From 8b5c07f8055d6888459fd662c85f706ef84e0471 Mon Sep 17 00:00:00 2001
From: Franz Zotter <fzotter@users.sourceforge.net>
Date: Sun, 11 Oct 2009 21:22:05 +0000
Subject: added [mtx_spherical_radial], the radial functions of the spherical
 base-solutions

svn path=/trunk/externals/iem/iemmatrix/; revision=12577
---
 src/mtx_spherical_harmonics/sph_radial.c | 82 ++++++++++++++++++++++++++++++++
 src/mtx_spherical_harmonics/sph_radial.h | 26 ++++++++++
 2 files changed, 108 insertions(+)
 create mode 100644 src/mtx_spherical_harmonics/sph_radial.c
 create mode 100644 src/mtx_spherical_harmonics/sph_radial.h

(limited to 'src/mtx_spherical_harmonics')

diff --git a/src/mtx_spherical_harmonics/sph_radial.c b/src/mtx_spherical_harmonics/sph_radial.c
new file mode 100644
index 0000000..ec3536e
--- /dev/null
+++ b/src/mtx_spherical_harmonics/sph_radial.c
@@ -0,0 +1,82 @@
+/*
+ * Recursive computation of (arbitrary degree) spherical Bessel/Neumann/Hankel functions, 
+ * according to Gumerov and Duraiswami,
+ * "The Fast Multipole Methods for the Helmholtz Equation in Three Dimensions",
+ * Elsevier, 2005.
+ *
+ * Implementation by Franz Zotter, Institute of Electronic Music and Acoustics
+ * (IEM), University of Music and Dramatic Arts (KUG), Graz, Austria
+ * http://iem.at/Members/zotter, 2007.
+ *
+ * This code is published under the Gnu General Public License, see
+ * "LICENSE.txt"
+ */
+
+#include <math.h>
+
+#include "sph_radial.h"
+
+#define EPS 1e-10
+
+static void radialRecurrence (double x, double *y, int n);
+
+// the two recurrences for higher n:
+// by now no numeric stabilization for the bessel function is performed
+
+static void radialRecurrence (double x, double *y, int n) {
+   int k;
+   for (k=1;k<n;k++) {
+      y[k+1] = -y[k-1] + y[k]/x * (2*k+1);
+   }
+}
+
+static void radialDiffRecurrence (double x, double *y1, double *yd, int n) {
+   int k;
+   for (k=0;k<n;k++) {
+      yd[k] = y1[k]/x * n - y1[k+1];
+   }
+}
+
+void sphBessel (double x, double *y, int n) { //TODO: small values!
+   if (y==0) 
+      return;
+   if (n>=0) 
+      y[0] = (x<EPS)?1.0:sin(x)/x;
+   if (n>=1) 
+      y[1] = -cos(x)/x + y[0]/x;
+   post("before %f %f %f",y[0],y[1],y[2]);
+   radialRecurrence (x,y,n);
+   post("after %f %f %f",y[0],y[1],y[2]);
+}
+
+void sphNeumann (double x, double *y, int n) {
+   if (y==0) 
+      return;
+   if (n>=0) 
+      y[0] = -cos(x)/x;
+   if (n>=1) 
+      y[1] = ((x<EPS)?1.0:sin(x)/x) - y[0]/x;
+   radialRecurrence (x,y,n);
+}
+
+void sphBesselDiff (double x, double *y, int n) {
+   double *y1;
+   if (n<0)
+      return;
+   if ((y1 = (double*)calloc(n+2,sizeof(double)))==0)
+      return;
+   sphBessel (x,y1,n+1);
+   radialDiffRecurrence (x,y1,y,n);
+   free(y1);
+}
+
+void sphNeumannDiff (double x, double *y, int n) {
+   double *y1;
+   if (n<0)
+      return;
+   if ((y1 = (double*)calloc(n+2,sizeof(double)))==0)
+      return;
+   sphNeumann (x,y,n+1);
+   radialDiffRecurrence (x,y1,y,n);
+   free(y1);
+}
diff --git a/src/mtx_spherical_harmonics/sph_radial.h b/src/mtx_spherical_harmonics/sph_radial.h
new file mode 100644
index 0000000..43661ce
--- /dev/null
+++ b/src/mtx_spherical_harmonics/sph_radial.h
@@ -0,0 +1,26 @@
+/*
+ * Recursive computation of (arbitrary degree) spherical Bessel/Neumann/Hankel functions, 
+ * according to Gumerov and Duraiswami,
+ * "The Fast Multipole Methods for the Helmholtz Equation in Three Dimensions",
+ * Elsevier, 2005.
+ *
+ * Implementation by Franz Zotter, Institute of Electronic Music and Acoustics
+ * (IEM), University of Music and Dramatic Arts (KUG), Graz, Austria
+ * http://iem.at/Members/zotter, 2007.
+ *
+ * This code is published under the Gnu General Public License, see
+ * "LICENSE.txt"
+ */
+
+#ifndef __SPH_RADIAL_H__
+#define __SPH_RADIAL_H__
+
+void sphBessel (double x, double *y, int n);
+
+void sphNeumann (double x, double *y, int n);
+
+void sphBesselDiff (double x, double *y, int n);
+
+void sphNeumannDiff (double x, double *y, int n);
+
+#endif  // __SPH_RADIAL_H__
-- 
cgit v1.2.1