renamed [mtx_sh] to [mtx_spherical_harmonics].

svn path=/trunk/externals/iem/iemmatrix/; revision=10549

1 files changed, 60 insertions, 0 deletions

diff --git a/src/mtx_spherical_harmonics/sharmonics_normalization.c b/src/mtx_spherical_harmonics/sharmonics_normalization.c
new file mode 100644
index 0000000..ca97292
--- /dev/null
+++ b/src/mtx_spherical_harmonics/sharmonics_normalization.c
@@ -0,0 +1,60 @@
+/*
+ * Recursive computation of (arbitrary degree) normalization constants
+ * for spherical harmonics, 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 "mtx_spherical_harmonics/sharmonics_normalization.h"
+
+SHNorml *sharmonics_normalization_new (const size_t nmax) {
+   SHNorml *wn;
+   int n,n0,m;
+   const double oneoversqrt2 = 1.0/sqrt(2);
+   
+   // memory allocation
+   if ((wn=(SHNorml*)calloc(1,sizeof(SHNorml)))!=0) {
+      wn->nmax=nmax;
+      if ((wn->n=(double*)calloc((nmax+1)*(nmax+2)/2,sizeof(double)))==0) {
+         free(wn);
+         wn=0;
+      }
+      else {
+         // computing N_n^m for m=0, wrongly normalized
+         wn->n[0]=sqrt(1/(2*M_PI));
+         for (n=1,n0=1; n<=nmax; n++) {
+            wn->n[n0]=wn->n[0] * sqrt(2*n+1);
+            n0+=n+1;
+         }
+         // computing N_n^m for 0<m<=n
+         for (n=1,n0=1; n<=nmax; n++) {
+            for (m=1; m<=n; m++) {
+               wn->n[n0+m]= - wn->n[n0+m-1] / sqrt((n+m)*(n-m+1));
+            }
+            n0+=n+1;
+         }
+         // correcting normalization of N_n^0
+         for (n=0,n0=0; n<=nmax; n++) {
+            wn->n[n0]*=oneoversqrt2;
+            n0+=n+1;
+         }
+      }
+   }
+   return wn;
+}
+
+void sharmonics_normalization_free(SHNorml *wn) {
+   if (wn!=0) {
+      free(wn->n);
+      free(wn);
+   }
+}
+
+