08-Jan-2022 09:49:38 spherical_harmonic_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 Test spherical_harmonic(). SPHERICAL_HARMONIC_TEST01: LEGENDRE_ASSOCIATED_NORMALIZED evaluates the associated Legrendre functions, using a normalization appropriate for spherical harmonics. LEGENDRE_ASSOCIATED_NORMALIZED_VALUES returns some exact values. N M X Exact F PNM(X) 0 0 0.500000 0.282095 0.282095 1 0 0.500000 0.244301 0.244301 1 1 0.500000 -0.299207 -0.299207 2 0 0.500000 -0.078848 -0.078848 2 1 0.500000 -0.334523 -0.334523 2 2 0.500000 0.289706 0.289706 3 0 0.500000 -0.326529 -0.326529 3 1 0.500000 -0.069971 -0.069971 3 2 0.500000 0.383245 0.383245 3 3 0.500000 -0.270995 -0.270995 4 0 0.500000 -0.244629 -0.244629 4 1 0.500000 0.256066 0.256066 4 2 0.500000 0.188169 0.188169 4 3 0.500000 -0.406492 -0.406492 4 4 0.500000 0.248925 0.248925 5 0 0.500000 0.084058 0.084058 5 1 0.500000 0.329379 0.329379 5 2 0.500000 -0.158885 -0.158885 5 3 0.500000 -0.280871 -0.280871 5 4 0.500000 0.412795 0.412795 5 5 0.500000 -0.226097 -0.226097 SPHERICAL_HARMONIC_TEST02: SPHERICAL_HARMONIC evaluates the spherical harmonic function. SPHERICAL_HARMONIC_VALUES returns some exact values. L M THETA PHI YR YI 0 0 0.523599 1.047198 0.282095 0.000000 0.282095 0.000000 1 0 0.523599 1.047198 0.423142 0.000000 0.423142 0.000000 2 1 0.523599 1.047198 -0.167262 -0.289706 -0.167262 -0.289706 3 2 0.523599 1.047198 -0.110633 0.191622 -0.110633 0.191622 4 3 0.523599 1.047198 0.135497 0.000000 0.135497 0.000000 5 5 0.261799 0.628319 0.000539 0.000000 0.000539 -0.000000 5 4 0.261799 0.628319 -0.005147 0.003739 -0.005147 0.003739 5 3 0.261799 0.628319 0.013710 -0.042195 0.013710 -0.042195 5 2 0.261799 0.628319 0.060964 0.187626 0.060964 0.187626 5 1 0.261799 0.628319 -0.417040 -0.302997 -0.417040 -0.302997 4 2 0.628319 0.785398 0.000000 0.413939 0.000000 0.413939 4 2 1.884956 0.785398 0.000000 -0.100323 -0.000000 -0.100323 4 2 3.141593 0.785398 0.000000 0.000000 0.000000 0.000000 4 2 4.398230 0.785398 0.000000 -0.100323 -0.000000 -0.100323 4 2 5.654867 0.785398 0.000000 0.413939 0.000000 0.413939 3 -1 0.392699 0.448799 0.364121 -0.175351 0.364121 -0.175351 3 -1 0.392699 0.897598 0.251979 -0.315972 0.251979 -0.315972 3 -1 0.392699 1.346397 0.089930 -0.394011 0.089930 -0.394011 3 -1 0.392699 1.795196 -0.089930 -0.394011 -0.089930 -0.394011 3 -1 0.392699 2.243995 -0.251979 -0.315972 -0.251979 -0.315972 spherical_harmonic_test(): Normal end of execution. 08-Jan-2022 09:49:38