C indexing functions to separate file, new normalizations in progress

Former-commit-id: 30b4ab302fe69fedc8c12bdb7b3b35f532cfc35d

qpms/indexing.h

@@ -0,0 +1,27 @@
+#ifndef QPMS_INDEXING_H
+#define QPMS_INDEXING_H
+
+#include "qpms_types.h"
+
+static inline qpms_y_t qpms_mn2y(qpms_m_t m, qpms_l_t n) {
+        return (qpms_y_t) n * (n + 1) + m - 1;
+}
+
+static inline qpms_lm_t qpms_y2n(qpms_y_t y) {
+        //return (sqrt(5+y)-2)/2; // the cast will truncate the fractional part, which is what we want
+        return sqrt(y+1);
+}
+
+static inline qpms_m_t qpms_yn2m(qpms_y_t y, qpms_l_t n) {
+        return y-qpms_mn2y(0,n);
+}
+
+static inline void qpms_y2mn_p(qpms_y_t y, qpms_m_t *m, qpms_l_t *n){
+        *m=qpms_yn2m(y,*n=qpms_y2n(y));
+}
+
+static inline qpms_y_t qpms_lMax2nelem(qpms_l_t lmax){
+	return lmax * ((qpms_y_t)lmax + 2);
+}
+
+#endif //QPMS_INDEXING_H

qpms/qpms_types.h

@@ -7,6 +7,8 @@
 
 // integer index types
 typedef int qpms_lm_t;
+typedef unsigned int qpms_l_t;
+typedef qpms_lm_t qpms_m_t;
 typedef size_t qpms_y_t;
 
 // Normalisations

qpms/translations.c

@@ -1,11 +1,17 @@
 #include <math.h>
 #include "gaunt.h"
 #include "translations.h"
+#include "indexing.h" // TODO replace size_t and int with own index types here
 #include <stdbool.h>
 #include <gsl/gsl_sf_legendre.h>
 #include <gsl/gsl_sf_bessel.h>
 #include "assert_cython_workaround.h"
+#include <stdlib.h> //abort()
 
+/*
+ * References:
+ * [1] Yu-Lin Xu, Journal of Computational Physics 127, 285–298 (1996)
+ */
 
 static const double sqrtpi = 1.7724538509055160272981674833411451827975494561223871;
 //static const double ln2 = 0.693147180559945309417232121458176568075500134360255254120;
@@ -61,9 +67,10 @@ int qpms_sph_bessel_array(qpms_bessel_t typ, int lmax, double x, complex double
 	assert(0);
 }
 
-
+// [1], eq. (82)
-complex double qpms_trans_single_A_Taylor(int m, int n, int mu, int nu, sph_t kdlj,
+complex double qpms_trans_single_A_Xu(int m, int n, int mu, int nu, sph_t kdlj,
-		bool r_ge_d, qpms_bessel_t J) { // TODO make J enum
+		bool r_ge_d, qpms_bessel_t J) {
+	abort(); // FIXME, THIS IS STILL TAYLOR
 	if(r_ge_d) J = QPMS_BESSEL_REGULAR;
 
 	double costheta = cos(kdlj.theta);
@@ -105,6 +112,155 @@ complex double qpms_trans_single_A_Taylor(int m, int n, int mu, int nu, sph_t kd
 	return (presum / prenormratio) * sum;
 }
 
+
+
+complex double qpms_trans_single_A_Kristensson(int m, int n, int mu, int nu, sph_t kdlj,
+		bool r_ge_d, qpms_bessel_t J) {
+	abort();// FIXME, THIS IS STILL TAYLOR
+	if(r_ge_d) J = QPMS_BESSEL_REGULAR;
+
+	double costheta = cos(kdlj.theta);
+
+	int qmax = gaunt_q_max(-m,n,mu,nu); // nemá tu být +m?
+	// N.B. -m !!!!!!
+	double a1q[qmax+1];
+	int err;
+	gaunt_xu(-m,n,mu,nu,qmax,a1q,&err);
+	double a1q0 = a1q[0];
+	if (err) abort();
+
+	double leg[gsl_sf_legendre_array_n(n+nu)];
+	if (gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu,costheta,-1,leg)) abort();
+	complex double bes[n+nu+1];
+	if (qpms_sph_bessel_array(J, n+nu, kdlj.r, bes)) abort();
+	complex double sum = 0;
+	for(int q = 0; q <= qmax; ++q) {
+		int p = n+nu-2*q;
+		int Pp_order = mu-m;
+		//if(p < abs(Pp_order)) continue; // FIXME raději nastav lépe meze
+		assert(p >= abs(Pp_order));
+		double a1q_n = a1q[q] / a1q0;
+		double Pp = leg[gsl_sf_legendre_array_index(p, abs(Pp_order))];
+		if (Pp_order < 0) Pp *= min1pow(mu-m) * exp(lgamma(1+p+Pp_order)-lgamma(1+p-Pp_order));
+		complex double zp = bes[p];
+		complex double summandq = (n*(n+1) + nu*(nu+1) - p*(p+1)) * min1pow(q) * a1q_n * zp * Pp;
+		sum += summandq;
+	}
+
+	double exponent=(lgamma(2*n+1)-lgamma(n+2)+lgamma(2*nu+3)-lgamma(nu+2)
+			+lgamma(n+nu+m-mu+1)-lgamma(n-m+1)-lgamma(nu+mu+1)
+			+lgamma(n+nu+1) - lgamma(2*(n+nu)+1));
+	complex double presum = exp(exponent);
+	presum *= cexp(I*(mu-m)*kdlj.phi) * min1pow(m) * ipow(nu+n) / (4*n);
+
+	complex double prenormratio = ipow(nu-n) *  sqrt(((2.*nu+1)/(2.*n+1))* exp(
+				lgamma(n+m+1)-lgamma(n-m+1)+lgamma(nu-mu+1)-lgamma(nu+mu+1)));
+	return (presum / prenormratio) * sum;
+}
+
+
+
+complex double qpms_trans_single_A_Taylor(int m, int n, int mu, int nu, sph_t kdlj,
+		bool r_ge_d, qpms_bessel_t J) {
+	if(r_ge_d) J = QPMS_BESSEL_REGULAR;
+
+	double costheta = cos(kdlj.theta);
+
+	int qmax = gaunt_q_max(-m,n,mu,nu); // nemá tu být +m?
+	// N.B. -m !!!!!!
+	double a1q[qmax+1];
+	int err;
+	gaunt_xu(-m,n,mu,nu,qmax,a1q,&err);
+	double a1q0 = a1q[0];
+	if (err) abort();
+
+	double leg[gsl_sf_legendre_array_n(n+nu)];
+	if (gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu,costheta,-1,leg)) abort();
+	complex double bes[n+nu+1];
+	if (qpms_sph_bessel_array(J, n+nu, kdlj.r, bes)) abort();
+	complex double sum = 0;
+	for(int q = 0; q <= qmax; ++q) {
+		int p = n+nu-2*q;
+		int Pp_order = mu-m;
+		//if(p < abs(Pp_order)) continue; // FIXME raději nastav lépe meze
+		assert(p >= abs(Pp_order));
+		double a1q_n = a1q[q] / a1q0;
+		double Pp = leg[gsl_sf_legendre_array_index(p, abs(Pp_order))];
+		if (Pp_order < 0) Pp *= min1pow(mu-m) * exp(lgamma(1+p+Pp_order)-lgamma(1+p-Pp_order));
+		complex double zp = bes[p];
+		complex double summandq = (n*(n+1) + nu*(nu+1) - p*(p+1)) * min1pow(q) * a1q_n * zp * Pp;
+		sum += summandq;
+	}
+
+	double exponent=(lgamma(2*n+1)-lgamma(n+2)+lgamma(2*nu+3)-lgamma(nu+2)
+			+lgamma(n+nu+m-mu+1)-lgamma(n-m+1)-lgamma(nu+mu+1)
+			+lgamma(n+nu+1) - lgamma(2*(n+nu)+1));
+	complex double presum = exp(exponent);
+	presum *= cexp(I*(mu-m)*kdlj.phi) * min1pow(m) * ipow(nu+n) / (4*n);
+
+	complex double prenormratio = ipow(nu-n) *  sqrt(((2.*nu+1)/(2.*n+1))* exp(
+				lgamma(n+m+1)-lgamma(n-m+1)+lgamma(nu-mu+1)-lgamma(nu+mu+1)));
+	return (presum / prenormratio) * sum;
+}
+
+// [1], 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) { 
+	abort(); // FIXME, this is still Taylor
+	if(r_ge_d) J = QPMS_BESSEL_REGULAR;
+	double costheta = cos(kdlj.theta);
+
+	int q2max = gaunt_q_max(-m-1,n+1,mu+1,nu);
+	int Qmax = gaunt_q_max(-m,n+1,mu,nu);
+	double a2q[q2max+1], a3q[Qmax+1], a2q0, a3q0;
+	int err;
+	if (mu == nu) {
+		for (int q = 0; q <= q2max; ++q) 
+			a2q[q] = 0;
+		a2q0 = 1;
+	}
+	else { 
+		gaunt_xu(-m-1,n+1,mu+1,nu,q2max,a2q,&err); if (err) abort();
+		a2q0 = a2q[0];
+	}
+	gaunt_xu(-m,n+1,mu,nu,Qmax,a3q,&err); if (err) abort();
+	a3q0 = a3q[0];
+
+	double leg[gsl_sf_legendre_array_n(n+nu+1)];
+	if (gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu+1,costheta,-1,leg)) abort();
+	complex double bes[n+nu+2];
+	if (qpms_sph_bessel_array(J, n+nu+1, kdlj.r, bes)) abort();
+
+	complex double sum = 0;
+	for (int q = 0; q <= Qmax; ++q) {
+		int p = n+nu-2*q;
+		double a2q_n = a2q[q]/a2q0;
+		double a3q_n = a3q[q]/a3q0;
+		complex double zp_ = bes[p+1];
+		int Pp_order_ = mu-m;
+		//if(p+1 < abs(Pp_order_)) continue; // FIXME raději nastav lépe meze
+		assert(p+1 >= abs(Pp_order_));
+		double Pp_ = leg[gsl_sf_legendre_array_index(p+1, abs(Pp_order_))];
+		if (Pp_order_ < 0) Pp_ *= min1pow(mu-m) * exp(lgamma(1+1+p+Pp_order_)-lgamma(1+1+p-Pp_order_));
+		complex double summandq = ((2*(n+1)*(nu-mu)*a2q_n
+					-(-nu*(nu+1) - n*(n+3) - 2*mu*(n+1)+p*(p+3))* a3q_n)
+				*min1pow(q) * zp_ * Pp_);
+		sum += summandq;
+	}
+
+	double exponent=(lgamma(2*n+3)-lgamma(n+2)+lgamma(2*nu+3)-lgamma(nu+2)
+			+lgamma(n+nu+m-mu+2)-lgamma(n-m+1)-lgamma(nu+mu+1)
+			+lgamma(n+nu+2) - lgamma(2*(n+nu)+3));
+	complex double presum = exp(exponent);
+	presum *= cexp(I*(mu-m)*kdlj.phi) * min1pow(m) * ipow(nu+n+1) / (
+			(4*n)*(n+1)*(n+m+1));
+
+	// Taylor normalisation v2, proven to be equivalent
+	complex double prenormratio = ipow(nu-n) * sqrt(((2.*nu+1)/(2.*n+1))* exp(
+				lgamma(n+m+1)-lgamma(n-m+1)+lgamma(nu-mu+1)-lgamma(nu+mu+1)));
+
+
+
 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) { 
 	if(r_ge_d) J = QPMS_BESSEL_REGULAR;
@@ -186,19 +342,6 @@ static inline size_t qpms_mn2y(int m, int n) {
 	return (size_t) n * (n + 1) + m - 1;
 }
 
-static inline int qpms_y2n(size_t y) {
-	//return (sqrt(5+y)-2)/2; // the cast will truncate the fractional part, which is what we want
-	return sqrt(y+1);
-}
-
-static inline int qpms_yn2m(size_t y, int n) {
-	return y-qpms_mn2y(0,n);
-}
-
-static inline void qpms_y2mn_p(size_t y, int *m, int *n){
-	*m=qpms_yn2m(y,*n=qpms_y2n(y));
-}
-
 static inline size_t qpms_trans_calculator_index_mnmunu(const qpms_trans_calculator *c,
 		int m, int n, int mu, int nu){
 	return c->nelem * qpms_mn2y(m,n) + qpms_mn2y(mu,nu);