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Práce na vswf ; jdu domů 

Former-commit-id: 112c65dcb0de85908b43cd488c63ac14072dc97e
This commit is contained in:
Marek Nečada 2018-01-26 15:07:29 +02:00
parent f6118d6ed9
commit 3312bc61e2
4 changed files with 86 additions and 22 deletions
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72
notes/ewald.lyx
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@ -915,7 +915,69 @@ reference "eq:2d long range regularisation problem statement"
\end_inset
might lead to satisfactory results; see below.
\end_layout
\begin_layout Standard
\begin_inset Note Note
status open
\begin_layout Plain Layout
In natural/dimensionless units;
\begin_inset Formula $x=k_{0}r$
\end_inset
,
\begin_inset Formula $\tilde{k}=k/k_{0}$
\end_inset
,
\begin_inset Formula $č=c/k_{0}$
\end_inset
\begin_inset Formula
\[
s_{q}(x)\equiv e^{ix}x^{-q}
\]
\end_inset
\begin_inset Formula
\[
\tilde{\rho}_{\kappa,č}(x)\equiv\left(1-e^{-čx}\right)^{\text{\kappa}}=\left(1-e^{-\frac{c}{k_{0}}k_{0}r}\right)^{\kappa}=\left(1-e^{-cr}\right)^{\kappa}=\rho_{\kappa,c}(r)
\]
\end_inset
\begin_inset Formula
\[
s_{q}^{\textup{L}}\left(x\right)\equiv s_{q}(x)\tilde{\rho}_{\kappa,č}(x)=e^{ix}x^{-q}\left(1-e^{-čx}\right)^{\text{\kappa}}
\]
\end_inset
\begin_inset Formula
\begin{eqnarray*}
\pht n{s_{q}^{\textup{L}}}\left(\tilde{k}\right) & = & \int_{0}^{\infty}s_{q}^{\textup{L}}\left(x\right)xJ_{n}\left(\tilde{k}x\right)\ud x=\int_{0}^{\infty}s_{q}\left(x\right)\tilde{\rho}_{\kappa,č}(x)xJ_{n}\left(\tilde{k}x\right)\ud x\\
& = & \int_{0}^{\infty}s_{k_{0},q}\left(r\right)\rho_{\kappa,c}(r)\left(k_{0}r\right)J_{n}\left(kr\right)\ud\left(k_{0}r\right)\\
& = & k_{0}^{2}\int_{0}^{\infty}s_{k_{0},q}\left(r\right)\rho_{\kappa,c}(r)rJ_{n}\left(kr\right)\ud r\\
& = & k_{0}^{2}\pht n{s_{k_{0},q}^{\textup{L}}}\left(k\right)
\end{eqnarray*}
\end_inset
\end_layout
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Note Note
status open
@ -3037,7 +3099,7 @@ where the spherical Hankel transform
2)
\begin_inset Formula
\[
\bsht lg(k)\equiv\int_{0}^{\infty}\ud r\, r^{2}g(r)j_{l}\left(kr\right).
\bsht lg(k)\equiv\int_{0}^{\infty}\ud r\,r^{2}g(r)j_{l}\left(kr\right).
\]
\end_inset
@ -3047,7 +3109,7 @@ Using this convention, the inverse spherical Hankel transform is given by
3)
\begin_inset Formula
\[
g(r)=\frac{2}{\pi}\int_{0}^{\infty}\ud k\, k^{2}\bsht lg(k)j_{l}(k),
g(r)=\frac{2}{\pi}\int_{0}^{\infty}\ud k\,k^{2}\bsht lg(k)j_{l}(k),
\]
\end_inset
@ -3060,7 +3122,7 @@ so it is not unitary.
An unitary convention would look like this:
\begin_inset Formula
\begin{equation}
\usht lg(k)\equiv\sqrt{\frac{2}{\pi}}\int_{0}^{\infty}\ud r\, r^{2}g(r)j_{l}\left(kr\right).\label{eq:unitary 3d Hankel tf definition}
\usht lg(k)\equiv\sqrt{\frac{2}{\pi}}\int_{0}^{\infty}\ud r\,r^{2}g(r)j_{l}\left(kr\right).\label{eq:unitary 3d Hankel tf definition}
\end{equation}
\end_inset
@ -3114,8 +3176,8 @@ where the Hankel transform of order
is defined as
\begin_inset Formula
\begin{eqnarray}
\pht mg\left(k\right) & = & \int_{0}^{\infty}\ud r\, g(r)J_{m}(kr)r\label{eq:unitary 2d Hankel tf definition}\\
& = & \left(-1\right)^{m}\int_{0}^{\infty}\ud r\, g(r)J_{\left|m\right|}(kr)r
\pht mg\left(k\right) & = & \int_{0}^{\infty}\ud r\,g(r)J_{m}(kr)r\label{eq:unitary 2d Hankel tf definition}\\
& = & \left(-1\right)^{m}\int_{0}^{\infty}\ud r\,g(r)J_{\left|m\right|}(kr)r
\end{eqnarray}
\end_inset

2
qpms/qpms_types.h
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@ -18,7 +18,9 @@ typedef enum {
// Normalisations
typedef enum {
// As in TODO
QPMS_NORMALIZATION_XU = 3, // NI!
// As in http://www.eit.lth.se/fileadmin/eit/courses/eit080f/Literature/book.pdf, power-normalised
QPMS_NORMALIZATION_KRISTENSSON = 2, // NI!
QPMS_NORMALIZATION_POWER = QPMS_NORMALIZATION_KRISTENSSON, // NI!
QPMS_NORMALIZATION_TAYLOR = 1,

18
qpms/vswf.c
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@ -2,7 +2,7 @@
#include <math.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,
int qpms_errno_t qpms_legendre_deriv_y_fill(double *target, double *target_deriv, double x, qpms_l_t lMax,
gsl_sf_legendre_t lnorm, double csphase)
{
size_t n = gsl_sf_legenre_array_n(lMax);
@ -12,7 +12,7 @@ qpms_errno_t qpms_legendre_deriv_y_fill(double *target, double *target_deriv, do
lnorm, (size_t)lMax, x, csphase, legendre_tmp,legendre_tmp_deriv);
for (qpms_l_t l = 0; l <= lMax; ++l)
for (qpms_m_t m = 0; m <= l; ++m) {
qpms_y_t y = gpms_mn2y(m,l);
qpms_y_t y = qpms_mn2y(m,l);
size_t i = gsl_sf_legenre_array_index(l,m);
target[y] = legendre_tmp[i];
target_deriv[y] = legendre_deriv_tmp[i];
@ -21,7 +21,7 @@ qpms_errno_t qpms_legendre_deriv_y_fill(double *target, double *target_deriv, do
case GSL_SF_LEGEDRE_NONE:
for (qpms_l_t l = 0; l <= lMax; ++l)
for (qpms_m_t m = 1; m <= l; ++m) {
qpms_y_t y = gpms_mn2y(-m,l);
qpms_y_t y = qpms_mn2y(-m,l);
size_t i = gsl_sf_legenre_array_index(l,m);
// viz DLMF 14.9.3, čert ví, jak je to s cs fasí.
double factor = exp(lgamma(l-m+1)-lgamma(n+m+1))*((m%2)?-1:1);
@ -34,7 +34,7 @@ qpms_errno_t qpms_legendre_deriv_y_fill(double *target, double *target_deriv, do
case GSL_SF_LEGENDRE_FULL:
for (qpms_l_t l = 0; l <= lMax; ++l)
for (qpms_m_t m = 1; m <= l; ++m) {
qpms_y_t y = gpms_mn2y(-m,l);
qpms_y_t y = qpms_mn2y(-m,l);
size_t i = gsl_sf_legenre_array_index(l,m);
// viz DLMF 14.9.3, čert ví, jak je to s cs fasí.
double factor = ((m%2)?-1:1); // this is the difference from the unnormalised case
@ -51,13 +51,13 @@ qpms_errno_t qpms_legendre_deriv_y_fill(double *target, double *target_deriv, do
return QPMS_SUCCESS;
}
// FIXME ZAPOMNĚL JSEM NA POLE DERIVACÍ (TÉŽ HLAVIČKOVÝ SOUBOR)
double *qpms_legendre_deriv_y_get(double x, qpms_l_t lMax, gsle_sf_legendre_t lnorm,
int qpms_legendre_deriv_y_get(double **target, double **dtarget, double x, qpms_l_t lMax, gsl_sf_legendre_t lnorm,
double csphase)
{
double *ar = malloc(sizeof(double)*qpms_lMaxnelem(lMax));
if (qpms_legendre_deriv_y_fill(ar, x, lMax, lnorm, csphase))
abort();
*target = malloc(sizeof(double)*qpms_lMax2nelem(lMax));
*dtarget = malloc(sizeof(double)*qpms_lMax2nelem(lMax));
return qpms_legendre_deriv_y_fill(ar, x, lMax, lnorm, csphase);
}

14
qpms/vswf.h
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@ -4,10 +4,10 @@
#include <gsl/gsl_sf_legendre.h>
// Electric wave N; NI
complex double qpms_vswf_single_el(int m, int n, sph_t kdlj,
csphvec_t qpms_vswf_single_el(int m, int n, sph_t kdlj,
qpms_bessel_t btyp, qpms_normalization_t norm);
// Magnetic wave M; NI
complex double qpms_vswf_single_mg(int m, int n, sph_t kdlj,
csphvec_t qpms_vswf_single_mg(int m, int n, sph_t kdlj,
qpms_bessel_t btyp, qpms_normalization_t norm);
// Set of electric and magnetic VSWF in spherical coordinate basis
@ -24,12 +24,12 @@ typedef struct {
* N.B. for the norm definitions, see
* https://www.gnu.org/software/gsl/manual/html_node/Associated-Legendre-Polynomials-and-Spherical-Harmonics.html
* ( gsl/specfunc/legendre_source.c and 7.24.2 of gsl docs
*
*/
double *qpms_legendre_deriv_y_get(double x, qpms_l_t lMax,
gsle_sf_legendre_t lnorm, double csphase); //FIXME what about derivative?
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); //NI
int qpms_legendre_deriv_y_get(double **result, double **result_deriv, double x, qpms_l_t lMax,
gsle_sf_legendre_t lnorm, double csphase);
int 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_vswfset_sph_t *qpms_vswfset_make(qpms_l_t lMax, sph_t kdlj,
qpms_bessel_t btyp, qpms_normalization_t norm);//NI