97 lines
3.7 KiB
C
97 lines
3.7 KiB
C
/*! \file groups.h
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* \brief Point groups.
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*
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* Right now, the instances of qpms_finite_group_t are created at compilation time
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* from source code generated by Python script TODO (output groups.c)
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* and they are not to be constructed dynamically.
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*
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* In the end, I might want to have a special type for 3D point groups
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* or more specifically, for the closed subgroups of O(3), see
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* https://en.wikipedia.org/wiki/Point_groups_in_three_dimensions.
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* They consist of the seven infinite series of axial groups
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* (characterized by the series index, the axis direction,
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* and the index \a n of the \a n-fold rotational symmetry)
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* and the seven remaining point groups + the finite groups.
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* All off them have a quite limited number of generators
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* (max. 4?; CHECKME).
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* The goal is to have some representation that would enable to
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* 1. fully describe the symmetries of abstract T-matrices/nanoparticles,
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* 2. quickly determine e.g. whether one is a subgroup of another,
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* 3. have all the irreps,
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* 4. have all in C and without excessive external dependencies,
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* etc.
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*/
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#ifndef QPMS_GROUPS_H
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#define QPMS_GROUPS_H
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#include "qpms_types.h"
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#include <assert.h>
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/// To be used only in qpms_finite_group_t
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struct qpms_finite_group_irrep_t {
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int dim; ///< Irrep dimension.
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char *name; ///< Irrep label.
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/// Irrep matrix data.
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/** The r-th row, c-th column of the representation of the i'th element is retrieved as
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* m[i * dim * dim + r * dim + c]
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*/
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complex double *m;
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};
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/// A point group with its irreducible representations and some metadata.
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/**
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* The structure of the group is given by the multiplication table \a mt.
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*
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* Each element of the group has its index from 0 to order.
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* The metadata about some element are then accessed using that index.
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*
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* All members are in principle optional except \a order and \a mt.
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*
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* Note: after changing this struct, don't forget to update the Python method
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* SVWFPointGroupInfo.generate_c_source().
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*/
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typedef struct qpms_finite_group_t {
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char *name;
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qpms_gmi_t order; ///< Group order (number of elements)
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qpms_gmi_t idi; ///< Identity element index
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qpms_gmi_t *mt; ///< Group multiplication table. If c = a*b, then ic = mt[order * ia + ib].
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qpms_gmi_t *invi; ///< Group elem inverse indices.
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qpms_gmi_t *gens; ///< A canonical set of group generators.
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int ngens; ///< Number of the generators in gens;
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qpms_permutation_t *permrep; ///< Permutation representations of the elements.
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char **elemlabels; ///< Optional human readable labels for the group elements.
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int permrep_nelem; ///< Number of the elements over which the permutation representation acts.
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struct qpms_irot3_t *rep3d; ///< The quaternion representation of a 3D point group (if applicable).
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qpms_iri_t nirreps; ///< How many irreps does the group have
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struct qpms_finite_group_irrep_t *irreps; ///< Irreducible representations of the group.
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} qpms_finite_group_t;
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/// Group multiplication.
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static inline qpms_gmi_t qpms_finite_group_mul(const qpms_finite_group_t *G,
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qpms_gmi_t a, qpms_gmi_t b) {
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assert(a < G->order);
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assert(b < G->order);
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return G->mt[G->order * a + b];
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}
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/// Group element inversion.
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static inline qpms_gmi_t qpms_finite_group_inv(const qpms_finite_group_t *G,
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qpms_gmi_t a) {
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assert(a < G->order);
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return G->invi[a];
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}
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static inline _Bool qpms_iri_is_valid(const qpms_finite_group_t *G, qpms_iri_t iri) {
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return (iri > G->nirreps || iri < 0) ? 0 : 1;
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}
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/// NOT IMPLEMENTED Get irrep index by name.
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qpms_iri_t qpms_finite_group_find_irrep_by_name(qpms_finite_group_t *G, char *name);
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extern const qpms_finite_group_t QPMS_FINITE_GROUP_TRIVIAL;
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extern const qpms_finite_group_t QPMS_FINITE_GROUP_TRIVIAL_G;
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#endif // QPMS_GROUPS_H
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