#N canvas 61 39 921 503 10;
#X msg 96 97 matrix 2 1 0 0;
#X obj 184 163 mtx_rand;
#X msg 187 141 2 10;
#X obj 96 197 mtx_print;
#X obj 96 157 mtx_sh 1;
#X text 95 54 [mtx_sh] spherical harmonics evaluated at a set of points
given in phi and theta coordinates.;
#X text 306 117 [mtx_sh] requires a numerical creation argument nmax
specifyiing the maximum order 0<=n<=nmax.;
#X text 305 160 for an L points 2xL input matrix \, [mtx_sh] evaluates
the (nmax+2)^2 spherical harmonics at L points and delivers an Lx(nmax+2)^2
output matrix.;
#X text 527 347 Franz Zotter \, 2009;
#X text 150 226 for -n<=m<=n:;
#X text 188 258 Y_n^m(phi \, theta) = N_n^m * sin(m*phi) * P_n^m(cos(theta))
;
#X text 188 242 Y_n^m(phi \, theta) = N_n^m * cos(m*phi) * P_n^m(cos(theta))
;
#X text 641 241 for m>=0;
#X text 640 257 for m< 0;
#X text 147 291 The order of the harmonics in the output columns is
specified by the linear index k=n^2+n+m+1.;
#X connect 0 0 4 0;
#X connect 1 0 4 0;
#X connect 2 0 1 0;
#X connect 4 0 3 0;