146 lines
5.2 KiB
C
146 lines
5.2 KiB
C
#ifndef EWALD_H
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#define EWALD_H
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#include <gsl/gsl_sf_result.h>
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#include <math.h> // for inlined lilgamma
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#include <complex.h>
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#include "qpms_types.h"
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/*
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* Implementation of two-dimensional lattice sum in three dimensions
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* according to:
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* [1] C.M. Linton, I. Thompson
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* Journal of Computational Physics 228 (2009) 1815–1829
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*/
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/*
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* N.B.!!! currently, the long-range parts are calculated not according to [1,(4.5)], but rather
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* according to the spherical-harmonic-normalisation-independent formulation in my notes
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* notes/ewald.lyx.
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* Both parts of lattice sums are then calculated with the P_n^|m| e^imf substituted in place
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* of Y_n^m (this is quite a weird normalisation especially for negative |m|, but it is consistent
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* with the current implementation of the translation coefficients in translations.c;
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* in the long run, it might make more sense to replace it everywhere with normalised
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* Legendre polynomials).
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*/
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/* Object holding the constant factors from [1, (4.5)] */
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typedef struct {
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qpms_l_t lMax;
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qpms_y_t nelem_sc;
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qpms_l_t *s1_jMaxes;
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complex double **s1_constfacs; // indices [y][j] where j is same as in [1, (4.5)]
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// TODO probably normalisation and equatorial legendre polynomials should be included, too
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complex double *s1_constfacs_base; // internal pointer holding the memory for the constants
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double *legendre0; /* now with GSL_SF_LEGENDRE_NONE normalisation, because this is what is
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* what the multipliers from translations.c count with.
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*/
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// gsl_sf_legendre_t legendre0_type;
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int legendre0_csphase; /* 1 or -1; csphase of the Legendre polynomials saved in legendre0.
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This is because I dont't actually consider this fixed in
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translations.c */
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} qpms_ewald32_constants_t;
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qpms_ewald32_constants_t *qpms_ewald32_constants_init(qpms_l_t lMax, int csphase);
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void qpms_ewald32_constants_free(qpms_ewald32_constants_t *);
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typedef struct { // as gsl_sf_result, but with complex val
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complex double val;
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double err;
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} qpms_csf_result;
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// [1, (A.9)]
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static inline complex double lilgamma(double t) {
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t = fabs(t);
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if (t >= 1)
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return sqrt(t*t - 1);
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else
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return -I * sqrt(1 - t*t);
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}
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// Incomplete Gamma function as series
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// DLMF 8.7.3 (latter expression) for complex second argument
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int cx_gamma_inc_series_e(double a, complex z, qpms_csf_result * result);
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// Incomplete gamma for complex second argument
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// if x is (almost) real, it just uses gsl_sf_gamma_inc_e
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int complex_gamma_inc_e(double a, complex double x, qpms_csf_result *result);
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#if 0
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// The integral from (4.6); maybe should be static and not here.
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int ewald32_sr_integral(double r, double k, double n, double eta, double *result, double *err, gsl_integration_workspace *workspace);
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#endif
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#include "lattices.h"
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int ewald32_sigma0(complex double *result, double *err,
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const qpms_ewald32_constants_t *c,
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double eta, double k
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);
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// TODO make "compressed versions" where the (m+n)-odd terms (which are zero)
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// are not included.
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int ewald32_sigma_long_shiftedpoints (
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complex double *target_sigmalr_y, // must be c->nelem_sc long
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double *target_sigmalr_y_err, // must be c->nelem_sc long or NULL
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const qpms_ewald32_constants_t *c,
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double eta, double k, double unitcell_area,
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size_t npoints, const point2d *Kpoints_plus_beta,
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//point2d beta,
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point2d particle_shift
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);
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int ewald32_sigma_long_points_and_shift (//NI
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complex double *target_sigmalr_y, // must be c->nelem_sc long
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double *target_sigmalr_y_err, // must be c->nelem_sc long or NULL
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const qpms_ewald32_constants_t *c,
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double eta, double k, double unitcell_area,
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size_t npoints, const point2d *Kpoints,
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point2d beta,
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point2d particle_shift
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);
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int ewald32_sigma_long_shiftedpoints_rordered(//NI
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complex double *target_sigmalr_y, // must be c->nelem_sc long
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double *target_sigmalr_y_err, // must be c->nelem_sc long or NULL
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const qpms_ewald32_constants_t *c,
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double eta, double k, double unitcell_area,
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const points2d_rordered_t *Kpoints_plus_beta_rordered,
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point2d particle_shift
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);
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int ewald32_sigma_short_shiftedpoints(
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complex double *target_sigmasr_y, // must be c->nelem_sc long
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double *target_sigmasr_y_err, // must be c->nelem_sc long or NULL
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const qpms_ewald32_constants_t *c, // N.B. not too useful here
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double eta, double k,
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size_t npoints, const point2d *Rpoints_plus_particle_shift,
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point2d beta,
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point2d particle_shift // used only in the very end to multiply it by the phase
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);
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int ewald32_sigma_short_points_and_shift(//NI
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complex double *target_sigmasr_y, // must be c->nelem_sc long
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double *target_sigmasr_y_err, // must be c->nelem_sc long or NULL
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const qpms_ewald32_constants_t *c, // N.B. not too useful here
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double eta, double k,
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size_t npoints, const point2d *Rpoints,
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point2d particle_shift
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);
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int ewald32_sigma_short_points_rordered(//NI
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complex double *target_sigmasr_y, // must be c->nelem_sc long
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double *target_sigmasr_y_err, // must be c->nelem_sc long or NULL
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const qpms_ewald32_constants_t *c, // N.B. not too useful here
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double eta, double k,
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const points2d_rordered_t *Rpoints_plus_particle_shift_rordered,
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point2d particle_shift // used only in the very end to multiply it by the phase
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);
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#endif //EWALD_H
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