286 lines
11 KiB
C
286 lines
11 KiB
C
/*! \file translations.h
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* \brief VSWF translation operator.
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*
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* ### Argument conventions
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*
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* A single wave with indices mu, nu is re-expanded at kdlj into waves with indices m, n,
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* i.e. in the following functions, the first arguments over which one sums (multiplied
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* by the waves with new origin).
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*
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* HOWEVER, this means that if a field has an expansion with coeffs a(mu, nu)
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* at the original origin, with the basis at the new origin, the coeffs will be
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* a(m, n) = \sum_{mu,nu} A(m, n, mu, nu) a(mu, nu).
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*
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* With qpms_trans_calculator_get_AB_arrays_buf (and other functions from *AB_arrays*
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* family), one can choose the stride. And it seems that the former stride argument (now called
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* destride) and the latter (now called srcstride) are connected to (m,n) and (mu,nu) indices,
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* respectively. Seems consistent.
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*
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*
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* #### r_ge_d argument:
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*
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* If r_ge_d == true, the translation coefficients are calculated using regular bessel functions,
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* regardless of what J argument is.
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*
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*
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*/
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#ifndef QPMS_TRANSLATIONS_H
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#define QPMS_TRANSLATIONS_H
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#include "vectors.h"
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#include "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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#ifdef LATTICESUMS_OLD
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#include "bessels.h"
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#endif
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#if defined LATTICESUMS32 || defined LATTICESUMS31
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#include "ewald.h"
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#endif
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// TODO replace the xplicit "Taylor" functions with general,
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// taking qpms_normalisation_t argument.
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complex double qpms_trans_single_A_Taylor(qpms_m_t m, qpms_l_t n, qpms_m_t mu, qpms_l_t nu, sph_t kdlj,
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bool r_ge_d, qpms_bessel_t J);
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complex double qpms_trans_single_B_Taylor(qpms_m_t m, qpms_l_t n, qpms_m_t mu, qpms_l_t nu, sph_t kdlj,
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bool r_ge_d, qpms_bessel_t J);
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complex double qpms_trans_single_A_Taylor_ext(qpms_m_t m, qpms_l_t n, qpms_m_t mu, qpms_l_t nu, double kdlj_r,
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double kdlj_th, double kdlj_phi, int r_ge_d, int J);
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complex double qpms_trans_single_B_Taylor_ext(qpms_m_t m, qpms_l_t n, qpms_m_t mu, qpms_l_t nu, double kdlj_r,
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double kdlj_th, double kdlj_phi, int r_ge_d, int J);
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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, sph_t kdlj,
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bool r_ge_d, qpms_bessel_t J);
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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, sph_t kdlj,
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bool r_ge_d, qpms_bessel_t J);
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/// Structure holding the constant factors in normalisation operators.
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/**
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* The VSWF translation operator elements are rather complicated linear
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* combinations of Bessel functions and spherical harmonics.
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* The preceding factors are rather complicated but need to be calculated
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* (for a single normalisation convention)
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* only once and then recycled during the operator evaluation for different
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* translations.
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*
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* This structure is initialised with qpms_trans_calculator_t() and
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* holds all the constant factors up to a truncation
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* degree \a lMax.
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*
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* The destructor function is qpms_trans_calculator_free().
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*
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* If Ewald sums are enabled at build, it also holds the constant
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* factors useful for lattice sums of translation operator.
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*/
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typedef struct qpms_trans_calculator {
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qpms_normalisation_t normalisation;
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qpms_l_t lMax;
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qpms_y_t nelem;
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complex double **A_multipliers;
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complex double **B_multipliers;
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#if 0
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// Normalised values of the Legendre functions and derivatives
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// for θ == π/2, i.e. for the 2D case.
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double *leg0;
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double *pi0;
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double *tau0;
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// Spherical Bessel function coefficients:
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// TODO
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#endif
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#if defined LATTICESUMS32 || defined LATTICESUMS31
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qpms_ewald3_constants_t *e3c;
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#endif
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#ifdef LATTICESUMS_OLD
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complex double *hct; // Hankel function coefficient table
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#endif
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double *legendre0; // Zero-argument Legendre functions – this might go outside #ifdef in the end...
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} qpms_trans_calculator;
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/// Initialise a qpms_trans_calculator_t instance for a given convention and truncation degree.
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qpms_trans_calculator *qpms_trans_calculator_init(qpms_l_t lMax, ///< Truncation degree.
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qpms_normalisation_t nt
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);
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/// Destructor for qpms_trans_calculator_t.
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void qpms_trans_calculator_free(qpms_trans_calculator *);
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complex double qpms_trans_calculator_get_A(const qpms_trans_calculator *c,
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qpms_m_t m, qpms_l_t n, qpms_m_t mu, qpms_l_t nu, sph_t kdlj,
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bool r_ge_d, qpms_bessel_t J);
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complex double qpms_trans_calculator_get_B(const qpms_trans_calculator *c,
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qpms_m_t m, qpms_l_t n, qpms_m_t mu, qpms_l_t nu, sph_t kdlj,
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bool r_ge_d, qpms_bessel_t J);
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int qpms_trans_calculator_get_AB_p(const qpms_trans_calculator *c,
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complex double *Adest, complex double *Bdest,
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qpms_m_t m, qpms_l_t n, qpms_m_t mu, qpms_l_t nu, sph_t kdlj,
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bool r_ge_d, qpms_bessel_t J);
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int qpms_trans_calculator_get_AB_arrays(const qpms_trans_calculator *c,
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complex double *Adest, complex double *Bdest,
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size_t deststride, size_t srcstride,
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sph_t kdlj, bool r_ge_d, qpms_bessel_t J);
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// TODO update the types later
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complex double qpms_trans_calculator_get_A_ext(const qpms_trans_calculator *c,
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int m, int n, int mu, int nu, double kdlj_r,
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double kdlj_th, double kdlj_phi, int r_ge_d, int J);
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complex double qpms_trans_calculator_get_B_ext(const qpms_trans_calculator *c,
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int m, int n, int mu, int nu, double kdlj_r,
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double kdlj_th, double kdlj_phi, int r_ge_d, int J);
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int qpms_trans_calculator_get_AB_p_ext(const qpms_trans_calculator *c,
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complex double *Adest, complex double *Bdest,
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int m, int n, int mu, int nu, double kdlj_r,
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double kdlj_th, double kdlj_phi, int r_ge_d, int J);
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int qpms_trans_calculator_get_AB_arrays_ext(const qpms_trans_calculator *c,
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complex double *Adest, complex double *Bdest,
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size_t deststride, size_t srcstride,
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double kdlj_r, double kdlj_theta, double kdlj_phi,
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int r_ge_d, int J);
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// Convenience functions using VSWF base specs
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qpms_errno_t qpms_trans_calculator_get_trans_array(const qpms_trans_calculator *c,
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complex double *target,
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/// Must be destspec->lMax <= c-> lMax && destspec->norm == c->norm.
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const qpms_vswf_set_spec_t *destspec, size_t deststride,
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/// Must be srcspec->lMax <= c-> lMax && srcspec->norm == c->norm.
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const qpms_vswf_set_spec_t *srcspec, size_t srcstride,
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sph_t kdlj, bool r_ge_d, qpms_bessel_t J);
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/// Version with \a k and cartesian particle positions
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/// and with automatic \a kdlj = false and \a J = QPMS_HANKEL_PLUS.
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qpms_errno_t qpms_trans_calculator_get_trans_array_lc3p(
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const qpms_trans_calculator *c,
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complex double *target,
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/// Must be destspec->lMax <= c-> lMax && destspec->norm == c->norm.
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const qpms_vswf_set_spec_t *destspec, size_t deststride,
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/// Must be srcspec->lMax <= c-> lMax && srcspec->norm == c->norm.
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const qpms_vswf_set_spec_t *srcspec, size_t srcstride,
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double k, cart3_t destpos, cart3_t srcpos
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/// Workspace has to be at least 2 * c->neleme**2 long
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);
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#ifdef LATTICESUMS_OLD
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// Short-range parts of the translation coefficients
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int qpms_trans_calculator_get_shortrange_AB_p(const qpms_trans_calculator *c,
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complex double *Adest, complex double *Bdest,
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qpms_m_t m, qpms_l_t n, qpms_m_t mu, qpms_l_t nu, sph_t kdlj,
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qpms_bessel_t J /* Only J=3 valid for now */,
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qpms_l_t longrange_order_cutoff, unsigned kappa, double cc);
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int qpms_trans_calculator_get_shortrange_AB_arrays(const qpms_trans_calculator *c,
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complex double *Adest, complex double *Bdest,
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size_t deststride, size_t srcstride,
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sph_t kdlj, qpms_bessel_t J /* Only J=3 valid for now */,
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qpms_l_t longrange_order_cutoff, unsigned kappa, double cc);
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// Fourier transforms of the long-range parts of the translation coefficients
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int qpms_trans_calculator_get_2DFT_longrange_AB_p(const qpms_trans_calculator *c,
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complex double *Adest, complex double *Bdest,
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qpms_m_t m, qpms_l_t n, qpms_m_t mu, qpms_l_t nu, sph_t k_sph,
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qpms_bessel_t J /* Only J=3 valid for now */,
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qpms_l_t longrange_order_cutoff, unsigned kappa, double cv, double k0);
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int qpms_trans_calculator_get_2DFT_longrange_AB_arrays(const qpms_trans_calculator *c,
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complex double *Adest, complex double *Bdest,
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size_t deststride, size_t srcstride,
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sph_t k_sph, qpms_bessel_t J /* Only J=3 valid for now */,
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qpms_l_t longrange_order_cutoff, unsigned kappa, double cv, double k0);
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#endif // LATTICESUMS_OLD
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#ifdef LATTICESUMS32
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// for the time being there are only those relatively low-level quick&dirty functions
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// according to what has been implemented from ewald.h;
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// TODO more high-level functions with more advanced lattice generators etc. (after
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// the prerequisities from lattices2d.h are implememted)
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#if 0 // NI
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int qpms_trans_calculator_e32_long_points_and_shift(const qpms_trans_calculator *c,
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complex double *Adest_long, double *Aerr_long,
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complex double *Bdest_long, double *Berr_long,
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double eta, double k, double unitcell_area,
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size_t npoints, const cart2_t *Kpoints,
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cart2_t beta,
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cart2_t particle_shift
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);
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int qpms_trans_calculator_e32_short_points_and_shift(const qpms_trans_calculator *c,
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complex double *Adest_short, double *Aerr_short,
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complex double *Bdest_short, double *Berr_short,
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double eta, double k,
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size_t npoints, const cart2_t *Rpoints,
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cart2_t beta,
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cart2_t particle_shift
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);
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#endif
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int qpms_trans_calculator_get_AB_arrays_e32_both_points_and_shift(const qpms_trans_calculator *c,
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complex double *Adest, double *Aerr,
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complex double *Bdest, double *Berr,
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const ptrdiff_t deststride, const ptrdiff_t srcstride,
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const double eta, const double k,
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const double unitcell_area,
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const size_t nRpoints, const cart2_t *Rpoints,
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const size_t nKpoints, const cart2_t *Kpoints,
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const cart2_t beta,
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const cart2_t particle_shift
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);
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int qpms_trans_calculator_get_AB_arrays_e32(const qpms_trans_calculator *c,
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complex double *Adest, double *Aerr,
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complex double *Bdest, double *Berr,
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const ptrdiff_t deststride, const ptrdiff_t srcstride,
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const double eta, const double k,
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cart2_t b1, cart2_t b2,
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const cart2_t beta,
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const cart2_t particle_shift,
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double maxR, double maxK
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);
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#endif //LATTICESUMS32
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#ifdef LATTICESUMS31
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// e31z means that the particles are positioned along the z-axis;
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// their positions and K-values are then denoted by a single z-coordinate
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int qpms_trans_calculator_get_AB_arrays_e31z_both_points_and_shift(const qpms_trans_calculator *c,
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complex double *Adest, double *Aerr,
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complex double *Bdest, double *Berr,
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const ptrdiff_t deststride, const ptrdiff_t srcstride,
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const double eta, const double k,
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const double unitcell_area, // just lattice period
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const size_t nRpoints, const cart2_t *Rpoints,
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const size_t nKpoints, const cart2_t *Kpoints,
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const double beta,
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const double particle_shift
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);
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#endif
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#ifdef QPMS_COMPILE_PYTHON_EXTENSIONS
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#include <Python.h>
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#include <numpy/npy_common.h>
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int qpms_cython_trans_calculator_get_AB_arrays_loop(
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const qpms_trans_calculator *c, qpms_bessel_t J, const int resnd,
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int daxis, int saxis,
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char *A_data, const npy_intp *A_shape, const npy_intp *A_strides,
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char *B_data, const npy_intp *B_shape, const npy_intp *B_strides,
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const char *r_data, const npy_intp *r_shape, const npy_intp *r_strides,
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const char *theta_data, const npy_intp *theta_shape, const npy_intp *theta_strides,
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const char *phi_data, const npy_intp *phi_shape, const npy_intp *phi_strides,
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const char *r_ge_d_data, const npy_intp *r_ge_d_shape, const npy_intp *r_ge_d_strides);
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#endif //QPMS_COMPILE_PYTHON_EXTENSIONS
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#endif // QPMS_TRANSLATIONS_H
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