Práce na vswf ; jdu domů
Former-commit-id: 112c65dcb0de85908b43cd488c63ac14072dc97e
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Marek Nečada
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@ -915,7 +915,69 @@ reference "eq:2d long range regularisation problem statement"
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\end_inset
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might lead to satisfactory results; see below.
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\end_layout
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\begin_layout Standard
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\begin_inset Note Note
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status open
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\begin_layout Plain Layout
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In natural/dimensionless units;
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\begin_inset Formula $x=k_{0}r$
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\end_inset
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,
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\begin_inset Formula $\tilde{k}=k/k_{0}$
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\end_inset
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,
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\begin_inset Formula $č=c/k_{0}$
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\end_inset
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\begin_inset Formula
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\[
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s_{q}(x)\equiv e^{ix}x^{-q}
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\]
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\end_inset
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\begin_inset Formula
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\[
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\tilde{\rho}_{\kappa,č}(x)\equiv\left(1-e^{-čx}\right)^{\text{\kappa}}=\left(1-e^{-\frac{c}{k_{0}}k_{0}r}\right)^{\kappa}=\left(1-e^{-cr}\right)^{\kappa}=\rho_{\kappa,c}(r)
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\]
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\end_inset
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\begin_inset Formula
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\[
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s_{q}^{\textup{L}}\left(x\right)\equiv s_{q}(x)\tilde{\rho}_{\kappa,č}(x)=e^{ix}x^{-q}\left(1-e^{-čx}\right)^{\text{\kappa}}
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\]
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\end_inset
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\begin_inset Formula
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\begin{eqnarray*}
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\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\\
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& = & \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)\\
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& = & k_{0}^{2}\int_{0}^{\infty}s_{k_{0},q}\left(r\right)\rho_{\kappa,c}(r)rJ_{n}\left(kr\right)\ud r\\
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& = & k_{0}^{2}\pht n{s_{k_{0},q}^{\textup{L}}}\left(k\right)
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\end{eqnarray*}
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\end_inset
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Standard
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\begin_inset Note Note
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status open
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@ -18,7 +18,9 @@ typedef enum {
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// Normalisations
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typedef enum {
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// As in TODO
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QPMS_NORMALIZATION_XU = 3, // NI!
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// As in http://www.eit.lth.se/fileadmin/eit/courses/eit080f/Literature/book.pdf, power-normalised
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QPMS_NORMALIZATION_KRISTENSSON = 2, // NI!
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QPMS_NORMALIZATION_POWER = QPMS_NORMALIZATION_KRISTENSSON, // NI!
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QPMS_NORMALIZATION_TAYLOR = 1,
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18
qpms/vswf.c
18
qpms/vswf.c
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@ -2,7 +2,7 @@
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#include <math.h>
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// Legendre functions also for negative m, see DLMF 14.9.3
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qpms_errno_t qpms_legendre_deriv_y_fill(double *target, double *target_deriv, double x, qpms_l_t lMax,
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int qpms_errno_t qpms_legendre_deriv_y_fill(double *target, double *target_deriv, double x, qpms_l_t lMax,
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gsl_sf_legendre_t lnorm, double csphase)
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{
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size_t n = gsl_sf_legenre_array_n(lMax);
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@ -12,7 +12,7 @@ qpms_errno_t qpms_legendre_deriv_y_fill(double *target, double *target_deriv, do
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lnorm, (size_t)lMax, x, csphase, legendre_tmp,legendre_tmp_deriv);
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for (qpms_l_t l = 0; l <= lMax; ++l)
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for (qpms_m_t m = 0; m <= l; ++m) {
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qpms_y_t y = gpms_mn2y(m,l);
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qpms_y_t y = qpms_mn2y(m,l);
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size_t i = gsl_sf_legenre_array_index(l,m);
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target[y] = legendre_tmp[i];
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target_deriv[y] = legendre_deriv_tmp[i];
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@ -21,7 +21,7 @@ qpms_errno_t qpms_legendre_deriv_y_fill(double *target, double *target_deriv, do
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case GSL_SF_LEGEDRE_NONE:
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for (qpms_l_t l = 0; l <= lMax; ++l)
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for (qpms_m_t m = 1; m <= l; ++m) {
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qpms_y_t y = gpms_mn2y(-m,l);
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qpms_y_t y = qpms_mn2y(-m,l);
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size_t i = gsl_sf_legenre_array_index(l,m);
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// viz DLMF 14.9.3, čert ví, jak je to s cs fasí.
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double factor = exp(lgamma(l-m+1)-lgamma(n+m+1))*((m%2)?-1:1);
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@ -34,7 +34,7 @@ qpms_errno_t qpms_legendre_deriv_y_fill(double *target, double *target_deriv, do
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case GSL_SF_LEGENDRE_FULL:
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for (qpms_l_t l = 0; l <= lMax; ++l)
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for (qpms_m_t m = 1; m <= l; ++m) {
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qpms_y_t y = gpms_mn2y(-m,l);
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qpms_y_t y = qpms_mn2y(-m,l);
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size_t i = gsl_sf_legenre_array_index(l,m);
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// viz DLMF 14.9.3, čert ví, jak je to s cs fasí.
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double factor = ((m%2)?-1:1); // this is the difference from the unnormalised case
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@ -51,13 +51,13 @@ qpms_errno_t qpms_legendre_deriv_y_fill(double *target, double *target_deriv, do
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return QPMS_SUCCESS;
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}
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// FIXME ZAPOMNĚL JSEM NA POLE DERIVACÍ (TÉŽ HLAVIČKOVÝ SOUBOR)
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double *qpms_legendre_deriv_y_get(double x, qpms_l_t lMax, gsle_sf_legendre_t lnorm,
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int qpms_legendre_deriv_y_get(double **target, double **dtarget, double x, qpms_l_t lMax, gsl_sf_legendre_t lnorm,
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double csphase)
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{
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double *ar = malloc(sizeof(double)*qpms_lMaxnelem(lMax));
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if (qpms_legendre_deriv_y_fill(ar, x, lMax, lnorm, csphase))
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abort();
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*target = malloc(sizeof(double)*qpms_lMax2nelem(lMax));
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*dtarget = malloc(sizeof(double)*qpms_lMax2nelem(lMax));
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return qpms_legendre_deriv_y_fill(ar, x, lMax, lnorm, csphase);
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}
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14
qpms/vswf.h
14
qpms/vswf.h
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@ -4,10 +4,10 @@
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#include <gsl/gsl_sf_legendre.h>
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// Electric wave N; NI
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complex double qpms_vswf_single_el(int m, int n, sph_t kdlj,
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csphvec_t qpms_vswf_single_el(int m, int n, sph_t kdlj,
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qpms_bessel_t btyp, qpms_normalization_t norm);
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// Magnetic wave M; NI
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complex double qpms_vswf_single_mg(int m, int n, sph_t kdlj,
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csphvec_t qpms_vswf_single_mg(int m, int n, sph_t kdlj,
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qpms_bessel_t btyp, qpms_normalization_t norm);
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// Set of electric and magnetic VSWF in spherical coordinate basis
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@ -24,12 +24,12 @@ typedef struct {
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* N.B. for the norm definitions, see
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* https://www.gnu.org/software/gsl/manual/html_node/Associated-Legendre-Polynomials-and-Spherical-Harmonics.html
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* ( gsl/specfunc/legendre_source.c and 7.24.2 of gsl docs
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*
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*/
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double *qpms_legendre_deriv_y_get(double x, qpms_l_t lMax,
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gsle_sf_legendre_t lnorm, double csphase); //FIXME what about derivative?
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qpms_errno_t qpms_legendre_deriv_y_fill(double *where, double *where_deriv, double x,
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qpms_l_t lMax, gsl_sf_legendre_t lnorm, double csphase); //NI
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int qpms_legendre_deriv_y_get(double **result, double **result_deriv, double x, qpms_l_t lMax,
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gsle_sf_legendre_t lnorm, double csphase);
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int qpms_errno_t qpms_legendre_deriv_y_fill(double *where, double *where_deriv, double x,
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qpms_l_t lMax, gsl_sf_legendre_t lnorm, double csphase);
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qpms_vswfset_sph_t *qpms_vswfset_make(qpms_l_t lMax, sph_t kdlj,
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qpms_bessel_t btyp, qpms_normalization_t norm);//NI
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