Functions providing point group operations operating on translation operators and T-matrices. More...

#include "qpms_types.h"
#include <cblas.h>

Include dependency graph for symmetries.h:

Functions
complex double *	qpms_zflip_uvswi_dense (complex double target, const qpms_vswf_set_spec_t bspec)
	Dense matrix representation of the z coordinate sign flip operation (xy-plane mirroring). More...

complex double *	qpms_yflip_uvswi_dense (complex double target, const qpms_vswf_set_spec_t bspec)
	Dense matrix representation of the y coordinate sign flip operation (xz-plane mirroring). More...

complex double *	qpms_xflip_uvswi_dense (complex double target, const qpms_vswf_set_spec_t bspec)
	Dense matrix representation of the x coordinate sign flip operation (yz-plane mirroring). More...

complex double *	qpms_zrot_uvswi_dense (complex double target, const qpms_vswf_set_spec_t bspec, double phi)
	Dense matrix representation of a rotation around the z-axis. More...

complex double *	qpms_zrot_rational_uvswi_dense (complex double target, const qpms_vswf_set_spec_t bspec, int N, int w)
	Dense matrix representation of a "rational" rotation around the z-axis. More...

complex double *	qpms_irot3_uvswfi_dense (complex double target, const qpms_vswf_set_spec_t bspec, const qpms_irot3_t transf)
	Dense matrix (uvswi-indexed) representation of any O(3) transformation. More...

size_t	qpms_zero_roundoff_clean (double *arr, size_t nmemb, double atol)
	Cleans the roundoff error of an array. More...

size_t	qpms_czero_roundoff_clean (complex double *arr, size_t nmemb, double atol)
	Cleans the roundoff error of an array. More...

Detailed Description

Functions providing point group operations operating on translation operators and T-matrices.

Here will be functions providing point group operations operating on translation operators and T-matrices similar to tmatrices.py.

At least I want:

Wigner D matrices
Basic mirror operations for T-matrices
Inversion operation for the translation matrices

Maybe (much later) also point and space group irrep functionality as in symmetries.py. However, I think that the group structures can be simply hard-coded/generated by a python script, then there is no need to check the group consistency etc. at runtime.

Function Documentation

◆ qpms_czero_roundoff_clean()

size_t qpms_czero_roundoff_clean	(	complex double *	arr,
		size_t	nmemb,
		double	atol
	)

Cleans the roundoff error of an array.

Works on real and imaginary parts separately. TODO doc.

◆ qpms_irot3_uvswfi_dense()

complex double* qpms_irot3_uvswfi_dense	(	complex double *	target,
		const qpms_vswf_set_spec_t *	bspec,
		const qpms_irot3_t	transf
	)

Dense matrix (uvswi-indexed) representation of any O(3) transformation.

Parameters

target If NULL, a new array is allocated.

◆ qpms_xflip_uvswi_dense()

complex double* qpms_xflip_uvswi_dense	(	complex double *	target,
		const qpms_vswf_set_spec_t *	bspec
	)

Dense matrix representation of the x coordinate sign flip operation (yz-plane mirroring).

Parameters

target If NULL, a new array is allocated.

◆ qpms_yflip_uvswi_dense()

complex double* qpms_yflip_uvswi_dense	(	complex double *	target,
		const qpms_vswf_set_spec_t *	bspec
	)

Dense matrix representation of the y coordinate sign flip operation (xz-plane mirroring).

Parameters

target If NULL, a new array is allocated.

◆ qpms_zero_roundoff_clean()

size_t qpms_zero_roundoff_clean	(	double *	arr,
		size_t	nmemb,
		double	atol
	)

Cleans the roundoff error of an array.

Replaces all the array members x for which |x| <= atol with exact zeros.

Returns the count of modified array members.

◆ qpms_zflip_uvswi_dense()

complex double* qpms_zflip_uvswi_dense	(	complex double *	target,
		const qpms_vswf_set_spec_t *	bspec
	)

Dense matrix representation of the z coordinate sign flip operation (xy-plane mirroring).

Parameters

target If NULL, a new array is allocated.

◆ qpms_zrot_rational_uvswi_dense()

complex double* qpms_zrot_rational_uvswi_dense	(	complex double *	target,
		const qpms_vswf_set_spec_t *	bspec,
		int	N,
		int	w
	)

Dense matrix representation of a "rational" rotation around the z-axis.

Just for convenience. Corresponds to the angle \( \phi = 2\piw/N \).

Parameters

target If NULL, a new array is allocated.

◆ qpms_zrot_uvswi_dense()

complex double* qpms_zrot_uvswi_dense	(	complex double *	target,
		const qpms_vswf_set_spec_t *	bspec,
		double	phi
	)

Dense matrix representation of a rotation around the z-axis.

Parameters

target	If NULL, a new array is allocated.
phi	Rotation angle