#N canvas 61 39 921 503 10; #X msg 96 97 matrix 2 1 0 0; #X obj 206 132 mtx_rand; #X msg 209 110 2 10; #X obj 96 197 mtx_print; #X text 537 377 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 text 95 54 [mtx_spherical_harmonics] spherical harmonics evaluated at a set of points given in phi and theta coordinates.; #X text 146 328 [mtx_spherical_harmonics] uses fully normalized Y_n^m with Condon-Shortley phase; #X text 305 160 for an L points 2xL input matrix \, [mtx_spherical_harmonics] evaluates the (nmax+2)^2 spherical harmonics at L points and delivers an Lx(nmax+2)^2 output matrix.; #X text 309 118 [mtx_spherical_harmonics] requires a numerical creation argument specifyiing the maximum order 0<=n<=nmax.; #X obj 96 157 mtx_spherical_harmonics 2; #X connect 0 0 15 0; #X connect 1 0 15 0; #X connect 2 0 1 0; #X connect 15 0 3 0;