Point group element generator and subgroup testing

Former-commit-id: 8d3e89facdac8e0744ada736d5b7453f23dc9ddc
This commit is contained in:
Marek Nečada 2019-07-24 14:20:50 +03:00
parent 36ea30952c
commit 6a34c71017
4 changed files with 55 additions and 2 deletions

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@ -1,5 +1,6 @@
#include "pointgroups.h" #include "pointgroups.h"
#include <search.h> #include <search.h>
#include <stdlib.h>
#define PAIRCMP(a, b) {\ #define PAIRCMP(a, b) {\
if ((a) < (b)) return -1;\ if ((a) < (b)) return -1;\
@ -89,6 +90,37 @@ qpms_irot3_t *qpms_pg_canonical_elems(qpms_irot3_t *target,
return target; return target;
} }
qpms_irot3_t *qpms_pg_elems(qpms_irot3_t *target, qpms_pointgroup_t g) {
QPMS_UNTESTED;
target = qpms_pg_canonical_elems(target, g.c, g.n);
qpms_gmi_t order = qpms_pg_order(g.c, g.n);
const qpms_irot3_t o = g.orientation, o_inv = qpms_irot3_inv(o);
for(qpms_gmi_t i = 0 ; i < order; ++i)
target[i] = qpms_irot3_mult(o_inv, qpms_irot3_mult(target[i], o));
return target;
}
_Bool qpms_pg_is_subgroup(qpms_pointgroup_t small, qpms_pointgroup_t big) {
QPMS_UNTESTED;
qpms_gmi_t order_big = qpms_pg_order(big.c, big.n);
qpms_gmi_t order_small = qpms_pg_order(small.c, small.n);
if (!order_big || !order_small)
QPMS_NOT_IMPLEMENTED("Subgroup testing for infinite groups not implemented");
if (order_big < order_small) return false;
// TODO maybe some other fast-track negative decisions
qpms_irot3_t *elems_small = qpms_pg_elems(NULL, small);
qpms_irot3_t *elems_big = qpms_pg_elems(NULL, small);
qsort(elems_big, order_big, sizeof(qpms_irot3_t), qpms_pg_irot3_cmp_v);
for(qpms_gmi_t smalli = 0; smalli < order_small; ++smalli) {
qpms_irot3_t *match = bsearch(&elems_small[smalli], elems_big, order_big,
sizeof(qpms_irot3_t), qpms_pg_irot3_approx_cmp_v);
if (!match) return false;
}
return true;
}
/// Returns the order of a given 3D point group type. /// Returns the order of a given 3D point group type.
/** For infinite groups returns 0. */ /** For infinite groups returns 0. */

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@ -74,4 +74,16 @@ qpms_gmi_t qpms_pg_genset(qpms_pointgroup_class cls, ///< Point group class.
qpms_irot3_t gen[] ///< Target generator array qpms_irot3_t gen[] ///< Target generator array
); );
/// Generates all elements of a given point group.
/** The order of elements corresponds to the one obtained from qpms_pg_canonical_elems().
*/
qpms_irot3_t *qpms_pg_elems(qpms_irot3_t *target, ///< Target array (optional; if NULL, a new one is allocated)
qpms_pointgroup_t g ///< Specification of the point group.
);
/// Checks whether \a a is subgroup of \a b (in a dirty general way).
_Bool qpms_pg_is_subgroup(qpms_pointgroup_t a, qpms_pointgroup_t b);
#endif //POINTGROUPS_H #endif //POINTGROUPS_H

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@ -366,7 +366,7 @@ typedef enum {
/// Full characterisation of a 3D point group. /// Full characterisation of a 3D point group.
typedef struct qpms_pointgroup_t { typedef struct qpms_pointgroup_t {
qpms_pointgroup_class c; ///< Point group classification. qpms_pointgroup_class c; ///< Point group classification.
size_t n; ///< Order of the rotational subgroup \f$ \mathrm{C_n} \f$ of finite axial groups. qpms_gmi_t n; ///< Order of the rotational subgroup \f$ \mathrm{C_n} \f$ of finite axial groups.
/// Transformation between this point group and the "canonical" point group of the same type. /// Transformation between this point group and the "canonical" point group of the same type.
/** /**
* Each 3D point group of a given type (specified by the \a c * Each 3D point group of a given type (specified by the \a c

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@ -203,6 +203,15 @@ static inline qpms_irot3_t qpms_irot3_mult(const qpms_irot3_t p, const qpms_irot
return r; return r;
} }
/// Improper rotation inverse operation.
static inline qpms_irot3_t qpms_irot3_inv(qpms_irot3_t p) {
#ifndef NDEBUG
qpms_irot3_checkdet(p);
#endif
p.rot = qpms_quat_inv(p.rot);
return p;
}
/// Improper rotation power \f$ p^n \f$. /// Improper rotation power \f$ p^n \f$.
static inline qpms_irot3_t qpms_irot3_pow(const qpms_irot3_t p, int n) { static inline qpms_irot3_t qpms_irot3_pow(const qpms_irot3_t p, int n) {
#ifndef NDEBUG #ifndef NDEBUG