Dudom

Former-commit-id: ade18052fd1fbc4c02557c8fad65d66ad0272f47

notes/Scattering and Shit.lyx

@@ -1473,6 +1473,54 @@ Mie decomposition of Green's function for single nanoparticle
 Translation of spherical waves: getting insane
 \end_layout
 
+\begin_layout Standard
+Cruzan's formulation, Xu's normalisation 
+\begin_inset CommandInset citation
+LatexCommand cite
+after "(59)"
+key "xu_efficient_1998"
+
+\end_inset
+
+:
+\begin_inset Formula 
+\[
+B_{m,n,\mu,\nu}=\underbrace{\left(-1\right)^{-m}\frac{\left(2\nu+1\right)\left(n+m\right)!\left(\nu-\mu\right)!}{2n\left(n+1\right)\left(n-m\right)!\left(\nu+\mu\right)!}\sum_{q=1}^{Q_{max}^{-m,n,\mu,\nu}}i^{p+1}\sqrt{\left(\left(p+1\right)^{2}-\left(n-\nu\right)^{2}\right)\left(\left(n+\nu+1\right)^{2}-\left(p+1\right)^{2}\right)}b_{-m,n,\mu,\nu}^{p,p+1}}_{\mbox{(without the \ensuremath{\sum})}\equiv B_{m,n,\mu,\nu}^{q}}z_{p+1}P_{p+1}e^{i\left(\mu-m\right)\phi},
+\]
+
+\end_inset
+
+where 
+\begin_inset CommandInset citation
+LatexCommand cite
+after "(28,5,60,61)"
+key "xu_efficient_1998"
+
+\end_inset
+
+ 
+\begin_inset Formula $p\equiv n+\nu-2q$
+\end_inset
+
+, 
+\begin_inset Formula $Q_{max}^{-m,n,\mu,\nu}\equiv\min\left(n,\nu,\frac{n+\nu+1-\left|\mu-m\right|}{2}\right)$
+\end_inset
+
+,
+\begin_inset Formula 
+\[
+b_{-m,n,\mu,\nu}^{p,p+1}\equiv\left(-1\right)^{\mu-m}\left(2p+3\right)\sqrt{\frac{\left(n-m\right)!\left(\nu+\mu\right)!\left(p+m-\mu+1\right)!}{\left(n+m\right)!\left(\nu-\mu\right)!\left(p-m+\mu+1\right)!}}\begin{pmatrix}n & \nu & p+1\\
+-m & \mu & m-\mu
+\end{pmatrix}\begin{pmatrix}n & \nu & p\\
+0 & 0 & 0
+\end{pmatrix}.
+\]
+
+\end_inset
+
+
+\end_layout
+
 \begin_layout Chapter
 Multiple scattering: nice linear algebra born from all the mess
 \end_layout
@@ -1484,7 +1532,7 @@ Quantisation of quasistatic modes of a sphere
 \begin_layout Standard
 \begin_inset CommandInset bibtex
 LatexCommand bibtex
-bibfiles "Electrodynamics,/home/mmn/repo/qpms/Electrodynamics"
+bibfiles "/l/necadam1/repo/qpms/Electrodynamics"
 options "plain"
 
 \end_inset

qpms/translations.c

@@ -8,6 +8,7 @@
 #include <gsl/gsl_sf_bessel.h>
 #include "assert_cython_workaround.h"
 #include <stdlib.h> //abort()
+#include <gsl/gsl_sf_coupling.h>
 
 // if defined, the pointer B_multipliers[y] corresponds to the q = 1 element;
 // otherwise, it corresponds to the q = 0 element, which should be identically zero
@@ -228,6 +229,7 @@ complex double qpms_trans_single_A_Taylor(int m, int n, int mu, int nu, sph_t kd
 // [Xu_old], eq. (83)
 complex double qpms_trans_single_B_Xu(int m, int n, int mu, int nu, sph_t kdlj,
 		bool r_ge_d, qpms_bessel_t J) { 
+	assert(0); // FIXME probably gives wrong values, do not use.
 	if(r_ge_d) J = QPMS_BESSEL_REGULAR;
 	double costheta = cos(kdlj.theta);
 
@@ -287,6 +289,7 @@ complex double qpms_trans_single_B_Xu(int m, int n, int mu, int nu, sph_t kdlj,
 complex double qpms_trans_single_B(qpms_normalisation_t norm,
 		int m, int n, int mu, int nu, sph_t kdlj,
 		bool r_ge_d, qpms_bessel_t J) { 
+	assert(0); // FIXME probably gives wrong values, do not use.
 	if(r_ge_d) J = QPMS_BESSEL_REGULAR;
 	double costheta = cos(kdlj.theta);
 
@@ -348,6 +351,7 @@ complex double qpms_trans_single_B(qpms_normalisation_t norm,
 
 complex double qpms_trans_single_B_Taylor(int m, int n, int mu, int nu, sph_t kdlj,
 		bool r_ge_d, qpms_bessel_t J) { 
+	assert(0); // FIXME probably gives wrong values, do not use.
 	if(r_ge_d) J = QPMS_BESSEL_REGULAR;
 	double costheta = cos(kdlj.theta);
 
@@ -480,9 +484,29 @@ static void qpms_trans_calculator_multipliers_A_general(
 }
 
 
-/*static*/ void qpms_trans_calculator_multipliers_B_general(
+void qpms_trans_calculator_multipliers_B_general(
+		qpms_normalisation_t norm,
+		complex double *dest, int m, int n, int mu, int nu, int Qmax){
+	// This is according to the Cruzan-type formula [Xu](59)
+	assert(Qmax == gauntB_Q_max(-m,n,mu,nu));
+
+	
+	
+	int csphase = qpms_normalisation_t_csphase(norm); //TODO FIXME use this
+        norm = qpms_normalisation_t_normonly(norm);
+        double normlogfac= qpms_trans_normlogfac(norm,m,n,mu,nu);
+        double normfac = qpms_trans_normfac(norm,m,n,mu,nu);
+        // TODO use csphase to modify normfac here!!!!
+        // normfac = xxx ? -normfac : normfac;
+        normfac *= min1pow(m);//different from old taylor
+
+
+}
+
+/*static*/ void qpms_trans_calculator_multipliers_B_general_oldXu(
 		qpms_normalisation_t norm,
 		complex double *dest, int m, int n, int mu, int nu, int Qmax) {
+	assert(0); // FIXME probably gives wrong values, do not use.
 	assert(Qmax == gauntB_Q_max(-m,n,mu,nu));
 	int q2max = gaunt_q_max(-m-1,n+1,mu+1,nu);
 	// assert(Qmax == q2max);
@@ -607,6 +631,7 @@ static void qpms_trans_calculator_multipliers_A_Taylor(
 
 static void qpms_trans_calculator_multipliers_B_Taylor(
 		complex double *dest, int m, int n, int mu, int nu, int Qmax) {
+	assert(0); // FIXME probably gives wrong values, do not use.
 	assert(Qmax == gauntB_Q_max(-m,n,mu,nu));
 	int q2max = gaunt_q_max(-m-1,n+1,mu+1,nu);
 	//assert(Qmax == q2max);