354 lines
12 KiB
C
354 lines
12 KiB
C
/*! \file qpms_types.h
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* \brief Common qpms types.
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*/
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#ifndef QPMS_TYPES_H
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#define QPMS_TYPES_H
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#include <complex.h>
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#include <stdbool.h>
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#include <stddef.h>
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#include <stdint.h>
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#ifndef M_PI_2
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#define M_PI_2 (1.570796326794896619231321691639751442098584699687552910487)
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#endif
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#ifndef M_PI
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#define M_PI (3.14159265358979323846)
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#endif
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// integer index types
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typedef int qpms_lm_t;
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/// Type for spherical harmonic degree \a l.
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typedef int qpms_l_t; /* can't be unsigned because of the behaviour under the - operator;
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also -1 needed as an invalid value for scalar waves. */
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/// Type for spherical harmonic order \a m.
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typedef qpms_lm_t qpms_m_t;
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/// Type for the (\a l, \a m) multiindex of transversal (\a M or \a N -type) VSWFs.
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/** This corresponds to the typical memory layout for various coefficient etc.
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* Corresponds to the l-primary, m-secondary ordering, i.e.
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* \f[ y = 0: l = 1, m = -1, \f]
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* \f[ y = 1: l = 1, m = 0, \f]
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* \f[ y = 2: l = 1, m = +1, \f]
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* \f[ y = 3: l = 2, m = -2, \f]
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* ...
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*
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* See also indexing.h.
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*/
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typedef size_t qpms_y_t;
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/// Type for the (\a l, \a m) multiindex of spherical harmonics, including (0, 0).
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/** This differs from qpms_y_t by being shifted by one and including
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* the \a l = 0 option. Suitable also for scalar and longitudinal waves.
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* Corresponds to the \a l -primary, \a m -secondary ordering, i.e.
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* \f[ y = 0: l = 0, m = 0, \f]
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* \f[ y = 1: l = 1, m = -1, \f]
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* \f[ y = 2: l = 1, m = 0, \f]
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* \f[ y = 3: l = 1, m = +1, \f]
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* \f[ y = 4: l = 2, m = -2, \f]
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* ...
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*
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* See also indexing.h.
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*/
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typedef size_t qpms_y_sc_t;
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/// Codes of the VSWF types (electric/N, magnetic/M, longitudinal/L).
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typedef enum {
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QPMS_VSWF_ELECTRIC = 2, ///< "Electric" (\a N -type) transversal wave.
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QPMS_VSWF_MAGNETIC = 1, ///< "Magnetic" (\a M -type) transversal wave.
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QPMS_VSWF_LONGITUDINAL = 0 ///< Longitudinal (\a L -type) wave (not relevant for radiation).
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} qpms_vswf_type_t;
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// FIXME DOC The references to the functions do not work in doxygen:
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/// Exhaustive index type for VSWF basis functions.
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/** Carries information about the wave being of \a M/N/L (magnetic, electric,
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* or longitudinal) type, as well as the wave's degree and order (\a l, \a m).
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*
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* The formula is 4 * (qpms_y_sc_t) y_sc + (qmps_vswf_type_t) type_code,
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* but don't rely on this and use the functions
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* \ref qpms_tmn2uvswfi() and \ref qpms_uvswfi2tmn()
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* from qpms_types.h instead
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* as the formula might change in future versions.
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*
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* See also indexing.h.
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*/
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typedef unsigned long long qpms_uvswfi_t;
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/// Error codes / return values for certain numerical functions.
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/** These are de facto a subset of the GSL error codes. */
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typedef enum {
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QPMS_SUCCESS = 0, ///< Success.
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QPMS_ERROR = 1, ///< Unspecified error.
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QPMS_ENOMEM = 8 ///< Out of memory.
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} qpms_errno_t;
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/// Vector spherical wavefuction normalisation (and sign) convention codes.
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/** Throughout the literature, various conventions for VSWF bases are used.
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* The meaningful ones are the "power" and "spherical harmonic" normalisation
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* conventions, as the (\a l, \a m) and (\a l, \a −m) waves of the same type have the same
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* intensities.
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* One might also encounter a very inconvenient and messy "antinormalisation"
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* used in Xu (TODO reference).
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*
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* Moreover, VSWFs might use various sign convention. Usually they either
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* carry the Condon-Shortley phase \f$ (-1)^m \f$ or not, which is also saved here.
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*
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* TODO references and exact definitions.
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*/
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typedef enum {
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#define QPMS_NORMALISATION_T_CSBIT 128 ///< A flag used in qpms_normalisation_t indicating the Condon-Shortley phase.
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#ifdef USE_XU_ANTINORMALISATION
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// As in TODO
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QPMS_NORMALISATION_XU = 4, ///< such that the numerical values in Xu's tables match, not recommended to use otherwise
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QPMS_NORMALISATION_XU_CS = QPMS_NORMALISATION_XU | QPMS_NORMALISATION_T_CSBIT,
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#endif
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QPMS_NORMALISATION_NONE = 3, ///< genuine unnormalised waves (with unnormalised Legendre polynomials)
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QPMS_NORMALISATION_KRISTENSSON = 2, ///< As in http://www.eit.lth.se/fileadmin/eit/courses/eit080f/Literature/book.pdf, power-normalised
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QPMS_NORMALISATION_POWER = QPMS_NORMALISATION_KRISTENSSON,
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// as in TODO
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QPMS_NORMALISATION_TAYLOR = 1,
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QPMS_NORMALISATION_SPHARM = QPMS_NORMALISATION_TAYLOR,
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// Variants with Condon-Shortley phase
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QPMS_NORMALISATION_NONE_CS = QPMS_NORMALISATION_NONE | QPMS_NORMALISATION_T_CSBIT,
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QPMS_NORMALISATION_KRISTENSSON_CS = QPMS_NORMALISATION_KRISTENSSON | QPMS_NORMALISATION_T_CSBIT,
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QPMS_NORMALISATION_POWER_CS = QPMS_NORMALISATION_KRISTENSSON_CS,
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QPMS_NORMALISATION_TAYLOR_CS = QPMS_NORMALISATION_TAYLOR | QPMS_NORMALISATION_T_CSBIT,
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QPMS_NORMALISATION_SPHARM_CS = QPMS_NORMALISATION_TAYLOR_CS,
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QPMS_NORMALISATION_UNDEF = 0
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} qpms_normalisation_t;
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/// Determine whether the convention includes Condon-Shortley phase (-1) or not (+1).
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static inline int qpms_normalisation_t_csphase(qpms_normalisation_t norm) {
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return (norm & QPMS_NORMALISATION_T_CSBIT)? -1 : 1;
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}
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/// Returns the normalisation convention code without the Condon-Shortley phase.
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static inline int qpms_normalisation_t_normonly(qpms_normalisation_t norm) {
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return norm & (~QPMS_NORMALISATION_T_CSBIT);
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}
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// TODO move the inlines elsewhere
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/* Normalisation of the spherical waves is now scattered in at least three different files:
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* here, we have the norm in terms of radiated power of outgoing wave.
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* In file legendre.c, function qpms_pitau_get determines the norm used in the vswf.c
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* spherical vector wave norms. The "dual" waves in vswf.c use the ..._abssquare function below.
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* In file translations.c, the normalisations are again set by hand using the normfac and lognormfac
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* functions.
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*/
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#include <math.h>
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#include <assert.h>
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// relative to QPMS_NORMALISATION_KRISTENSSON_CS, i.e.
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// P_l^m[normtype] = P_l^m[Kristensson]
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static inline double qpms_normalisation_t_factor(qpms_normalisation_t norm, qpms_l_t l, qpms_m_t m) {
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int csphase = qpms_normalisation_t_csphase(norm);
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norm = qpms_normalisation_t_normonly(norm);
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double factor;
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switch (norm) {
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case QPMS_NORMALISATION_KRISTENSSON:
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factor = 1.;
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break;
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case QPMS_NORMALISATION_TAYLOR:
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factor = sqrt(l*(l+1));
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break;
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case QPMS_NORMALISATION_NONE:
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factor = sqrt(l*(l+1) * 4 * M_PI / (2*l+1) * exp(lgamma(l+m+1)-lgamma(l-m+1)));
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break;
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#ifdef USE_XU_ANTINORMALISATION // broken probably in legendre.c
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case QPMS_NORMALISATION_XU:
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factor = sqrt(4 * M_PI) / (2*l+1) * exp(lgamma(l+m+1)-lgamma(l-m+1));
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break;
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#endif
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default:
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assert(0);
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}
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factor *= (m%2)?(-csphase):1;
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return factor;
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}
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// TODO move elsewhere
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static inline double qpms_normalisation_t_factor_abssquare(qpms_normalisation_t norm, qpms_l_t l, qpms_m_t m) {
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norm = qpms_normalisation_t_normonly(norm);
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switch (norm) {
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case QPMS_NORMALISATION_KRISTENSSON:
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return 1.;
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break;
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case QPMS_NORMALISATION_TAYLOR:
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return l*(l+1);
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break;
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case QPMS_NORMALISATION_NONE:
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return l*(l+1) * 4 * M_PI / (2*l+1) * exp(lgamma(l+m+1)-lgamma(l-m+1));
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break;
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#ifdef USE_XU_ANTINORMALISATION // broken probably in legendre.c
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case QPMS_NORMALISATION_XU:
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{
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double fac = sqrt(4 * M_PI) / (2*l+1) * exp(lgamma(l+m+1)-lgamma(l-m+1));
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return fac * fac;
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}
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break;
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#endif
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default:
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assert(0);
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return NAN;
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}
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}
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/// Bessel function kinds.
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typedef enum {
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QPMS_BESSEL_REGULAR = 1, ///< regular (spherical) Bessel function \a j (Bessel function of the first kind)
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QPMS_BESSEL_SINGULAR = 2, ///< singular (spherical) Bessel function \a y (Bessel function of the second kind)
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QPMS_HANKEL_PLUS = 3, ///< (spherical) Hankel function \f$ h_1 = j + iy \f$
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QPMS_HANKEL_MINUS = 4, ///< (spherical) Hankel function \f$ h_2 = j - iy \f$
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QPMS_BESSEL_UNDEF = 0 ///< invalid / unspecified kind
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} qpms_bessel_t;
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// coordinate system types
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/// 3D cartesian coordinates. See also vectors.h.
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typedef struct cart3_t {
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double x, y, z;
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} cart3_t;
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/// 3D complex (actually 6D) coordinates. See also vectors.h.
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typedef struct ccart3_t {
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complex double x, y, z;
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} ccart3_t;
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/// 2D cartesian coordinates. See also vectors.h.
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/** See also vectors.h */
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typedef struct cart2_t {
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double x, y;
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} cart2_t;
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/// Spherical coordinates. See also vectors.h.
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typedef struct sph_t {
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double r, theta, phi;
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} sph_t;
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/// Spherical coordinates with complex radial component. See also vectors.h.
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typedef struct csph_t { // Do I really need this???
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complex double r;
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double theta, phi;
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} csph_t;
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/// 3D complex vector components in local spherical basis. See also vectors.h.
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typedef struct csphvec_t {
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complex double rc, thetac, phic;
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} csphvec_t;
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/// 2D polar coordinates. See also vectors.h.
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typedef struct pol_t {
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double r, phi;
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} pol_t;
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/// Union type capable to contain various 1D, 2D and 3D coordinates.
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typedef union anycoord_point_t {
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double z; ///< 1D cartesian coordinate.
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cart3_t cart3;
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cart2_t cart2;
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sph_t sph;
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pol_t pol;
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} anycoord_point_t;
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/// Enum codes for common coordinate systems.
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typedef enum {
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// IF EVER CHANGING THE CONSTANT VALUES HERE,
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// CHECK THAT THEY DO NOT CLASH WITH THOSE IN PGenPointFlags!
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QPMS_COORDS_CART1 = 64, ///< 1D cartesian (= double).
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QPMS_COORDS_POL = 128, ///< 2D polar.
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QPMS_COORDS_SPH = 256, ///< 3D spherical.
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QPMS_COORDS_CART2 = 512, ///< 2D cartesian.
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QPMS_COORDS_CART3 = 1024, ///< 3D cartesian.
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} qpms_coord_system_t;
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/// Quaternion type.
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/**
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* Internaly represented as a pair of complex numbers,
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* \f$ Q_a = Q_1 + iQ_z, Q_b = Q_y + i Q_x\f$.
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*
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* See wigner.h for "methods".
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*/
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typedef struct qpms_quat_t {
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complex double a, b;
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} qpms_quat_t;
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/// Quaternion type as four doubles.
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/** See wigner.h for "methods".
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*/
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typedef struct qpms_quat4d_t {
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double c1, ci, cj, ck;
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} qpms_quat4d_t;
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/// 3D improper rotations represented as a quaternion and a sign of the determinant.
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/** See wigner.h for "methods".
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*/
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typedef struct qpms_irot3_t {
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qpms_quat_t rot; ///< Quaternion representing the rotation part.
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short det; ///< Determinant of the transformation (valid values are 1 (rotation) or -1 (improper rotation)
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} qpms_irot3_t;
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/// Specifies a finite set of VSWFs.
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/**
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* When for example not all the M and N -type waves up to a degree lMax
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* need to be computed, this will specify the subset.
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*
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* A typical use case would be when only even/odd fields wrt. z-plane
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* mirror symmetry are considered.
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*
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* See vswf.h for "methods".
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*/
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typedef struct qpms_vswf_set_spec_t {
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size_t n; ///< Actual number of VSWF indices included in ilist.
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qpms_uvswfi_t *ilist; ///< List of wave indices.
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qpms_l_t lMax; ///< Maximum degree of the waves specified in ilist.
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qpms_l_t lMax_M, ///< Maximum degree of the magnetic (M-type) waves.
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lMax_N, ///< Maximum degree of the electric (N-type) waves.
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lMax_L; ///< Maximum degree of the longitudinal (L-type) waves.
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size_t capacity; ///< Allocated capacity of ilist.
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qpms_normalisation_t norm; ///< Normalisation convention. To be set manually if needed.
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} qpms_vswf_set_spec_t;
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/// T-matrix index used in qpms_scatsys_t and related structures.
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typedef int32_t qpms_ss_tmi_t;
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/// Particle index used in qpms_scatsys_t and related structures.
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typedef int32_t qpms_ss_pi_t;
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// These types are mainly used in groups.h:
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/// Finite group member index. See also groups.h.
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typedef int qpms_gmi_t;
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/// Irreducible representation index. See also groups.h.
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typedef int qpms_iri_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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/// A T-matrix.
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/** In the future, I might rather use a more abstract approach in which T-matrix
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* is a mapping (function) of the field expansion coefficients.
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* So the interface might change.
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* For now, let me stick to the square dense matrix representation.
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*/
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typedef struct qpms_tmatrix_t {
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/** \brief VSWF basis specification, NOT owned by qpms_tmatrix_t by default.
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*
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* Usually not checked for meaningfulness by the functions (methods),
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* so the caller should take care that \a spec->ilist does not
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* contain any duplicities and that for each wave with order \a m
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* there is also one with order \a −m.
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*/
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const qpms_vswf_set_spec_t *spec;
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complex double *m; ///< Matrix elements in row-major order.
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bool owns_m; ///< Information wheter m shall be deallocated with qpms_tmatrix_free()
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} qpms_tmatrix_t;
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#define lmcheck(l,m) assert((l) >= 1 && abs(m) <= (l))
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#endif // QPMS_TYPES
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