Rozbil jsem to, jdu domů.
Former-commit-id: 77490824d9a8f975ec4ebe98d8cfa104093884e4
This commit is contained in:
Marek Nečada
parent
155859d8a7
commit
2a7015b80b
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@ -683,6 +683,19 @@ In the usual cases we encounter, the part described by the magnetic waves
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is pretty small.
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\end_layout
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\begin_layout Standard
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The expression with Bessel function derivatives appearing below in the electric
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waves can be rewritten using (DLMF 10.51.2)
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\begin_inset Formula
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\[
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\frac{1}{kr}\frac{\ud\left(kr\,z_{n}^{j}\left(kr\right)\right)}{\ud(kr)}=\frac{\ud z_{n}^{j}\left(kr\right)}{\ud(kr)}+\frac{z_{n}^{j}\left(kr\right)}{kr}=z_{n-1}^{j}\left(kr\right)-n\frac{z_{n}^{j}\left(kr\right)}{kr}.
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\]
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\end_inset
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\end_layout
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\begin_layout Subsection
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Taylor
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\end_layout
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@ -0,0 +1,38 @@
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#include "translations.h"
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#include <stdlib.h>
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#include <gsl/gsl_sf_bessel.h>
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#include <assert.h>
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int qpms_sph_bessel_fill(qpms_bessel_t typ, int lmax, double x, complex double *result_array) {
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int retval;
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double tmparr[lmax+1];
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switch(typ) {
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case QPMS_BESSEL_REGULAR:
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retval = gsl_sf_bessel_jl_steed_array(lmax, x, tmparr);
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for (int l = 0; l <= lmax; ++l) result_array[l] = tmparr[l];
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return retval;
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break;
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case QPMS_BESSEL_SINGULAR: //FIXME: is this precise enough? Would it be better to do it one-by-one?
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retval = gsl_sf_bessel_yl_array(lmax,x,tmparr);
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for (int l = 0; l <= lmax; ++l) result_array[l] = tmparr[l];
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return retval;
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break;
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case QPMS_HANKEL_PLUS:
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case QPMS_HANKEL_MINUS:
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retval = gsl_sf_bessel_jl_steed_array(lmax, x, tmparr);
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for (int l = 0; l <= lmax; ++l) result_array[l] = tmparr[l];
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if(retval) return retval;
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retval = gsl_sf_bessel_yl_array(lmax, x, tmparr);
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if (typ==QPMS_HANKEL_PLUS)
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for (int l = 0; l <= lmax; ++l) result_array[l] += I * tmparr[l];
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else
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for (int l = 0; l <= lmax; ++l) result_array[l] +=-I * tmparr[l];
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return retval;
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break;
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default:
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abort();
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//return GSL_EDOM;
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}
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assert(0);
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}
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@ -63,6 +63,10 @@ typedef struct {
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double x, y, z;
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} cart3_t;
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typedef struct {
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complex double x, y, z;
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} ccart3_t;
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typedef struct {
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double x, y;
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} cart2_t;
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@ -80,4 +84,6 @@ typedef struct {
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double r, phi;
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} pol_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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@ -1,4 +1,5 @@
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#include <math.h>
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#include "qpms_types.h"
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#include "gaunt.h"
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#include "translations.h"
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#include "indexing.h" // TODO replace size_t and int with own index types here
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@ -34,7 +35,7 @@ double qpms_legendreD0(int m, int n) {
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return -2 * qpms_legendre0(m, n);
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}
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int qpms_sph_bessel_array(qpms_bessel_t typ, int lmax, double x, complex double *result_array) {
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int qpms_sph_bessel_fill(qpms_bessel_t typ, int lmax, double x, complex double *result_array) {
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int retval;
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double tmparr[lmax+1];
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switch(typ) {
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@ -86,7 +87,7 @@ complex double qpms_trans_single_A_Xu(int m, int n, int mu, int nu, sph_t kdlj,
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double leg[gsl_sf_legendre_array_n(n+nu)];
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if (gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu,costheta,-1,leg)) abort();
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complex double bes[n+nu+1];
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if (qpms_sph_bessel_array(J, n+nu, kdlj.r, bes)) abort();
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if (qpms_sph_bessel_fill(J, n+nu, kdlj.r, bes)) abort();
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complex double sum = 0;
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for(int q = 0; q <= qmax; ++q) {
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int p = n+nu-2*q;
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@ -132,7 +133,7 @@ complex double qpms_trans_single_A_Kristensson(int m, int n, int mu, int nu, sph
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double leg[gsl_sf_legendre_array_n(n+nu)];
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if (gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu,costheta,-1,leg)) abort();
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complex double bes[n+nu+1];
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if (qpms_sph_bessel_array(J, n+nu, kdlj.r, bes)) abort();
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if (qpms_sph_bessel_fill(J, n+nu, kdlj.r, bes)) abort();
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complex double sum = 0;
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for(int q = 0; q <= qmax; ++q) {
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int p = n+nu-2*q;
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@ -177,7 +178,7 @@ complex double qpms_trans_single_A_Taylor(int m, int n, int mu, int nu, sph_t kd
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double leg[gsl_sf_legendre_array_n(n+nu)];
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if (gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu,costheta,-1,leg)) abort();
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complex double bes[n+nu+1];
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if (qpms_sph_bessel_array(J, n+nu, kdlj.r, bes)) abort();
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if (qpms_sph_bessel_fill(J, n+nu, kdlj.r, bes)) abort();
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complex double sum = 0;
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for(int q = 0; q <= qmax; ++q) {
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int p = n+nu-2*q;
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@ -229,7 +230,7 @@ complex double qpms_trans_single_B_Xu(int m, int n, int mu, int nu, sph_t kdlj,
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double leg[gsl_sf_legendre_array_n(n+nu+1)];
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if (gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu+1,costheta,-1,leg)) abort();
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complex double bes[n+nu+2];
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if (qpms_sph_bessel_array(J, n+nu+1, kdlj.r, bes)) abort();
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if (qpms_sph_bessel_fill(J, n+nu+1, kdlj.r, bes)) abort();
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complex double sum = 0;
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for (int q = 0; q <= Qmax; ++q) {
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@ -285,7 +286,7 @@ complex double qpms_trans_single_B_Taylor(int m, int n, int mu, int nu, sph_t kd
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double leg[gsl_sf_legendre_array_n(n+nu+1)];
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if (gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu+1,costheta,-1,leg)) abort();
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complex double bes[n+nu+2];
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if (qpms_sph_bessel_array(J, n+nu+1, kdlj.r, bes)) abort();
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if (qpms_sph_bessel_fill(J, n+nu+1, kdlj.r, bes)) abort();
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complex double sum = 0;
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for (int q = 0; q <= Qmax; ++q) {
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@ -338,10 +339,6 @@ void qpms_trans_calculator_free(qpms_trans_calculator *c) {
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free(c);
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}
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static inline size_t qpms_mn2y(int m, int n) {
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return (size_t) n * (n + 1) + m - 1;
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}
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static inline size_t qpms_trans_calculator_index_mnmunu(const qpms_trans_calculator *c,
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int m, int n, int mu, int nu){
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return c->nelem * qpms_mn2y(m,n) + qpms_mn2y(mu,nu);
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@ -470,9 +467,9 @@ static void qpms_trans_calculator_multipliers_B_Taylor(
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}
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}
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int qpms_trans_calculator_multipliers_A(qpms_normalization_t norm, complex double *dest, int m, int n, int mu, int nu, int qmax) {
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int qpms_trans_calculator_multipliers_A(qpms_normalisation_t norm, complex double *dest, int m, int n, int mu, int nu, int qmax) {
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switch (norm) {
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case QPMS_NORMALIZATION_TAYLOR:
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case QPMS_NORMALISATION_TAYLOR:
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qpms_trans_calculator_multipliers_A_Taylor(dest,m,n,mu,nu,qmax);
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return 0;
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break;
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@ -482,9 +479,9 @@ int qpms_trans_calculator_multipliers_A(qpms_normalization_t norm, complex doubl
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assert(0);
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}
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int qpms_trans_calculator_multipliers_B(qpms_normalization_t norm, complex double *dest, int m, int n, int mu, int nu, int qmax) {
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int qpms_trans_calculator_multipliers_B(qpms_normalisation_t norm, complex double *dest, int m, int n, int mu, int nu, int qmax) {
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switch (norm) {
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case QPMS_NORMALIZATION_TAYLOR:
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case QPMS_NORMALISATION_TAYLOR:
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qpms_trans_calculator_multipliers_B_Taylor(dest,m,n,mu,nu,qmax);
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return 0;
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break;
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@ -495,14 +492,14 @@ int qpms_trans_calculator_multipliers_B(qpms_normalization_t norm, complex doubl
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}
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qpms_trans_calculator
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*qpms_trans_calculator_init (int lMax, qpms_normalization_t normalization) {
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*qpms_trans_calculator_init (int lMax, qpms_normalisation_t normalisation) {
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assert(lMax > 0);
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qpms_trans_calculator *c = malloc(sizeof(qpms_trans_calculator));
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c->lMax = lMax;
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c->nelem = lMax * (lMax+2);
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c->A_multipliers = malloc((1+SQ(c->nelem)) * sizeof(complex double *));
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c->B_multipliers = malloc((1+SQ(c->nelem)) * sizeof(complex double *));
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c->normalization = normalization;
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c->normalisation = normalisation;
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size_t *qmaxes = malloc(SQ(c->nelem) * sizeof(size_t));
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size_t qmaxsum = 0;
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for(size_t y = 0; y < c->nelem; y++)
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@ -525,7 +522,7 @@ qpms_trans_calculator
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int m, n, mu, nu;
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qpms_y2mn_p(y, &m, &n);
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qpms_y2mn_p(yu, &mu, &nu);
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qpms_trans_calculator_multipliers_A(normalization,
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qpms_trans_calculator_multipliers_A(normalisation,
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c->A_multipliers[i], m, n, mu, nu, qmaxes[i]);
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}
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@ -550,7 +547,7 @@ qpms_trans_calculator
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int m, n, mu, nu;
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qpms_y2mn_p(y, &m, &n);
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qpms_y2mn_p(yu, &mu, &nu);
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qpms_trans_calculator_multipliers_B(normalization,
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qpms_trans_calculator_multipliers_B(normalisation,
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c->B_multipliers[i], m, n, mu, nu, qmaxes[i]);
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}
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@ -586,13 +583,13 @@ complex double qpms_trans_calculator_get_A_buf(const qpms_trans_calculator *c,
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if (0 == kdlj.r && J != QPMS_BESSEL_REGULAR)
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// TODO warn?
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return NAN+I*NAN;
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switch(c->normalization) {
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case QPMS_NORMALIZATION_TAYLOR:
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switch(c->normalisation) {
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case QPMS_NORMALISATION_TAYLOR:
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{
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double costheta = cos(kdlj.theta);
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if (gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu,
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costheta,-1,legendre_buf)) abort();
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if (qpms_sph_bessel_array(J, n+nu+1, kdlj.r, bessel_buf)) abort();
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if (qpms_sph_bessel_fill(J, n+nu+1, kdlj.r, bessel_buf)) abort();
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return qpms_trans_calculator_get_A_precalcbuf(c,m,n,mu,nu,
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kdlj,r_ge_d,J,bessel_buf,legendre_buf);
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}
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@ -631,13 +628,13 @@ complex double qpms_trans_calculator_get_B_buf(const qpms_trans_calculator *c,
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if (0 == kdlj.r && J != QPMS_BESSEL_REGULAR)
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// TODO warn?
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return NAN+I*NAN;
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switch(c->normalization) {
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case QPMS_NORMALIZATION_TAYLOR:
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switch(c->normalisation) {
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case QPMS_NORMALISATION_TAYLOR:
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{
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double costheta = cos(kdlj.theta);
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if (gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu+1,
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costheta,-1,legendre_buf)) abort();
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if (qpms_sph_bessel_array(J, n+nu+2, kdlj.r, bessel_buf)) abort();
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if (qpms_sph_bessel_fill(J, n+nu+2, kdlj.r, bessel_buf)) abort();
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return qpms_trans_calculator_get_B_precalcbuf(c,m,n,mu,nu,
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kdlj,r_ge_d,J,bessel_buf,legendre_buf);
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}
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@ -660,13 +657,13 @@ int qpms_trans_calculator_get_AB_buf_p(const qpms_trans_calculator *c,
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// TODO warn? different return value?
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return 0;
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}
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switch(c->normalization) {
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case QPMS_NORMALIZATION_TAYLOR:
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switch(c->normalisation) {
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case QPMS_NORMALISATION_TAYLOR:
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{
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double costheta = cos(kdlj.theta);
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if (gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu+1,
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costheta,-1,legendre_buf)) abort();
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if (qpms_sph_bessel_array(J, n+nu+2, kdlj.r, bessel_buf)) abort();
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if (qpms_sph_bessel_fill(J, n+nu+2, kdlj.r, bessel_buf)) abort();
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*Adest = qpms_trans_calculator_get_A_precalcbuf(c,m,n,mu,nu,
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kdlj,r_ge_d,J,bessel_buf,legendre_buf);
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*Bdest = qpms_trans_calculator_get_B_precalcbuf(c,m,n,mu,nu,
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@ -698,13 +695,13 @@ int qpms_trans_calculator_get_AB_arrays_buf(const qpms_trans_calculator *c,
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// TODO warn? different return value?
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return 0;
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}
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switch(c->normalization) {
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case QPMS_NORMALIZATION_TAYLOR:
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switch(c->normalisation) {
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case QPMS_NORMALISATION_TAYLOR:
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{
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double costheta = cos(kdlj.theta);
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if (gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,2*c->lMax+1,
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costheta,-1,legendre_buf)) abort();
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if (qpms_sph_bessel_array(J, 2*c->lMax+2, kdlj.r, bessel_buf)) abort();
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if (qpms_sph_bessel_fill(J, 2*c->lMax+2, kdlj.r, bessel_buf)) abort();
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size_t desti = 0, srci = 0;
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for (int n = 1; n <= c->lMax; ++n) for (int m = -n; m <= n; ++m) {
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for (int nu = 1; nu <= c->lMax; ++nu) for (int mu = -nu; mu <= nu; ++mu) {
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@ -9,7 +9,8 @@
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double qpms_legendre0(int m, int n);
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// Associated Legendre polynomial derivative at zero argument (DLMF 14.5.2)
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double qpms_legendred0(int m, int n);
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int qpms_sph_bessel_array(qpms_bessel_t typ, int lmax, double x, complex double *result_array);
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// TODO unify types
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int qpms_sph_bessel_fill(qpms_bessel_t typ, int lmax, double x, complex double *result_array);
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// TODO replace the xplicit "Taylor" functions with general,
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// taking qpms_bessel_t argument.
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@ -30,10 +31,10 @@ typedef struct qpms_trans_calculator {
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size_t nelem;
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complex double **A_multipliers;
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complex double **B_multipliers;
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qpms_normalization_t normalization;
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qpms_normalisation_t normalisation;
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} qpms_trans_calculator;
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qpms_trans_calculator *qpms_trans_calculator_init(int lMax, qpms_normalization_t nt);
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qpms_trans_calculator *qpms_trans_calculator_init(int lMax, qpms_normalisation_t nt);
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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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@ -6,11 +6,11 @@
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//static inline double vectors_h_sq(double x) {return x*x;}
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static inline double cart3norm(cart3_t v) {
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static inline double cart3norm(const cart3_t v) {
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return sqrt(v.x*v.x + v.y*v.y + v.z*v.z);
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}
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static inline sph_t cart2sph(cart3_t cart) {
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static inline sph_t cart2sph(const cart3_t cart) {
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sph_t sph;
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sph.r = cart3norm(cart);
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sph.theta = sph.r ? acos(cart.z / sph.r) : M_PI_2;
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@ -18,7 +18,7 @@ static inline sph_t cart2sph(cart3_t cart) {
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return sph;
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}
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static inline cart3_t sph2cart(sph_t sph) {
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static inline cart3_t sph2cart(const sph_t sph) {
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cart3_t cart;
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double sin_th = sin(sph.theta);
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cart.x = sph.r * sin_th * cos(sph.phi);
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@ -27,5 +27,28 @@ static inline cart3_t sph2cart(sph_t sph) {
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return cart;
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}
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// equivalent to sph_loccart2cart in qpms_p.py
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static inline ccart3_t csphvec2cart(const csphvec_t sphvec, const sph_t at) {
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ccart3_t res = {0, 0, 0};
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const double st = sin(at.theta);
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const double ct = cos(at.theta);
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const double sf = sin(at.phi);
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const double cf = cos(at.phi);
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const double rx = st * cf;
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const double ry = st * sf;
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const double rz = ct;
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const double tx = ct * cf;
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const double ty = ct * sf;
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const double tz = -st;
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const double fx = -sf;
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const double fy = cf;
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const double fz = 0.;
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res.x = rx * sphvec.rc + tx * sphvec.thetac + fx * sphvec.phic;
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res.y = ry * sphvec.rc + ty * sphvec.thetac + fy * sphvec.phic;
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res.z = rz * sphvec.rc + tz * sphvec.thetac + fz * sphvec.phic;
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return sphvec;
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}
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||||
|
||||
|
||||
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||||
#endif //VECTORS_H
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|
|
|
|||
92
qpms/vswf.c
92
qpms/vswf.c
|
|
@ -1,10 +1,12 @@
|
|||
#include "vswf.h"
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#include "indexing.h"
|
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#include "translations.h" // TODO move qpms_sph_bessel_fill elsewhere
|
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#include <math.h>
|
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#include <gsl/gsl_math.h>
|
||||
#include <gsl/gsl_sf_legendre.h>
|
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#include <stdlib.h>
|
||||
#include <string.h>
|
||||
#include "assert_cython_workaround.h"
|
||||
|
||||
// Legendre functions also for negative m, see DLMF 14.9.3
|
||||
qpms_errno_t qpms_legendre_deriv_y_fill(double *target, double *target_deriv, double x, qpms_l_t lMax,
|
||||
|
|
@ -156,3 +158,93 @@ void qpms_pitau_free(qpms_pitau_t x) {
|
|||
free(x.pi);
|
||||
free(x.tau);
|
||||
}
|
||||
|
||||
|
||||
csphvec_t qpms_vswf_single_el(qpms_m_t m, qpms_l_t l, sph_t kdlj,
|
||||
qpms_bessel_t btyp, qpms_normalisation_t norm) {
|
||||
lmcheck(l,m);
|
||||
csphvec_t N;
|
||||
complex double *bessel = malloc((l+1)*sizeof(complex double));
|
||||
if(qpms_sph_bessel_fill(btyp, l, kdlj.r, bessel)) abort();
|
||||
qpms_pitau_t pt = qpms_pitau_get(kdlj.theta, l, norm);
|
||||
complex double eimf = cexp(m * kdlj.phi * I);
|
||||
qpms_y_t y = qpms_mn2y(m,l);
|
||||
|
||||
N.rc = l*(l+1) * pt.leg[y] * bessel[l] / kdlj.r * eimf;
|
||||
complex double besselfac = bessel[l-1] - l * bessel[l] / kdlj.r;
|
||||
N.thetac = pt.tau[y] * besselfac * eimf;
|
||||
N.phic = pt.pi[y] * besselfac * I * eimf;
|
||||
|
||||
qpms_pitau_free(pt);
|
||||
free(bessel);
|
||||
return N;
|
||||
}
|
||||
csphvec_t qpms_vswf_single_mg(qpms_m_t m, qpms_l_t l, sph_t kdlj,
|
||||
qpms_bessel_t btyp, qpms_normalisation_t norm) {
|
||||
lmcheck(l,m);
|
||||
csphvec_t M;
|
||||
complex double *bessel = malloc((l+1)*sizeof(complex double));
|
||||
if(qpms_sph_bessel_fill(btyp, l, kdlj.r, bessel)) abort();
|
||||
qpms_pitau_t pt = qpms_pitau_get(kdlj.theta, l, norm);
|
||||
complex double eimf = cexp(m * kdlj.phi * I);
|
||||
qpms_y_t y = qpms_mn2y(m,l);
|
||||
|
||||
M.rc = 0.;
|
||||
M.thetac = pt.pi[y] * bessel[l] * I * eimf;
|
||||
M.phic = -pt.tau[y] * bessel[l] * eimf;
|
||||
|
||||
qpms_pitau_free(pt);
|
||||
free(bessel);
|
||||
return M;
|
||||
}
|
||||
|
||||
qpms_vswfset_sph_t *qpms_vswfset_make(qpms_l_t lMax, sph_t kdlj,
|
||||
qpms_bessel_t btyp, qpms_normalisation_t norm) {
|
||||
qpms_vswfset_sph_t *res = malloc(sizeof(qpms_vswfset_sph_t));
|
||||
res->lMax = lMax;
|
||||
qpms_y_t nelem = qpms_lMax2nelem(lMax);
|
||||
res->el = malloc(sizeof(csphvec_t)*nelem);
|
||||
res->mg = malloc(sizeof(csphvec_t)*nelem);
|
||||
if(QPMS_SUCCESS != qpms_vswf_fill(res->mg, res->el, lMax, kdlj, btyp, norm))
|
||||
abort(); // or return NULL? or rather assert?
|
||||
return res;
|
||||
}
|
||||
|
||||
void qpms_vswfset_sph_pfree(qpms_vswfset_sph_t *w) {
|
||||
assert(NULL != w && NULL != w->el && NULL != w->mg);
|
||||
free(w->el);
|
||||
free(w->mg);
|
||||
free(w);
|
||||
}
|
||||
|
||||
qpms_errno_t qpms_vswf_fill(csphvec_t *mgtarget, csphvec_t *eltarget,
|
||||
qpms_l_t lMax, sph_t kr,
|
||||
qpms_bessel_t btyp, qpms_normalisation_t norm) {
|
||||
assert(lMax >= 1);
|
||||
complex double *bessel = malloc((lMax+1)*sizeof(complex double));
|
||||
if(qpms_sph_bessel_fill(btyp, lMax, kr.r, bessel)) abort();
|
||||
qpms_pitau_t pt = qpms_pitau_get(kr.theta, lMax, norm);
|
||||
complex double const *pbes = bessel + 1; // starting from l = 1
|
||||
double const *pleg = pt.leg;
|
||||
double const *ppi = pt.pi;
|
||||
double const *ptau = pt.tau;
|
||||
csphvec_t *pmg = mgtarget, *pel = eltarget;
|
||||
for(qpms_l_t l = 1; l <= lMax; ++l) {
|
||||
complex double besfac = *pbes / kr.r;
|
||||
complex double besderfac = *(pbes-1) - l * besfac;
|
||||
for(qpms_m_t m = -l; m <= l; ++m) {
|
||||
complex double eimf = cexp(m * kr.phi * I);
|
||||
pel->rc = l*(l+1) * (*pleg) * besfac * eimf;
|
||||
pel->thetac = *ptau * besderfac * eimf;
|
||||
pel->phic = *ppi * besderfac * I * eimf;
|
||||
pmg->rc = 0.;
|
||||
pmg->thetac = *ppi * (*pbes) * I * eimf;
|
||||
pmg->phic = - *ptau * (*pbes) * eimf;
|
||||
++pleg; ++ppi; ++ptau; ++pel; ++pmg;
|
||||
}
|
||||
++pbes;
|
||||
}
|
||||
free(bessel);
|
||||
qpms_pitau_free(pt);
|
||||
return QPMS_SUCCESS;
|
||||
}
|
||||
|
|
|
|||
|
|
@ -31,6 +31,9 @@ qpms_errno_t qpms_legendre_deriv_y_get(double **result, double **result_deriv, d
|
|||
qpms_errno_t qpms_legendre_deriv_y_fill(double *where, double *where_deriv, double x,
|
||||
qpms_l_t lMax, gsl_sf_legendre_t lnorm, double csphase);
|
||||
|
||||
qpms_errno_t qpms_vswf_fill(csphvec_t *resultM, csphvec_t *resultN, qpms_l_t lMax, sph_t kdrj,
|
||||
qpms_bessel_t btyp, qpms_normalisation_t norm);
|
||||
|
||||
qpms_vswfset_sph_t *qpms_vswfset_make(qpms_l_t lMax, sph_t kdlj,
|
||||
qpms_bessel_t btyp, qpms_normalisation_t norm);//NI
|
||||
void qpms_vswfset_sph_pfree(qpms_vswfset_sph_t *);//NI
|
||||
|
|
|
|||
Loading…
Reference in New Issue