qpms/symmetries.h

   1 /*! \file symmetries.h
   2  * \brief Functions providing point group operations operating on translation
   3  * operators and T-matrices.
   4  *
   5  * Here will be functions providing point group operations
   6  * operating on translation operators and T-matrices
   7  * similar to tmatrices.py.
   8  *
   9  * At least I want:
  10  * - Wigner D matrices
  11  * - Basic mirror operations for T-matrices
  12  * - Inversion operation for the translation matrices
  13  *
  14  * Maybe (much later) also point and space group irrep
  15  * functionality as in symmetries.py.
  16  * However, I think that the group structures can be simply
  17  * hard-coded/generated by a python script, then there is
  18  * no need to check the group consistency etc. at runtime.
  19  *
  20  *
  21  */
  22 #ifndef SYMMETRIES_H
  23 #define SYMMETRIES_H
  24 #include "qpms_types.h"
  25 #include <cblas.h>
  26
  27 /// Dense matrix representation of the z coordinate sign flip operation (xy-plane mirroring).
  28 complex double *qpms_zflip_uvswi_dense(
  29                 complex double *target, ///< If NULL, a new array is allocated.
  30                 const qpms_vswf_set_spec_t *bspec);
  31 /// Dense matrix representation of the y coordinate sign flip operation (xz-plane mirroring).
  32 complex double *qpms_yflip_uvswi_dense(
  33                 complex double *target, ///< If NULL, a new array is allocated.
  34                 const qpms_vswf_set_spec_t *bspec);
  35 /// Dense matrix representation of the x coordinate sign flip operation (yz-plane mirroring).
  36 complex double *qpms_xflip_uvswi_dense(
  37                 complex double *target, ///< If NULL, a new array is allocated.
  38                 const qpms_vswf_set_spec_t *bspec);
  39 /// Dense matrix representation of a rotation around the z-axis
  40 complex double *qpms_zrot_uvswi_dense(
  41                 complex double *target, ///< If NULL, a new array is allocated.
  42                 const qpms_vswf_set_spec_t *bspec,
  43                 double phi ///< Rotation angle
  44                 );
  45 /// Dense matrix representation of a "rational" rotation around the z-axis
  46 /** Just for convenience. Corresponds to the angle \f$ \phi = 2\piw/N \f$.
  47  */
  48 complex double *qpms_zrot_rational_uvswi_dense(
  49                 complex double *target, ///< If NULL, a new array is allocated.
  50                 const qpms_vswf_set_spec_t *bspec,
  51                 int N,
  52                 int w
  53                 );
  54
  55 /// Dense matrix (uvswi-indexed) representation of any O(3) transformation.
  56 complex double *qpms_irot3_uvswfi_dense(
  57                 complex double *target, ///< If NULL, a new array is allocated.
  58                 const qpms_vswf_set_spec_t *bspec,
  59                 const qpms_irot3_t transf);
  60
  61 // Some auxilliary functions for "numerical cleaning" of the roundoff error
  62
  63 /// Cleans the roundoff error of an array.
  64 /**
  65  * Replaces all the array members \a x for which |\a x| <= \a atol
  66  * with exact zeros.
  67  *
  68  * Returns the count of modified array members.
  69  */
  70 size_t qpms_zero_roundoff_clean(double *arr, size_t nmemb, double atol);
  71
  72 /// Cleans the roundoff error of an array.
  73 /**
  74  * Works on real and imaginary parts separately.
  75  * TODO doc.
  76  */
  77 size_t qpms_czero_roundoff_clean(complex double *arr, size_t nmemb, double atol);
  78 #endif // SYMMETRIES_H