qpms/qpms/translations.h

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/*! \file translations.h
* \brief VSWF translation operator.
*
* ### Argument conventions
*
* A single wave with indices mu, nu is re-expanded at kdlj into waves with indices m, n,
* i.e. in the following functions, the first arguments over which one sums (multiplied
* by the waves with new origin).
*
* HOWEVER, this means that if a field has an expansion with coeffs a(mu, nu)
* at the original origin, with the basis at the new origin, the coeffs will be
* a(m, n) = \sum_{mu,nu} A(m, n, mu, nu) a(mu, nu).
*
* With qpms_trans_calculator_get_AB_arrays_buf (and other functions from *AB_arrays*
* family), one can choose the stride. And it seems that the former stride argument (now called
* destride) and the latter (now called srcstride) are connected to (m,n) and (mu,nu) indices,
* respectively. Seems consistent.
*
*
* #### r_ge_d argument:
*
* If r_ge_d == true, the translation coefficients are calculated using regular bessel functions,
* regardless of what J argument is.
*
*
*/
#ifndef QPMS_TRANSLATIONS_H
#define QPMS_TRANSLATIONS_H
#include "vectors.h"
#include "qpms_types.h"
#include <complex.h>
#include <stdbool.h>
#include <stddef.h>
#if defined LATTICESUMS32 || defined LATTICESUMS31
#include "ewald.h"
#endif
complex double qpms_trans_single_A(qpms_normalisation_t norm, qpms_m_t m, qpms_l_t n, qpms_m_t mu, qpms_l_t nu, csph_t kdlj,
bool r_ge_d, qpms_bessel_t J);
complex double qpms_trans_single_B(qpms_normalisation_t norm, qpms_m_t m, qpms_l_t n, qpms_m_t mu, qpms_l_t nu, csph_t kdlj,
bool r_ge_d, qpms_bessel_t J);
/// Structure holding the constant factors in normalisation operators.
/**
* The VSWF translation operator elements are rather complicated linear
* combinations of Bessel functions and spherical harmonics.
* The preceding factors are rather complicated but need to be calculated
* (for a single normalisation convention)
* only once and then recycled during the operator evaluation for different
* translations.
*
* This structure is initialised with qpms_trans_calculator_t() and
* holds all the constant factors up to a truncation
* degree \a lMax.
*
* The destructor function is qpms_trans_calculator_free().
*
* If Ewald sums are enabled at build, it also holds the constant
* factors useful for lattice sums of translation operator.
*/
typedef struct qpms_trans_calculator {
qpms_normalisation_t normalisation;
qpms_l_t lMax;
qpms_y_t nelem;
complex double **A_multipliers;
complex double **B_multipliers;
#if 0
// Normalised values of the Legendre functions and derivatives
// for θ == π/2, i.e. for the 2D case.
double *leg0;
double *pi0;
double *tau0;
// Spherical Bessel function coefficients:
// TODO
#endif
#if defined LATTICESUMS32 || defined LATTICESUMS31
qpms_ewald3_constants_t *e3c;
#endif
double *legendre0; // Zero-argument Legendre functions this might go outside #ifdef in the end...
} qpms_trans_calculator;
/// Initialise a qpms_trans_calculator_t instance for a given convention and truncation degree.
qpms_trans_calculator *qpms_trans_calculator_init(qpms_l_t lMax, ///< Truncation degree.
qpms_normalisation_t nt
);
/// Destructor for qpms_trans_calculator_t.
void qpms_trans_calculator_free(qpms_trans_calculator *);
complex double qpms_trans_calculator_get_A(const qpms_trans_calculator *c,
qpms_m_t m, qpms_l_t n, qpms_m_t mu, qpms_l_t nu, csph_t kdlj,
bool r_ge_d, qpms_bessel_t J);
complex double qpms_trans_calculator_get_B(const qpms_trans_calculator *c,
qpms_m_t m, qpms_l_t n, qpms_m_t mu, qpms_l_t nu, csph_t kdlj,
bool r_ge_d, qpms_bessel_t J);
int qpms_trans_calculator_get_AB_p(const qpms_trans_calculator *c,
complex double *Adest, complex double *Bdest,
qpms_m_t m, qpms_l_t n, qpms_m_t mu, qpms_l_t nu, csph_t kdlj,
bool r_ge_d, qpms_bessel_t J);
int qpms_trans_calculator_get_AB_arrays(const qpms_trans_calculator *c,
complex double *Adest, complex double *Bdest,
size_t deststride, size_t srcstride,
csph_t kdlj, bool r_ge_d, qpms_bessel_t J);
// TODO update the types later
complex double qpms_trans_calculator_get_A_ext(const qpms_trans_calculator *c,
int m, int n, int mu, int nu, complex double kdlj_r,
double kdlj_th, double kdlj_phi, int r_ge_d, int J);
complex double qpms_trans_calculator_get_B_ext(const qpms_trans_calculator *c,
int m, int n, int mu, int nu, complex double kdlj_r,
double kdlj_th, double kdlj_phi, int r_ge_d, int J);
int qpms_trans_calculator_get_AB_p_ext(const qpms_trans_calculator *c,
complex double *Adest, complex double *Bdest,
int m, int n, int mu, int nu, complex double kdlj_r,
double kdlj_th, double kdlj_phi, int r_ge_d, int J);
int qpms_trans_calculator_get_AB_arrays_ext(const qpms_trans_calculator *c,
complex double *Adest, complex double *Bdest,
size_t deststride, size_t srcstride,
complex double kdlj_r, double kdlj_theta, double kdlj_phi,
int r_ge_d, int J);
// Convenience functions using VSWF base specs
qpms_errno_t qpms_trans_calculator_get_trans_array(const qpms_trans_calculator *c,
complex double *target,
/// Must be destspec->lMax <= c-> lMax && destspec->norm == c->norm.
const qpms_vswf_set_spec_t *destspec, size_t deststride,
/// Must be srcspec->lMax <= c-> lMax && srcspec->norm == c->norm.
const qpms_vswf_set_spec_t *srcspec, size_t srcstride,
csph_t kdlj, bool r_ge_d, qpms_bessel_t J);
/// Version with \a k and cartesian particle positions
/// and with automatic \a r_ge_d = `false`.
qpms_errno_t qpms_trans_calculator_get_trans_array_lc3p(
const qpms_trans_calculator *c,
complex double *target,
/// Must be destspec->lMax <= c-> lMax && destspec->norm == c->norm.
const qpms_vswf_set_spec_t *destspec, size_t deststride,
/// Must be srcspec->lMax <= c-> lMax && srcspec->norm == c->norm.
const qpms_vswf_set_spec_t *srcspec, size_t srcstride,
complex double k, cart3_t destpos, cart3_t srcpos,
qpms_bessel_t J
/// Workspace has to be at least 2 * c->neleme**2 long
);
#ifdef LATTICESUMS32
// for the time being there are only those relatively low-level quick&dirty functions
// according to what has been implemented from ewald.h;
// TODO more high-level functions with more advanced lattice generators etc. (after
// the prerequisities from lattices2d.h are implememted)
int qpms_trans_calculator_get_AB_arrays_e32(const qpms_trans_calculator *c,
complex double *Adest, double *Aerr,
complex double *Bdest, double *Berr,
const ptrdiff_t deststride, const ptrdiff_t srcstride,
const double eta, const complex double wavenumber,
cart2_t b1, cart2_t b2,
const cart2_t beta,
const cart3_t particle_shift,
double maxR, double maxK
);
int qpms_trans_calculator_get_AB_arrays_e32_e(const qpms_trans_calculator *c,
complex double *Adest, double *Aerr,
complex double *Bdest, double *Berr,
const ptrdiff_t deststride, const ptrdiff_t srcstride,
const double eta, const complex double wavenumber,
cart2_t b1, cart2_t b2,
const cart2_t beta,
const cart3_t particle_shift,
double maxR, double maxK,
qpms_ewald_part parts
);
// Convenience functions using VSWF base specs
qpms_errno_t qpms_trans_calculator_get_trans_array_e32(const qpms_trans_calculator *c,
complex double *target, double *err,
/// Must be destspec->lMax <= c-> lMax && destspec->norm == c->norm.
const qpms_vswf_set_spec_t *destspec, size_t deststride,
/// Must be srcspec->lMax <= c-> lMax && srcspec->norm == c->norm.
const qpms_vswf_set_spec_t *srcspec, size_t srcstride,
const double eta, const complex double wavenumber,
cart2_t b1, cart2_t b2,
const cart2_t beta,
const cart3_t particle_shift,
double maxR, double maxK
);
qpms_errno_t qpms_trans_calculator_get_trans_array_e32_e(const qpms_trans_calculator *c,
complex double *target, double *err,
/// Must be destspec->lMax <= c-> lMax && destspec->norm == c->norm.
const qpms_vswf_set_spec_t *destspec, size_t deststride,
/// Must be srcspec->lMax <= c-> lMax && srcspec->norm == c->norm.
const qpms_vswf_set_spec_t *srcspec, size_t srcstride,
const double eta, const complex double wavenumber,
cart2_t b1, cart2_t b2,
const cart2_t beta,
const cart3_t particle_shift,
double maxR, double maxK,
qpms_ewald_part parts
);
#endif //LATTICESUMS32
#ifdef LATTICESUMS31
// e31z means that the particles are positioned along the z-axis;
// their positions and K-values are then denoted by a single z-coordinate
int qpms_trans_calculator_get_AB_arrays_e31z_both_points_and_shift(const qpms_trans_calculator *c,
complex double *Adest, double *Aerr,
complex double *Bdest, double *Berr,
const ptrdiff_t deststride, const ptrdiff_t srcstride,
const double eta, const double k,
const double unitcell_area, // just lattice period
const size_t nRpoints, const cart2_t *Rpoints,
const size_t nKpoints, const cart2_t *Kpoints,
const double beta,
const double particle_shift
);
#endif
#ifdef QPMS_COMPILE_PYTHON_EXTENSIONS
#include <Python.h>
#include <numpy/npy_common.h>
int qpms_cython_trans_calculator_get_AB_arrays_loop(
const qpms_trans_calculator *c, qpms_bessel_t J, const int resnd,
int daxis, int saxis,
char *A_data, const npy_intp *A_shape, const npy_intp *A_strides,
char *B_data, const npy_intp *B_shape, const npy_intp *B_strides,
const char *r_data, const npy_intp *r_shape, const npy_intp *r_strides,
const char *theta_data, const npy_intp *theta_shape, const npy_intp *theta_strides,
const char *phi_data, const npy_intp *phi_shape, const npy_intp *phi_strides,
const char *r_ge_d_data, const npy_intp *r_ge_d_shape, const npy_intp *r_ge_d_strides);
#endif //QPMS_COMPILE_PYTHON_EXTENSIONS
#endif // QPMS_TRANSLATIONS_H