qpms_finite_group_t and hard-coded group code generator
Former-commit-id: dca27ced8fda8b33e86a89fdba802172d71d9c10
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Marek Nečada
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290cfbdd90
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c5600a8558
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/*! \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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#ifndef QPMS_GROUPS_H
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#define QPMS_GROUPS_H
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/// Group member index.
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typedef int qpms_gmi_t;
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/// Permutation representation of a group element.
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/** For now, it's just a string of the form "(0,1)(3,4,5)"
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*/
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typedef const char * qpms_permutation_t;
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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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size_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 *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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cmatrix3d rep3d[]; ///< The 'natural' 3D matrix representation of a 3D point group.
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int 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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#endif // QPMS_GROUPS_H
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@ -177,4 +177,8 @@ qpms_tmatrix_interpolator_t *qpms_tmatrix_interpolator_create(size_t n, ///< Num
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//, bool copy_bspec ///< if true, copies its own copy of basis spec from the first T-matrix.
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/*, ...? */);
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typedef struct qpms_scatsys_t {
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;
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} qpms_scatsys_t;
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#endif //QPMS_SCATSYSTEM_H
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@ -34,6 +34,7 @@ class SVWFPointGroupInfo: # only for point groups, coz in svwf_rep() I use I_tyt
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permgroupgens, # permutation group generators
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irrepgens_dict, # dictionary with irrep generators,
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svwf_rep_gen_func, # function that generates a tuple with svwf representation generators
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rep3d_gens = None, # 3d representation generators of a point group
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):
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self.name = name
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self.permgroupgens = permgroupgens
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@ -50,6 +51,13 @@ class SVWFPointGroupInfo: # only for point groups, coz in svwf_rep() I use I_tyt
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immultop = None if is1d else np.dot,
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imcmp = None if is1d else np.allclose
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)
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self.rep3d_gens = rep3d_gens
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self.rep3d = None if rep3d_gens is None else generate_grouprep(
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self.permgroup,
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np.eye(3),
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permgroupgens, rep3d_gens,
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immultop = np.dot, imcmp = np.allclose
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)
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def svwf_rep(self, lMax, *rep_gen_func_args, **rep_gen_func_kwargs):
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'''
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@ -71,6 +79,88 @@ class SVWFPointGroupInfo: # only for point groups, coz in svwf_rep() I use I_tyt
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def svwf_irrep_projectors2_w_bases(self, lMax, *rep_gen_func_args, **rep_gen_func_kwargs):
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return gen_point_group_svwfrep_projectors2_w_bases(self.permgroup, self.irreps, self.svwf_rep(lMax, *rep_gen_func_args, **rep_gen_func_kwargs))
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def generate_c_source(self):
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'''
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Generates a string with a chunk of C code with a definition of a qpms_finite_group_t instance.
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See also groups.h.
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'''
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self = point_group_info['D3h']
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permlist = list(self.permgroup.elements) # all elements ordered
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order = len(permlist)
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permindices = {perm: i for i, perm in enumerate(permlist)} # 'invert' permlist
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identity = self.permgroup.identity
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s = "{\n"
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# char *name
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s += ' "%s", // name\n' % self.name
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# size_t order;
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s += ' %d, // order\n' % order
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# qpms_gmi_t idi
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s += ' %d, // idi\n' % permindices[identity]
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# qpms_gmi_t *mt
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s += ' { // mt\n'
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for i in range(order):
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ss = ', '.join([str(permindices[permlist[i]*permlist[j]]) for j in range(order)])
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s += ' ' + ss + ',\n'
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s += ' },\n'
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# qpms_gmi_t *gens
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s += ' {' + ', '.join([str(permindices[g]) for g in self.permgroupgens]) + '}, // gens\n'
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# int ngens
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s += ' %d, // ngens\n' % len(self.permgroupgens)
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# qpms_permutation_t permrep[]
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s += ' { // permrep\n'
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for i in range(order):
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s += ' "%s",\n' % str(permlist[i])
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s += ' }\n'
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# char **elemlabels
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s += ' NULL, // elemlabels\n'
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# int permrep_nelem
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s += ' %d, // permrep_nelem\n' % self.permgroup.degree
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# cmatrix3d rep3d[]
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if True: #self.rep3d is None:
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s += ' NULL, // rep3d TODO!!!\n'
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else:
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s += ' { // rep3d\n'
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for i in range(order):
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s += ' { '
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s += '\n '.join(
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['{' + ' ,'.join([str(rep3d[permlist[i]][row][col]) for col in range(3)])
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+'}' for row in range(3) ]
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)
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s += '\n },\n'
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s += ' },\n'
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# int nirreps
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s += ' %d, // nirreps\n' % len(self.irreps)
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# struct qpms_finite_grep_irrep_t irreps[]
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s += ' { // irreps\n'
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for irname, irrep in self.irreps.items():
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s += ' {\n'
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is1d = isinstance(irrep[identity], (int, float, complex))
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dim = 1 if is1d else irrep[identity].shape[0]
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# int dim
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s += ' %d, // dim\n' % dim
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# char name[]
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s += ' "%s", //name\n' % re.escape(irname)
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# complex double *m
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if (is1d):
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s += ' {' + ', '.join([str(irrep[permlist[i]]) for i in range(order)]) + '} // m\n'
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else:
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s += ' {\n'
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for i in range(order):
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s += ' // %s\n' % str(permlist[i])
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for row in range(dim):
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s += ' '
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for col in range(dim):
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s += '%s, ' % re.sub('j', '*I', str(irrep[permlist[i]][row,col]))
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s += '\n'
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mat = irrep[permlist[i]]
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s += ' }\n'
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#s += ' %d, // dim\n' %
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s += ' },\n'
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s += ' } // end of irreps\n'
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s += '}'
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return s
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# srcgroup is expected to be PermutationGroup and srcgens of the TODO
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# imcmp returns True if two elements of the image group are 'equal', otherwise False
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@ -248,4 +248,8 @@ static inline double csphvec_reldiff(const csphvec_t a, const csphvec_t b) {
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return csphvec_reldiff_abstol(a, b, 0);
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}
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typedef double[3][3] matrix3d;
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typedef double[2][2] matrix2d;
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typedef complex double[3][3] cmatrix3d;
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typedef complex double[2][2] cmatrix2d;
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#endif //VECTORS_H
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