236 lines
10 KiB
C
236 lines
10 KiB
C
/*! \file vswf.h
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* \brief Vector spherical wavefunctions.
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*
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* N.B. for the Legendre polynomial norm definitions, see
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* <a href="https://www.gnu.org/software/gsl/doc/html/specfunc.html#associated-legendre-polynomials-and-spherical-harmonics">the corresponding section of GSL docs</a>
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* or <a href="http://git.savannah.gnu.org/cgit/gsl.git/tree/specfunc/legendre_source.c">gsl/specfunc/legendre_source.c</a>.
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*/
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#ifndef QPMS_VSWF_H
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#define QPMS_VSWF_H
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#include <unistd.h> // ssize_t
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#include "qpms_types.h"
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#include <gsl/gsl_sf_legendre.h>
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// -------------- Typedefs (function prototypes) for qpms_vswf_spec_t ----------------------
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/// Calculates the (regular VSWF) expansion coefficients of an external incident field.
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typedef qpms_errno_t (*qpms_incfield_t)(
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/// Target non-NULL array of the regular VSWF expansion coefficients of length bspec->n.
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complex double *target,
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const qpms_vswf_set_spec_t *bspec,
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const cart3_t evalpoint, ///< Point at which the VSWF expansion is made.
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const void *args, ///< Pointer to additional function-specific arguments.
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bool add ///< If true, add to target; rewrite target if false.
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);
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// ---------------Methods for qpms_vswf_set_spec_t-----------------------
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//
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/// Creates a qpms_vswf_set_spec_t structure with an empty list of wave indices.
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qpms_vswf_set_spec_t *qpms_vswf_set_spec_init(void);
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/// Appends a VSWF index to a \ref qpms_vswf_set_spec_t, also updating metadata.
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qpms_errno_t qpms_vswf_set_spec_append(qpms_vswf_set_spec_t *self, qpms_uvswfi_t u);
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/// Destroys a \ref qpms_vswf_set_spec_t.
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void qpms_vswf_set_spec_free(qpms_vswf_set_spec_t *);
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/// Compares two vswf basis specs.
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/**
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* Checks whether ilist is the same and of the same length.
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* If yes, returns true, else returns false.
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*/
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bool qpms_vswf_set_spec_isidentical(const qpms_vswf_set_spec_t *a,
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const qpms_vswf_set_spec_t *b);
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/// Copies an instance of qpms_vswf_set_spec_t
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qpms_vswf_set_spec_t *qpms_vswf_set_spec_copy(const qpms_vswf_set_spec_t *orig);
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/// Creates an instance of qpms_vswf_set_spec_t in the 'traditional' layout.
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qpms_vswf_set_spec_t *qpms_vswf_set_spec_from_lMax(qpms_l_t lMax,
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qpms_normalisation_t norm);
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/// Finds the position of a given index in the bspec's ilist.
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/** If not found, returns -1. */
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// TODO more consistency in types (here size_t vs. ptrdiff_t).
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static inline ssize_t qpms_vswf_set_spec_find_uvswfi(const qpms_vswf_set_spec_t *bspec,
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const qpms_uvswfi_t index) {
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for(size_t i = 0; i < bspec->n; ++i)
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if (bspec->ilist[i] == index)
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return i;
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return -1;
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}
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/// Creates an index mapping between two bspecs.
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/**
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* Creates an array r such that small->ilist[i] == big->ilist[r[i]].
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* It's not lossless if the two bspecs contain different combinations of waves.
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*
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* Preferably, big->ilist contains everything small->ilist does.
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* If small->ilist[i] is not found in big->ilist, r[i] will be set to ~(size_t)0.
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*
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* Discard with free() after use.
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*/
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size_t *qpms_vswf_set_reindex(const qpms_vswf_set_spec_t *small, const qpms_vswf_set_spec_t *big);
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/// Evaluates a set of VSWF basis functions at a given point.
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/** The list of basis wave indices is specified in \a setspec;
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* \a setspec->norm must be set as well.
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*/
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qpms_errno_t qpms_uvswf_fill(
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csphvec_t *const target, ///< Target array of size at least setspec->n.
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const qpms_vswf_set_spec_t *setspec,
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csph_t kr, ///< Evaluation point.
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qpms_bessel_t btyp);
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/// Evaluates field specified by SVWF coefficients at a given point.
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/** SVWF coefficients in \a coeffs must be ordered according to \a setspec->ilist.
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*/
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csphvec_t qpms_eval_uvswf(const qpms_vswf_set_spec_t *setspec,
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const complex double *coeffs, ///< SVWF coefficient vector of size setspec->n.
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csph_t kr, ///< Evaluation point.
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qpms_bessel_t btyp);
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// --- qpms_incfield_t instances and their arguments
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/// Parameter structure for qpms_incfield_planewave()
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typedef struct qpms_incfield_planewave_params_t {
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bool use_cartesian; ///< If true, wave direction k and amplitude E are specified in cartesian coordinates (via k.cart, E.cart). If false, k is specified in spherical coordinates and E are specified in the corresponding geographical coordinates (via k.sph, E.sph).
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union {
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ccart3_t cart;
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csph_t sph;
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} k; ///< Wave vector.
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union {
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ccart3_t cart;
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csphvec_t sph;
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} E; ///< Electric field amplitude at origin.
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} qpms_incfield_planewave_params_t;
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/// Calculates the (regular VSWF) expansion coefficients of a plane wave.
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/** The wave amplitude and wave vector is defined by struct qpms_incfield_planewave_params_t.
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*
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* If the wave vector and amplitude are not orthogonal (i.e. the plane wave is not
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* fully transversal) and bspec->lMaxL is non-negative,
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* the corresponding longitudinal components are calculated as well.
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*
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* For complex k vectors, the implementation is not completely correct right now.
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* Locally, it corresponds to decomposition of a plane wave with a real \a k
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* (using the real part of the \a k supplied), just the whole decomposition
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* is modulated by the origin-dependent factor \f$ \vect E e^{i \vect k \cdot \vect r} \f$
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* with \f$ \vect k \f$ complex.
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*/
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qpms_errno_t qpms_incfield_planewave(
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/// Target non-NULL array of the regular VSWF expansion coefficients of length bspec->n.
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complex double *target,
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const qpms_vswf_set_spec_t *bspec,
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const cart3_t evalpoint, ///< Point at which the VSWF expansion is made.
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const void *args, ///< Pointer to additional function-specific arguments (converted to (const qpms_incfield_planewave_params_t *)).
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bool add ///< If true, add to target; rewrite target if false.
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);
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// -----------------------------------------------------------------------
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/// Electric wave N.
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csphvec_t qpms_vswf_single_el(qpms_m_t m, qpms_l_t n, sph_t kdlj,
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qpms_bessel_t btyp, qpms_normalisation_t norm);
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/// Magnetic wave M.
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csphvec_t qpms_vswf_single_mg(qpms_m_t m, qpms_l_t n, sph_t kdlj,
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qpms_bessel_t btyp, qpms_normalisation_t norm);
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/// Electric wave N, complex wave number version.
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csphvec_t qpms_vswf_single_el_csph(qpms_m_t m, qpms_l_t n, csph_t kdlj,
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qpms_bessel_t btyp, qpms_normalisation_t norm);
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/// Magnetic wave M, complex wave number version..
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csphvec_t qpms_vswf_single_mg_csph(qpms_m_t m, qpms_l_t n, csph_t kdlj,
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qpms_bessel_t btyp, qpms_normalisation_t norm);
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/// Set of electric and magnetic VSWF values in spherical coordinate basis.
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/** This is supposed to contain all the waves up to $l = lMax$.
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*
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* For a completely custom set of waves, use \ref qpms_uvswfset_sph_t instead.
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*/
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typedef struct qpms_vswfset_sph_t {
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//qpms_normalisation_t norm;
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qpms_l_t lMax;
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//qpms_y_t nelem;
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//sph_t kdlj
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csphvec_t *el, *mg;
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} qpms_vswfset_sph_t;
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qpms_errno_t qpms_legendre_deriv_y_get(double **result, double **result_deriv, double x, qpms_l_t lMax,
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gsl_sf_legendre_t lnorm, double csphase); // free() result and result_deriv yourself!
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qpms_errno_t qpms_legendre_deriv_y_fill(double *where, double *where_deriv, double x,
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qpms_l_t lMax, gsl_sf_legendre_t lnorm, double csphase);
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/// Evaluate the zeroth-degree longitudinal VSWF \f$ \mathbf{L}_0^0 \f$.
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/**
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* Any `norm` is being ignored right now.
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*/
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csphvec_t qpms_vswf_L00(
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csph_t kdrj, //< VSWF evaluation point.
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qpms_bessel_t btyp,
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qpms_normalisation_t norm //< Ignored!
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);
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/// Evaluate VSWFs at a given point from \a l = 1 up to a given degree \a lMax.
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/**
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* The target arrays \a resultL, \a resultM, \a resultN have to be large enough to contain
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* \a lMax * (\a lMax + 2) elements. If NULL is passed instead, the corresponding SVWF type
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* is not evaluated.
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*
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* Does not evaluate the zeroth-order wave \f$ \mathbf{L}_0^0 \f$.
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* If you need that, use qpms_vswf_L00().
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*/
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qpms_errno_t qpms_vswf_fill(
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csphvec_t *resultL, //< Target array for longitudinal VSWFs.
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csphvec_t *resultM, //< Target array for magnetic VSWFs.
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csphvec_t *resultN, //< Target array for electric VSWFs.
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qpms_l_t lMax, //< Maximum multipole degree to be calculated.
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sph_t kdrj, //< VSWF evaluation point.
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qpms_bessel_t btyp, qpms_normalisation_t norm);
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// Should give the same results: for consistency checks
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qpms_errno_t qpms_vswf_fill_alternative(csphvec_t *resultL, csphvec_t *resultM, csphvec_t *resultN, qpms_l_t lMax, sph_t kdrj,
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qpms_bessel_t btyp, qpms_normalisation_t norm);
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/// Evaluate VSWFs at a given point from \a l = 1 up to a given degree \a lMax (complex \a kr version).
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/**
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* The target arrays \a resultL, \a resultM, \a resultN have to be large enough to contain
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* \a lMax * (\a lMax + 2) elements. If NULL is passed instead, the corresponding SVWF type
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* is not evaluated.
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*
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* Does not evaluate the zeroth-order wave \f$ \mathbf{L}_0^0 \f$.
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* If you need that, use qpms_vswf_L00().
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*/
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qpms_errno_t qpms_vswf_fill_csph(
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csphvec_t *resultL, //< Target array for longitudinal VSWFs.
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csphvec_t *resultM, //< Target array for magnetic VSWFs.
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csphvec_t *resultN, //< Target array for electric VSWFs.
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qpms_l_t lMax, //< Maximum multipole degree to be calculated.
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csph_t kdrj, //< VSWF evaluation point.
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qpms_bessel_t btyp, qpms_normalisation_t norm);
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qpms_errno_t qpms_vecspharm_fill(csphvec_t *const a1target, csphvec_t *const a2target, csphvec_t *const a3target,
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qpms_l_t lMax, sph_t dir, qpms_normalisation_t norm);
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qpms_errno_t qpms_vecspharm_dual_fill(csphvec_t *const a1target, csphvec_t *const a2target, csphvec_t *const a3target,
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qpms_l_t lMax, sph_t dir, qpms_normalisation_t norm);
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qpms_errno_t qpms_planewave2vswf_fill_cart(cart3_t wavedir, ccart3_t amplitude,
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complex double *targt_longcoeff, complex double *target_mgcoeff, complex double *target_elcoeff,
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qpms_l_t lMax, qpms_normalisation_t norm);
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qpms_errno_t qpms_planewave2vswf_fill_sph(sph_t wavedir, csphvec_t amplitude,
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complex double *targt_longcoeff, complex double *target_mgcoeff, complex double *target_elcoeff,
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qpms_l_t lMax, qpms_normalisation_t norm);
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csphvec_t qpms_eval_vswf(sph_t where,
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complex double *longcoeffs, complex double *mgcoeffs, complex double *elcoeffs,
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qpms_l_t lMax, qpms_bessel_t btyp, qpms_normalisation_t norm);
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csphvec_t qpms_eval_vswf_csph(csph_t where,
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complex double *longcoeffs, complex double *mgcoeffs, complex double *elcoeffs,
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qpms_l_t lMax, qpms_bessel_t btyp, qpms_normalisation_t norm);
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qpms_vswfset_sph_t *qpms_vswfset_make(qpms_l_t lMax, sph_t kdlj,
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qpms_bessel_t btyp, qpms_normalisation_t norm);//NI
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void qpms_vswfset_sph_pfree(qpms_vswfset_sph_t *);//NI
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#endif // QPMS_VSWF_H
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