, -1.0/2, 0, 0, 0, 0, 0, },
{ 0, -1, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 8 */
{ -1, 0, 0, 0, -1, 0, 1.0/2, 0, -1.0/2, },
{ 0, 0, 0, 0, -1, 0, 1.0/2, 0, -1.0/2, },
{ 1, 0, 0, 0, 1, 0, -1, 0, 0, },
},
};
static int tetra_generators[][3][9] =
{
{ /* 1 */
{ 0, -1, 0, 1, 0, 0, 0, 0, 1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 2 */
{ 0, -1, 0, 1, 0, 0, 0, 0, 1, },
{ 1, 0, 0, 0, -1, 0, 0, 0, -1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 3 */
{ 0, -1, 0, 1, 0, 0, 0, 0, 1, },
{ -1, 0, 0, 0, 1, 0, 0, 0, 1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 4 */
{ 0, 1, 0, -1, 0, 0, 0, 0, -1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 5 */
{ 0, 1, 0, -1, 0, 0, 0, 0, -1, },
{ 1, 0, 0, 0, -1, 0, 0, 0, -1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 6 */
{ 0, 1, 0, -1, 0, 0, 0, 0, -1, },
{ -1, 0, 0, 0, 1, 0, 0, 0, 1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 7 */
{ 0, -1, 0, 1, 0, 0, 0, 0, 1, },
{ -1, 0, 0, 0, -1, 0, 0, 0, -1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 8 */
{ 0, -1, 0, 1, 0, 0, 0, 0, 1, },
{ 1, 0, 0, 0, -1, 0, 0, 0, -1, },
{ -1, 0, 0, 0, -1, 0, 0, 0, -1, },
},
};
static double trigo_VSpU[][3][9] =
{
{ /* 1 */
{ -2.0/3, 1.0/3, 0, 0, 0, 0, 0, 0, 0, },
{ -1.0/3, -1.0/3, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 2 */
{ 0, 1.0/3, 0, -2.0/3, 0, 0, 0, 0, 0, },
{ 0, -1.0/3, 0, -1.0/3, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, -1.0/2, 0, 0, 0, },
},
{ /* 3 */
{ 0, -1, 0, -2, 0, 0, 0, 0, 0, },
{ 0, -1, 0, -1, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, -1.0/2, 0, 0, 0, },
},
{ /* 4 */
{ 0, -1, 0, -2, 0, 0, 0, 0, 0, },
{ 0, -1, 0, -1, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 5 */
{ 0, 1.0/3, 0, -2.0/3, 0, 0, 0, 0, 0, },
{ 0, -1.0/3, 0, -1.0/3, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 6 */
{ 0, -1, 0, 0, 0, 0, 0, 0, 0, },
{ 1, -1, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, -1.0/2, 0, 0, 0, 0, 0, 0, },
},
{ /* 7 */
{ 0, -1, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 1, 0, -1, 0, 0, 0, 0, 0, },
{ 0, 0, -1.0/2, 0, 0, 0, 0, 0, 0, },
},
{ /* 8 */
{ 0, -1, 0, 0, 0, 0, 0, 0, 0, },
{ 0, -1, 0, 1, 0, 0, 0, 0, 0, },
{ 0, 0, -1.0/2, 0, 0, 0, 0, 0, 0, },
},
{ /* 9 */
{ 0, -1, 0, 0, 0, 0, 0, 0, 0, },
{ 0, -1, 0, 1, 0, 0, 0, 0, 0, },
{ 0, 0, -1.0/2, 0, 0, 0, 0, 0, 0, },
},
{ /* 10 */
{ 0, -1, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 1, 0, -1, 0, 0, 0, 0, 0, },
{ 0, 0, -1.0/2, 0, 0, 0, 0, 0, 0, },
},
{ /* 11 */
{ -6, 3, 0, 4, 0, 0, 0, 0, 0, },
{ -3, 1, 0, 2, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, -1.0/2, 0, 0, 0, },
},
{ /* 12 */
{ 0, 1, 0, -2, 0, 0, 1, 0, 0, },
{ 0, -1, 0, 1, 0, 0, -1, 0, 0, },
{ 0, 0, 0, 0, 0, -1.0/2, 0, 0, 0, },
},
{ /* 13 */
{ 0, -1, 0, -2, 0, 0, 0, 0, 0, },
{ 0, -1, 0, -1, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, -1.0/2, 0, 0, 0, },
},
};
static int trigo_generators[][3][9] =
{
{ /* 1 */
{ 0, -1, 0, 1, -1, 0, 0, 0, 1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 2 */
{ 0, -1, 0, 1, -1, 0, 0, 0, 1, },
{ 0, -1, 0, -1, 0, 0, 0, 0, -1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 3 */
{ 0, -1, 0, 1, -1, 0, 0, 0, 1, },
{ 0, 1, 0, 1, 0, 0, 0, 0, -1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 4 */
{ 0, -1, 0, 1, -1, 0, 0, 0, 1, },
{ 0, 1, 0, 1, 0, 0, 0, 0, 1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 5 */
{ 0, -1, 0, 1, -1, 0, 0, 0, 1, },
{ 0, -1, 0, -1, 0, 0, 0, 0, 1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 6 */
{ 0, 1, 0, -1, 1, 0, 0, 0, -1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 7 */
{ 0, 1, 0, -1, 1, 0, 0, 0, -1, },
{ 0, -1, 0, -1, 0, 0, 0, 0, -1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 8 */
{ 0, 1, 0, -1, 1, 0, 0, 0, -1, },
{ 0, 1, 0, 1, 0, 0, 0, 0, -1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 9 */
{ 0, 1, 0, -1, 1, 0, 0, 0, -1, },
{ 0, 1, 0, 1, 0, 0, 0, 0, 1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 10 */
{ 0, 1, 0, -1, 1, 0, 0, 0, -1, },
{ 0, -1, 0, -1, 0, 0, 0, 0, 1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 11 */
{ 0, -1, 0, 1, -1, 0, 0, 0, 1, },
{ -1, 0, 0, 0, -1, 0, 0, 0, -1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 12 */
{ 0, -1, 0, 1, -1, 0, 0, 0, 1, },
{ 0, -1, 0, -1, 0, 0, 0, 0, -1, },
{ -1, 0, 0, 0, -1, 0, 0, 0, -1, },
},
{ /* 13 */
{ 0, -1, 0, 1, -1, 0, 0, 0, 1, },
{ 0, 1, 0, 1, 0, 0, 0, 0, -1, },
{ -1, 0, 0, 0, -1, 0, 0, 0, -1, },
},
};
static double rhombo_h_VSpU[][3][9] =
{
{ /* 1 */
{ -1, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 1, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 2 */
{ -1.0/2, 0, 0, -1.0/2, 0, 0, 0, 0, 0, },
{ -1.0/2, -1, 0, -1.0/2, 0, 0, 0, 0, 0, },
{ 1.0/2, 0, 0, -1.0/2, 0, 0, 0, 0, 0, },
},
{ /* 3 */
{ 0, 0, 0, -1, 0, 0, 0, 0, 0, },
{ 0, -1, 0, -1, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 4 */
{ -1.0/2, -1.0/2, 1.0/2, 0, 0, 0, 0, 0, 0, },
{ 1.0/2, -1.0/2, -1.0/2, 0, 0, 0, 0, 0, 0, },
{ -1.0/2, 1.0/2, -1.0/2, 0, 0, 0, 0, 0, 0, },
},
{ /* 5 */
{ 0, -1, 0, 0, 1.0/2, 0, 0, 0, 0, },
{ 0, 0, 0, 0, -1.0/2, 0, 0, 0, 0, },
{ 0, 1, 0, -1, -1.0/2, 0, 0, 0, 0, },
},
{ /* 6 */
{ -1.0/2, 0, 0, -1.0/2, 0, 0, 0, 0, 0, },
{ 1.0/2, -1, 0, 1.0/2, 0, 0, 0, 0, 0, },
{ -1.0/2, 0, 0, 1.0/2, 0, 0, 0, 0, 0, },
},
{ /* 7 */
{ 0, 0, 0, -1.0/2, 0, 0, 0, 0, 0, },
{ 1, 0, 1, -1.0/2, 0, 0, 0, 0, 0, },
{ 1, 0, 0, -1.0/2, 0, 0, 0, 0, 0, },
},
{ /* 8 */
{ 0, 0, 0, 0, 0, 0, -1.0/2, 0, 0, },
{ 0, -1, 0, 0, 0, 0, -1.0/2, 0, 0, },
{ 0, 0, 0, -1, 0, 0, 1.0/2, 0, 0, },
},
};
static int rhombo_h_generators[][3][9] =
{
{ /* 1 */
{ 0, -1, 0, 1, -1, 0, 0, 0, 1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 2 */
{ 0, -1, 0, 1, -1, 0, 0, 0, 1, },
{ 0, 1, 0, 1, 0, 0, 0, 0, -1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 3 */
{ 0, -1, 0, 1, -1, 0, 0, 0, 1, },
{ 0, -1, 0, -1, 0, 0, 0, 0, 1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 4 */
{ 0, 1, 0, -1, 1, 0, 0, 0, -1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 5 */
{ 0, 1, 0, -1, 1, 0, 0, 0, -1, },
{ 0, 1, 0, 1, 0, 0, 0, 0, -1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 6 */
{ 0, 1, 0, -1, 1, 0, 0, 0, -1, },
{ 0, -1, 0, -1, 0, 0, 0, 0, 1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 7 */
{ 0, -1, 0, 1, -1, 0, 0, 0, 1, },
{ -1, 0, 0, 0, -1, 0, 0, 0, -1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 8 */
{ 0, -1, 0, 1, -1, 0, 0, 0, 1, },
{ 0, 1, 0, 1, 0, 0, 0, 0, -1, },
{ -1, 0, 0, 0, -1, 0, 0, 0, -1, },
},
};
static double rhombo_p_VSpU[][3][9] =
{
{ /* 1 */
{ -1, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 1, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 2 */
{ -1.0/2, 0, 0, -1.0/2, 0, 0, 0, 0, 0, },
{ -1.0/2, -1, 0, -1.0/2, 0, 0, 0, 0, 0, },
{ 1.0/2, 0, 0, -1.0/2, 0, 0, 0, 0, 0, },
},
{ /* 3 */
{ 0, 0, 0, -1, 0, 0, 0, 0, 0, },
{ 0, -1, 0, -1, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 4 */
{ -1.0/2, -1.0/2, 1.0/2, 0, 0, 0, 0, 0, 0, },
{ 1.0/2, -1.0/2, -1.0/2, 0, 0, 0, 0, 0, 0, },
{ -1.0/2, 1.0/2, -1.0/2, 0, 0, 0, 0, 0, 0, },
},
{ /* 5 */
{ 0, -1, 0, 0, 1.0/2, 0, 0, 0, 0, },
{ 0, 0, 0, 0, -1.0/2, 0, 0, 0, 0, },
{ 0, 1, 0, -1, -1.0/2, 0, 0, 0, 0, },
},
{ /* 6 */
{ -1.0/2, 0, 0, -1.0/2, 0, 0, 0, 0, 0, },
{ 1.0/2, -1, 0, 1.0/2, 0, 0, 0, 0, 0, },
{ -1.0/2, 0, 0, 1.0/2, 0, 0, 0, 0, 0, },
},
{ /* 7 */
{ 0, 0, 0, -1.0/2, 0, 0, 0, 0, 0, },
{ 1, 0, 1, -1.0/2, 0, 0, 0, 0, 0, },
{ 1, 0, 0, -1.0/2, 0, 0, 0, 0, 0, },
},
{ /* 8 */
{ 0, 0, 0, 0, 0, 0, -1.0/2, 0, 0, },
{ 0, -1, 0, 0, 0, 0, -1.0/2, 0, 0, },
{ 0, 0, 0, -1, 0, 0, 1.0/2, 0, 0, },
},
};
static int rhombo_p_generators[][3][9] =
{
{ /* 1 */
{ 0, 0, 1, 1, 0, 0, 0, 1, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 2 */
{ 0, 0, 1, 1, 0, 0, 0, 1, 0, },
{ 0, 0, -1, 0, -1, 0, -1, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 3 */
{ 0, 0, 1, 1, 0, 0, 0, 1, 0, },
{ 0, 0, 1, 0, 1, 0, 1, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 4 */
{ 0, 0, -1, -1, 0, 0, 0, -1, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 5 */
{ 0, 0, -1, -1, 0, 0, 0, -1, 0, },
{ 0, 0, -1, 0, -1, 0, -1, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 6 */
{ 0, 0, -1, -1, 0, 0, 0, -1, 0, },
{ 0, 0, 1, 0, 1, 0, 1, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 7 */
{ 0, 0, 1, 1, 0, 0, 0, 1, 0, },
{ -1, 0, 0, 0, -1, 0, 0, 0, -1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 8 */
{ 0, 0, 1, 1, 0, 0, 0, 1, 0, },
{ 0, 0, -1, 0, -1, 0, -1, 0, 0, },
{ -1, 0, 0, 0, -1, 0, 0, 0, -1, },
},
};
static double hexa_VSpU[][3][9] =
{
{ /* 1 */
{ -1, 1, 0, 0, 0, 0, 0, 0, 0, },
{ -1, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 2 */
{ 1, 0, 0, -1, 0, 0, 0, 0, 0, },
{ -1, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, -1.0/2, 0, 0, 0, },
},
{ /* 3 */
{ -1, 0, 0, -1, 0, 0, 0, 0, 0, },
{ -1, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 4 */
{ -1.0/3, -1.0/3, 0, 0, 0, 0, 0, 0, 0, },
{ 1.0/3, -2.0/3, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, -1.0/2, 0, 0, 0, 0, 0, 0, },
},
{ /* 5 */
{ -1.0/3, 0, 0, -1.0/3, 0, 0, 0, 0, 0, },
{ 1.0/3, 0, 0, -2.0/3, 0, 0, 0, 0, 0, },
{ 0, 0, -1.0/2, 0, 0, 0, 0, 0, 0, },
},
{ /* 6 */
{ -1, 0, 0, 1, 0, 0, 0, 0, 0, },
{ -1, 0, 0, 2, 0, 0, 0, 0, 0, },
{ 0, 0, -1.0/2, 0, 0, 0, 0, 0, 0, },
},
{ /* 7 */
{ -1, 1, 0, 0, 0, 0, 0, 0, 0, },
{ -1, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, -1.0/2, 0, 0, 0, },
},
{ /* 8 */
{ 1, 0, 0, -1, 0, 0, 0, 0, 0, },
{ -1, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, -1.0/2, 0, 0, 0, },
},
};
static int hexa_generators[][3][9] =
{
{ /* 1 */
{ 1, -1, 0, 1, 0, 0, 0, 0, 1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 2 */
{ 1, -1, 0, 1, 0, 0, 0, 0, 1, },
{ 0, -1, 0, -1, 0, 0, 0, 0, -1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 3 */
{ 1, -1, 0, 1, 0, 0, 0, 0, 1, },
{ 0, 1, 0, 1, 0, 0, 0, 0, 1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 4 */
{ -1, 1, 0, -1, 0, 0, 0, 0, -1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 5 */
{ -1, 1, 0, -1, 0, 0, 0, 0, -1, },
{ 0, -1, 0, -1, 0, 0, 0, 0, -1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 6 */
{ -1, 1, 0, -1, 0, 0, 0, 0, -1, },
{ 0, 1, 0, 1, 0, 0, 0, 0, 1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 7 */
{ 1, -1, 0, 1, 0, 0, 0, 0, 1, },
{ -1, 0, 0, 0, -1, 0, 0, 0, -1, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 8 */
{ 1, -1, 0, 1, 0, 0, 0, 0, 1, },
{ 0, -1, 0, -1, 0, 0, 0, 0, -1, },
{ -1, 0, 0, 0, -1, 0, 0, 0, -1, },
},
};
static double cubic_VSpU[][3][9] =
{
{ /* 1 */
{ -1.0/2, 1.0/2, 0, 0, 0, 0, 0, 0, 0, },
{ -1.0/2, -1.0/2, 0, 0, 0, 0, 0, 0, 0, },
{ -1.0/2, 1.0/2, 0, 1, 0, 0, 0, 0, 0, },
},
{ /* 2 */
{ -1.0/2, 1.0/2, 0, 0, 0, 0, 0, 0, 0, },
{ -1.0/2, -1.0/2, 0, 0, 0, 0, 0, 0, 0, },
{ 1.0/2, -1.0/2, 0, -1, 0, 0, 0, 0, 0, },
},
{ /* 3 */
{ 0, -1.0/2, 0, -1, 0, -1, 0, 0, 0, },
{ 0, -1.0/2, 0, 0, 0, 0, 0, 0, 0, },
{ 0, -1.0/2, 0, 0, 0, -1, 0, 0, 0, },
},
{ /* 4 */
{ 0, -1.0/2, 0, -1, 0, 1, 0, 0, 0, },
{ 0, -1.0/2, 0, 0, 0, 0, 0, 0, 0, },
{ 0, 1.0/2, 0, 0, 0, -1, 0, 0, 0, },
},
{ /* 5 */
{ -1.0/2, -1.0/2, 0, 0, 0, 0, 0, 0, 0, },
{ 1.0/2, -1.0/2, 0, 0, 0, 0, 0, 0, 0, },
{ -1.0/2, -1.0/2, 0, 1, 0, 0, 0, 0, 0, },
},
{ /* 6 */
{ -1.0/2, -1.0/2, 0, 0, 0, 0, 0, 0, 0, },
{ 1.0/2, -1.0/2, 0, 0, 0, 0, 0, 0, 0, },
{ 1.0/2, 1.0/2, 0, -1, 0, 0, 0, 0, 0, },
},
{ /* 7 */
{ 0, 0, -1.0/2, -1, 0, 0, 0, 0, 0, },
{ 0, 0, -1.0/2, 0, 0, 1, 0, 0, 0, },
{ 0, 0, -1.0/2, 0, 0, 0, 0, 0, 0, },
},
{ /* 8 */
{ 0, 0, 1.0/2, -1, 0, 0, 0, 0, 0, },
{ 0, 0, 1.0/2, 0, 0, -1, 0, 0, 0, },
{ 0, 0, -1.0/2, 0, 0, 0, 0, 0, 0, },
},
{ /* 9 */
{ 0, 0, 0, 0, 0, 0, -1.0/2, 0, 0, },
{ 0, -1, 0, 0, 0, 0, -1.0/2, 0, 0, },
{ 0, 0, 0, 1, 0, 0, -1.0/2, 0, 0, },
},
{ /* 10 */
{ 0, 0, 0, 0, 0, 0, -1.0/2, 0, 0, },
{ 0, 0, 0, 1, 0, 1, -1.0/2, 0, 0, },
{ 0, 0, 0, 1, 0, 0, -1.0/2, 0, 0, },
},
};
static double cubic_F_VSpU[][3][9] =
{
{ /* 1 */
{ 0, 0, -1.0/2, -1.0/2, 0, 0, 0, 0, 0, },
{ 0, -1, 1.0/2, -1.0/2, 0, 0, 0, 0, 0, },
{ 0, 0, -1.0/2, 1.0/2, 0, 0, 0, 0, 0, },
},
{ /* 2 */
{ 0, 1.0/2, -1.0/2, 0, -1.0/2, 0, 0, 0, 0, },
{ 0, -1.0/2, 1.0/2, 0, -1.0/2, 0, 0, 0, 0, },
{ 0, -1.0/2, -1.0/2, 0, 1.0/2, 0, 0, 0, 0, },
},
{ /* 3 */
{ 0, 1.0/4, -1.0/4, -1.0/2, 0, 0, 0, 0, 0, },
{ 0, -3.0/4, -1.0/4, -1.0/2, 0, 0, 0, 0, 0, },
{ 0, 1.0/4, -1.0/4, 1.0/2, 0, 0, 0, 0, 0, },
},
{ /* 4 */
{ 0, 1.0/2, 0, 0, -1.0/2, 0, 0, 0, 0, },
{ 0, -1.0/2, 0, 0, -1.0/2, 0, 0, 0, 0, },
{ 0, -1.0/2, 0, -1, 1.0/2, 0, 0, 0, 0, },
},
{ /* 5 */
{ -1.0/4, 1.0/4, 0, -1.0/2, 0, 0, 0, 0, 0, },
{ -1.0/4, -3.0/4, 0, 1.0/2, 0, 0, 0, 0, 0, },
{ -1.0/4, 1.0/4, 0, 1.0/2, 0, 0, 0, 0, 0, },
},
{ /* 6 */
{ 0, 0, 1.0/2, -1.0/2, 0, 0, 0, 0, 0, },
{ 0, -1, -1.0/2, -1.0/2, 0, 0, 0, 0, 0, },
{ 0, 0, -1.0/2, -1.0/2, 0, 0, 0, 0, 0, },
},
{ /* 7 */
{ 0, -1.0/2, 0, -1.0/2, 0, -1.0/2, 0, 0, 0, },
{ 0, -1.0/2, 0, 1.0/2, 0, 1.0/2, 0, 0, 0, },
{ 0, -1.0/2, 0, 1.0/2, 0, -1.0/2, 0, 0, 0, },
},
{ /* 8 */
{ 0, 0, 1.0/2, -1.0/2, 0, 1.0/2, 0, 0, 0, },
{ 0, 0, 1.0/2, 1.0/2, 0, -1.0/2, 0, 0, 0, },
{ 0, 0, -1.0/2, -1.0/2, 0, -1.0/2, 0, 0, 0, },
},
{ /* 9 */
{ 0, 0, 0, 0, 0, 0, -1.0/2, 0, 0, },
{ 0, -1, 0, -1, 0, 0, 1.0/2, 0, 0, },
{ 0, 0, 0, 1, 0, 0, -1.0/2, 0, 0, },
},
{ /* 10 */
{ 0, 0, 0, 0, 0, 0, -1.0/2, 0, 0, },
{ 0, 0, -1, -2, 0, 0, 3.0/2, 0, 0, },
{ 0, 0, 0, 1, 0, 0, -1.0/2, 0, 0, },
},
};
static double cubic_I_VSpU[][3][9] =
{
{ /* 1 */
{ 0, -1, 0, -1, 0, 0, 0, 0, 0, },
{ 1, -1, 0, -1, 0, 0, 0, 0, 0, },
{ 0, -1, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 2 */
{ -1, 0, 1, -1, 0, 0, 0, 0, 0, },
{ 0, 0, 1, -1, 0, 0, 0, 0, 0, },
{ 1, 0, -1, 0, 0, 0, 0, 0, 0, },
},
{ /* 3 */
{ 1, 0, -1, -2, 0, -1, 0, 0, 0, },
{ 1, 0, -1, -1, 0, 0, 0, 0, 0, },
{ 1, 0, -1, -1, 0, -1, 0, 0, 0, },
},
{ /* 4 */
{ -1, 0, 1, 0, 0, -1, 0, 0, 0, },
{ 3, 0, -1, -3, 0, 2, 0, 0, 0, },
{ -3, 0, 1, 3, 0, -3, 0, 0, 0, },
},
{ /* 5 */
{ 1, 2, -5, -7, 0, 0, 0, 0, 0, },
{ 1, 1, -4, -5, 0, 0, 0, 0, 0, },
{ 0, 1, -2, -2, 0, 0, 0, 0, 0, },
},
{ /* 6 */
{ -2, 1, 0, 1, 0, 0, 0, 0, 0, },
{ 1, -1, 0, -1, 0, 0, 0, 0, 0, },
{ 2, -1, 0, -2, 0, 0, 0, 0, 0, },
},
{ /* 7 */
{ -1, 0, 0, 0, 0, -1, 0, 0, 0, },
{ -1, 0, 0, 1, 0, 0, 0, 0, 0, },
{ -1, 0, 0, 1, 0, -1, 0, 0, 0, },
},
{ /* 8 */
{ 1, 0, 0, 0, -2, 1, 0, 0, 0, },
{ -1, 0, 0, 0, 1, -1, 0, 0, 0, },
{ 1, 0, 0, 0, -1, 0, 0, 0, 0, },
},
{ /* 9 */
{ -2, -3, 0, -1, 0, 0, 1, -1, 1, },
{ -1, -3, 0, -1, 0, 0, 1, -1, 1, },
{ 0, -1, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 10 */
{ -1, 0, 0, 0, 0, -1, 0, -1, 1, },
{ -1, 0, 0, 1, 0, 0, 0, -1, 1, },
{ -1, 0, 0, 1, 0, -1, 0, -1, 1, },
},
};
static int cubic_generators[][3][9] =
{
{ /* 1 */
{ 0, -1, 0, 1, 0, 0, 0, 0, 1, },
{ 0, 0, 1, 1, 0, 0, 0, 1, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 2 */
{ 0, -1, 0, 1, 0, 0, 0, 0, 1, },
{ 0, 0, -1, -1, 0, 0, 0, -1, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 3 */
{ -1, 0, 0, 0, -1, 0, 0, 0, 1, },
{ 0, 0, 1, 1, 0, 0, 0, 1, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 4 */
{ -1, 0, 0, 0, -1, 0, 0, 0, 1, },
{ 0, 0, -1, -1, 0, 0, 0, -1, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 5 */
{ 0, 1, 0, -1, 0, 0, 0, 0, -1, },
{ 0, 0, 1, 1, 0, 0, 0, 1, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 6 */
{ 0, 1, 0, -1, 0, 0, 0, 0, -1, },
{ 0, 0, -1, -1, 0, 0, 0, -1, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 7 */
{ 1, 0, 0, 0, 1, 0, 0, 0, -1, },
{ 0, 0, 1, 1, 0, 0, 0, 1, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 8 */
{ 1, 0, 0, 0, 1, 0, 0, 0, -1, },
{ 0, 0, -1, -1, 0, 0, 0, -1, 0, },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, },
},
{ /* 9 */
{ 0, -1, 0, 1, 0, 0, 0, 0, 1, },
{ 0, 0, 1, 1, 0, 0, 0, 1, 0, },
{ -1, 0, 0, 0, -1, 0, 0, 0, -1, },
},
{ /* 10 */
{ -1, 0, 0, 0, -1, 0, 0, 0, 1, },
{ 0, 0, 1, 1, 0, 0, 0, 1, 0, },
{ -1, 0, 0, 0, -1, 0, 0, 0, -1, },
},
};
static int find_hall_symbol(double origin_shift[3],
SPGCONST double bravais_lattice[3][3],
const int hall_number,
const Centering centering,
SPGCONST Symmetry *symmetry,
const double symprec);
static int is_hall_symbol(double shift[3],
const int hall_number,
SPGCONST double primitive_lattice[3][3],
SPGCONST Symmetry *symmetry,
Centering centering,
SPGCONST int generators[3][9],
SPGCONST double VSpU[3][9],
const double symprec);
static int is_hall_symbol_cubic(double shift[3],
const int hall_number,
SPGCONST double primitive_lattice[3][3],
SPGCONST Symmetry *symmetry,
const Centering centering,
const double symprec);
static int is_hall_symbol_hexa(double shift[3],
const int hall_number,
SPGCONST double primitive_lattice[3][3],
SPGCONST Symmetry *symmetry,
const double symprec);
static int is_hall_symbol_rhombo(double shift[3],
const int hall_number,
SPGCONST double primitive_lattice[3][3],
SPGCONST Symmetry *symmetry,
const double symprec);
static int is_hall_symbol_trigonal(double shift[3],
const int hall_number,
SPGCONST double primitive_lattice[3][3],
SPGCONST Symmetry *symmetry,
const double symprec);
static int is_hall_symbol_tetra(double shift[3],
const int hall_number,
SPGCONST double primitive_lattice[3][3],
SPGCONST Symmetry *symmetry,
const Centering centering,
const double symprec);
static int is_hall_symbol_ortho(double shift[3],
const int hall_number,
SPGCONST double primitive_lattice[3][3],
SPGCONST Symmetry *symmetry,
const Centering centering,
const double symprec);
static int is_hall_symbol_monocli(double shift[3],
const int hall_number,
SPGCONST double primitive_lattice[3][3],
SPGCONST Symmetry *symmetry,
const Centering centering,
const double symprec);
static int is_hall_symbol_tricli(double shift[3],
const int hall_number,
SPGCONST double primitive_lattice[3][3],
SPGCONST Symmetry *symmetry,
const double symprec);
static int get_translations(double trans[3][3],
SPGCONST Symmetry *symmetry,
SPGCONST int rot[3][3][3]);
static void transform_translation(double trans_reduced[3],
const Centering centering,
const double trans[3]);
static void transform_rotation(double rot_reduced[3][3],
const Centering centering,
SPGCONST int rot[3][3]);
static int get_origin_shift(double shift[3],
const int hall_number,
SPGCONST int rot[3][3][3],
SPGCONST double trans[3][3],
const Centering centering,
SPGCONST double VSpU[3][9]);
static void unpack_generators(int rot[3][3][3], int generators[3][9]);
static int set_dw(double dw[3],
const int operation_index[2],
SPGCONST int rot[3][3],
const double trans[3],
const Centering centering);
static int is_match_database(const int hall_number,
const double shift[3],
SPGCONST double primitive_lattice[3][3],
const Centering centering,
SPGCONST Symmetry *symmetry,
const double symprec);
int hal_match_hall_symbol_db(double origin_shift[3],
SPGCONST double bravais_lattice[3][3],
const int hall_number,
const Centering centering,
SPGCONST Symmetry *symmetry,
const double symprec)
{
return find_hall_symbol(origin_shift,
bravais_lattice,
hall_number,
centering,
symmetry,
symprec);
}
static int find_hall_symbol(double origin_shift[3],
SPGCONST double bravais_lattice[3][3],
const int hall_number,
const Centering centering,
SPGCONST Symmetry *symmetry,
const double symprec)
{
double primitive_lattice[3][3];
switch (centering) {
case PRIMITIVE:
mat_copy_matrix_d3(primitive_lattice, bravais_lattice);
break;
case BODY:
mat_multiply_matrix_d3(primitive_lattice, bravais_lattice, M_bcc_inv);
break;
case FACE:
mat_multiply_matrix_d3(primitive_lattice, bravais_lattice, M_fcc_inv);
break;
case A_FACE:
mat_multiply_matrix_d3(primitive_lattice, bravais_lattice, M_ac_inv);
break;
case B_FACE:
mat_multiply_matrix_d3(primitive_lattice, bravais_lattice, M_bc_inv);
break;
case C_FACE:
mat_multiply_matrix_d3(primitive_lattice, bravais_lattice, M_cc_inv);
break;
case R_CENTER:
mat_multiply_matrix_d3(primitive_lattice, bravais_lattice, M_rc_inv);
break;
default:
break;
}
/* CUBIC IT: 195-230, Hall: 489-530 */
if (489 <= hall_number && hall_number <= 530) {
if (is_hall_symbol_cubic(origin_shift,
hall_number,
primitive_lattice,
symmetry,
centering,
symprec)) {goto found;}
return 0;
}
/* HEXA, IT: 168-194, Hall: 462-488 */
if (462 <= hall_number && hall_number <= 488) {
if (is_hall_symbol_hexa(origin_shift,
hall_number,
primitive_lattice,
symmetry,
symprec)) {goto found;}
return 0;
}
/* TRIGO, IT: 143-167, Hall: 430-461 */
if (430 <= hall_number && hall_number <= 461) {
if (centering == R_CENTER) {
if (is_hall_symbol_rhombo(origin_shift,
hall_number,
primitive_lattice,
symmetry,
symprec)) {goto found;}
} else {
if (is_hall_symbol_trigonal(origin_shift,
hall_number,
primitive_lattice,
symmetry,
symprec)) {goto found;}
}
return 0;
}
/* TETRA, IT: 75-142, Hall: 349-429 */
if (349 <= hall_number && hall_number <= 429) {
if (is_hall_symbol_tetra(origin_shift,
hall_number,
primitive_lattice,
symmetry,
centering,
symprec)) {goto found;}
return 0;
}
/* ORTHO, IT: 16-74, Hall: 108-348 */
if (108 <= hall_number && hall_number <= 348) {
if (is_hall_symbol_ortho(origin_shift,
hall_number,
primitive_lattice,
symmetry,
centering,
symprec)) {goto found;}
return 0;
}
/* MONOCLI, IT: 3-15, Hall: 3-107 */
if (3 <= hall_number && hall_number <= 107) {
if (is_hall_symbol_monocli(origin_shift,
hall_number,
primitive_lattice,
symmetry,
centering,
symprec)) {goto found;}
return 0;
}
/* TRICLI, IT: 1-2, Hall: 1-2 */
if (1 <= hall_number && hall_number <= 2) {
if (is_hall_symbol_tricli(origin_shift,
hall_number,
primitive_lattice,
symmetry,
symprec)) {goto found;}
return 0;
}
return 0;
found:
switch (centering) {
case PRIMITIVE:
break;
case BODY:
mat_multiply_matrix_vector_d3(origin_shift, M_bcc_inv, origin_shift);
break;
case FACE:
mat_multiply_matrix_vector_d3(origin_shift, M_fcc_inv, origin_shift);
break;
case A_FACE:
mat_multiply_matrix_vector_d3(origin_shift, M_ac_inv, origin_shift);
break;
case B_FACE:
mat_multiply_matrix_vector_d3(origin_shift, M_bc_inv, origin_shift);
break;
case C_FACE:
mat_multiply_matrix_vector_d3(origin_shift, M_cc_inv, origin_shift);
break;
case R_CENTER:
mat_multiply_matrix_vector_d3(origin_shift, M_rc_inv, origin_shift);
break;
default:
break;
}
return 1;
}
static int is_hall_symbol_cubic(double shift[3],
const int hall_number,
SPGCONST double primitive_lattice[3][3],
SPGCONST Symmetry *symmetry,
const Centering centering,
const double symprec)
{
int i;
for (i = 0; i < 10; i++) {
if (centering == PRIMITIVE) {
if (is_hall_symbol(shift,
hall_number,
primitive_lattice,
symmetry,
centering,
cubic_generators[i],
cubic_VSpU[i],
symprec)) {return 1;}
}
if (centering == BODY) {
if (is_hall_symbol(shift,
hall_number,
primitive_lattice,
symmetry,
centering,
cubic_generators[i],
cubic_I_VSpU[i],
symprec)) {return 1;}
}
if (centering == FACE) {
if (is_hall_symbol(shift,
hall_number,
primitive_lattice,
symmetry,
centering,
cubic_generators[i],
cubic_F_VSpU[i],
symprec)) {return 1;}
}
}
return 0;
}
static int is_hall_symbol_hexa(double shift[3],
const int hall_number,
SPGCONST double primitive_lattice[3][3],
SPGCONST Symmetry *symmetry,
const double symprec)
{
int i;
for (i = 0; i < 8; i++) {
if (is_hall_symbol(shift,
hall_number,
primitive_lattice,
symmetry,
PRIMITIVE,
hexa_generators[i],
hexa_VSpU[i],
symprec)) {return 1;}
}
return 0;
}
static int is_hall_symbol_trigonal(double shift[3],
const int hall_number,
SPGCONST double primitive_lattice[3][3],
SPGCONST Symmetry *symmetry,
const double symprec)
{
int i;
for (i = 0; i < 13; i++) {
if (is_hall_symbol(shift,
hall_number,
primitive_lattice,
symmetry,
PRIMITIVE,
trigo_generators[i],
trigo_VSpU[i],
symprec)) {return 1;}
}
return 0;
}
static int is_hall_symbol_rhombo(double shift[3],
const int hall_number,
SPGCONST double primitive_lattice[3][3],
SPGCONST Symmetry *symmetry,
const double symprec)
{
int i;
if (hall_number == 433 ||
hall_number == 436 ||
hall_number == 444 ||
hall_number == 450 ||
hall_number == 452 ||
hall_number == 458 ||
hall_number == 460) {
/* hP */
for (i = 0; i < 8; i++) {
if (is_hall_symbol(shift,
hall_number,
primitive_lattice,
symmetry,
R_CENTER,
rhombo_h_generators[i],
rhombo_h_VSpU[i],
symprec)) {return 1;}
}
} else {
/* hR */
for (i = 0; i < 8; i++) {
if (is_hall_symbol(shift,
hall_number,
primitive_lattice,
symmetry,
PRIMITIVE,
rhombo_p_generators[i],
rhombo_p_VSpU[i],
symprec)) {return 1;}
}
}
return 0;
}
static int is_hall_symbol_tetra(double shift[3],
const int hall_number,
SPGCONST double primitive_lattice[3][3],
SPGCONST Symmetry *symmetry,
const Centering centering,
const double symprec)
{
int i;
for (i = 0; i < 8; i++) {
if (centering==PRIMITIVE) {
if (is_hall_symbol(shift,
hall_number,
primitive_lattice,
symmetry,
centering,
tetra_generators[i],
tetra_VSpU[i],
symprec)) {return 1;}
}
if (centering==BODY) {
if (is_hall_symbol(shift,
hall_number,
primitive_lattice,
symmetry,
centering,
tetra_generators[i],
tetra_I_VSpU[i],
symprec)) {return 1;}
}
}
return 0;
}
static int is_hall_symbol_ortho(double shift[3],
const int hall_number,
SPGCONST double primitive_lattice[3][3],
SPGCONST Symmetry *symmetry,
const Centering centering,
const double symprec)
{
int i;
for (i = 0; i < 5; i++) {
if (centering == PRIMITIVE) {
if (is_hall_symbol(shift,
hall_number,
primitive_lattice,
symmetry,
centering,
ortho_generators[i],
ortho_VSpU[i],
symprec)) {return 1;}
}
if (centering == BODY) {
if (is_hall_symbol(shift,
hall_number,
primitive_lattice,
symmetry,
centering,
ortho_generators[i],
ortho_I_VSpU[i],
symprec)) {return 1;}
}
if (centering == FACE) {
if (is_hall_symbol(shift,
hall_number,
primitive_lattice,
symmetry,
centering,
ortho_generators[i],
ortho_F_VSpU[i],
symprec)) {return 1;}
}
if (centering == A_FACE) {
if (is_hall_symbol(shift,
hall_number,
primitive_lattice,
symmetry,
centering,
ortho_generators[i],
ortho_A_VSpU[i],
symprec)) {return 1;}
}
if (centering == B_FACE) {
if (is_hall_symbol(shift,
hall_number,
primitive_lattice,
symmetry,
centering,
ortho_generators[i],
ortho_B_VSpU[i],
symprec)) {return 1;}
}
if (centering == C_FACE) {
if (is_hall_symbol(shift,
hall_number,
primitive_lattice,
symmetry,
centering,
ortho_generators[i],
ortho_C_VSpU[i],
symprec)) {return 1;}
}
}
return 0;
}
static int is_hall_symbol_monocli(double shift[3],
const int hall_number,
SPGCONST double primitive_lattice[3][3],
SPGCONST Symmetry *symmetry,
const Centering centering,
const double symprec)
{
int i;
for (i = 0; i < 9; i++) {
if (centering == PRIMITIVE) {
if (is_hall_symbol(shift,
hall_number,
primitive_lattice,
symmetry,
centering,
monocli_generators[i],
monocli_VSpU[i],
symprec)) {return 1;}
}
if (centering == A_FACE) {
if (is_hall_symbol(shift,
hall_number,
primitive_lattice,
symmetry,
centering,
monocli_generators[i],
monocli_A_VSpU[i],
symprec)) {return 1;}
}
if (centering == B_FACE) {
if (is_hall_symbol(shift,
hall_number,
primitive_lattice,
symmetry,
centering,
monocli_generators[i],
monocli_B_VSpU[i],
symprec)) {return 1;}
}
if (centering == C_FACE) {
if (is_hall_symbol(shift,
hall_number,
primitive_lattice,
symmetry,
centering,
monocli_generators[i],
monocli_C_VSpU[i],
symprec)) {return 1;}
}
if (centering == BODY) {
if (is_hall_symbol(shift,
hall_number,
primitive_lattice,
symmetry,
centering,
monocli_generators[i],
monocli_I_VSpU[i],
symprec)) {return 1;}
}
}
return 0;
}
static int is_hall_symbol_tricli(double shift[3],
const int hall_number,
SPGCONST double primitive_lattice[3][3],
SPGCONST Symmetry *symmetry,
const double symprec)
{
int i;
for (i = 0; i < 2; i++) {
if (is_hall_symbol(shift,
hall_number,
primitive_lattice,
symmetry,
PRIMITIVE,
tricli_generators[i],
tricli_VSpU[i],
symprec)) {return 1;}
}
return 0;
}
static void unpack_generators(int rot[3][3][3], int generators[3][9])
{
int i, j, k;
for (i = 0; i < 3; i++) {
for (j = 0; j < 3; j++) {
for (k = 0; k < 3; k++) {
rot[i][j][k] = generators[i][j*3+k];
}
}
}
}
static int is_hall_symbol(double shift[3],
const int hall_number,
SPGCONST double primitive_lattice[3][3],
SPGCONST Symmetry *symmetry,
Centering centering,
SPGCONST int generators[3][9],
SPGCONST double VSpU[3][9],
const double symprec)
{
int is_origin_shift;
int operation_index[2];
int rot[3][3][3];
double trans[3][3];
spgdb_get_operation_index(operation_index, hall_number);
if (! (operation_index[0] == symmetry->size)) {
goto not_found;
}
unpack_generators(rot, generators);
if (get_translations(trans, symmetry, rot)) {
is_origin_shift = get_origin_shift(shift,
hall_number,
rot,
trans,
centering,
VSpU);
if (is_origin_shift) {
if (is_match_database(hall_number,
shift,
primitive_lattice,
centering,
symmetry,
symprec)) {goto found;}
}
} else {
goto not_found;
}
not_found:
return 0;
found:
return 1;
}
static int get_translations(double trans[3][3],
SPGCONST Symmetry *symmetry,
SPGCONST int rot[3][3][3])
{
int i, j;
int is_found;
static SPGCONST int zero[3][3] = { { 0, 0, 0 },
{ 0, 0, 0 },
{ 0, 0, 0 }, };
for (i = 0; i < 3; i++) {
for (j = 0; j < 3; j++) {
trans[i][j] = 0;
}
}
for (i = 0; i < 3; i++) {
if (mat_check_identity_matrix_i3(rot[i], zero)) { continue; }
is_found = 0;
for (j = 0; j < symmetry->size; j++) {
if (mat_check_identity_matrix_i3(symmetry->rot[j], rot[i])) {
mat_copy_vector_d3(trans[i], symmetry->trans[j]);
is_found = 1;
break;
}
}
if (! is_found) {
goto not_found;
}
}
return 1;
not_found:
return 0;
}
static void transform_translation(double trans_reduced[3],
const Centering centering,
const double trans[3])
{
int i;
switch (centering) {
case PRIMITIVE:
mat_copy_vector_d3(trans_reduced, trans);
break;
case BODY:
mat_multiply_matrix_vector_id3(trans_reduced, M_bcc, trans);
break;
case FACE:
mat_multiply_matrix_vector_id3(trans_reduced, M_fcc, trans);
break;
case A_FACE:
mat_multiply_matrix_vector_id3(trans_reduced, M_ac, trans);
break;
case B_FACE:
mat_multiply_matrix_vector_id3(trans_reduced, M_bc, trans);
break;
case C_FACE:
mat_multiply_matrix_vector_id3(trans_reduced, M_cc, trans);
break;
case R_CENTER:
mat_multiply_matrix_vector_id3(trans_reduced, M_rc, trans);
break;
default:
break;
}
for (i = 0; i < 3; i++) {
trans_reduced[i] = mat_Dmod1(trans_reduced[i]);
}
}
static void transform_rotation(double rot_reduced[3][3],
const Centering centering,
SPGCONST int rot[3][3])
{
mat_cast_matrix_3i_to_3d(rot_reduced, rot);
if (centering != PRIMITIVE) {
switch (centering) {
case BODY:
mat_get_similar_matrix_d3(rot_reduced, rot_reduced, M_bcc_inv, 0);
break;
case FACE:
mat_get_similar_matrix_d3(rot_reduced, rot_reduced, M_fcc_inv, 0);
break;
case A_FACE:
mat_get_similar_matrix_d3(rot_reduced, rot_reduced, M_ac_inv, 0);
break;
case B_FACE:
mat_get_similar_matrix_d3(rot_reduced, rot_reduced, M_bc_inv, 0);
break;
case C_FACE:
mat_get_similar_matrix_d3(rot_reduced, rot_reduced, M_cc_inv, 0);
break;
case R_CENTER:
mat_get_similar_matrix_d3(rot_reduced, rot_reduced, M_rc_inv, 0);
break;
default:
break;
}
}
}
static int get_origin_shift(double shift[3],
const int hall_number,
SPGCONST int rot[3][3][3],
SPGCONST double trans[3][3],
const Centering centering,
SPGCONST double VSpU[3][9])
{
int i, j;
int operation_index[2];
double dw[9], tmp_dw[3];
spgdb_get_operation_index(operation_index, hall_number);
/* The obtained dw is reduced to that of primitve cell by centerings. */
for (i = 0; i < 3; i++) {
/* Zero matrix is the sign to set dw 0 */
if (mat_get_determinant_i3(rot[i]) == 0) {
for (j = 0; j < 3; j++) {
dw[i * 3 + j] = 0;
}
} else {
if (set_dw(tmp_dw, operation_index, rot[i], trans[i], centering)) {
for (j = 0; j < 3; j++) {
dw[i * 3 + j] = tmp_dw[j];
}
} else {
goto not_found;
}
}
}
/* VSpU*dw is given for the primitive cell if there is centering. */
for (i = 0; i < 3; i++) {
shift[i] = 0;
for (j = 0; j < 9; j++) {
shift[i] += VSpU[i][j] * dw[j];
}
shift[i] = mat_Dmod1(shift[i]);
}
return 1;
not_found:
return 0;
}
static int set_dw(double dw[3],
const int operation_index[2],
SPGCONST int rot[3][3],
const double trans[3],
const Centering centering)
{
int i, j;
int rot_db[3][3];
double trans_db[3], trans_prim[3], trans_db_prim[3];
transform_translation(trans_prim, centering, trans);
for (i = 0; i < operation_index[0]; i++) {
spgdb_get_operation(rot_db, trans_db, operation_index[1] + i);
transform_translation(trans_db_prim, centering, trans_db);
if (mat_check_identity_matrix_i3(rot_db, rot)) {
for (j = 0; j < 3; j++) {
dw[j] = trans_prim[j] - trans_db_prim[j];
dw[j] = mat_Dmod1(dw[j]);
}
goto found;
}
}
/* Not found */
return 0;
found:
return 1;
}
static int is_match_database(const int hall_number,
const double origin_shift[3],
SPGCONST double primitive_lattice[3][3],
const Centering centering,
SPGCONST Symmetry *symmetry,
const double symprec)
{
int i, j, k, is_found;
int operation_index[2];
int rot_db[3][3];
int found_list[192];
double trans_db[3], trans_db_prim[3], trans_prim[3], diff[3], shift_rot[3];
double rot_prim[3][3];
spgdb_get_operation_index(operation_index, hall_number);
for (i = 0; i < symmetry->size; i++) {found_list[i] = 0;}
for (i = 0; i < symmetry->size; i++) {
is_found = 0;
for (j = 0; j < operation_index[0]; j++) {
spgdb_get_operation(rot_db, trans_db, operation_index[1] + j);
if (mat_check_identity_matrix_i3(symmetry->rot[i], rot_db)) {
transform_translation(trans_db_prim, centering, trans_db);
transform_translation(trans_prim, centering, symmetry->trans[i]);
transform_rotation(rot_prim, centering, rot_db);
for (k = 0; k < 3; k++) {
diff[k] = trans_prim[k] - trans_db_prim[k] + origin_shift[k];
}
mat_multiply_matrix_vector_d3(shift_rot, rot_prim, origin_shift);
if (cel_is_overlap(diff, shift_rot, primitive_lattice, symprec)) {
if (! found_list[j]) {
found_list[j] = 1;
is_found = 1;
break;
}
}
}
}
if (! is_found) {
goto not_found;
}
}
return 1;
not_found:
return 0;
}
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