Compute the S2-Fourier/harmonic coefficients of an given S2Fun or given evaluations on a specific quadrature grid.
Therefore we obtain the Fourier coefficients with numerical integration (quadrature), i.e. we choose a quadrature scheme of meaningful quadrature nodes vm and quadrature weights ωm and compute
ˆfkn=∫S2f(v)¯Ykn(v)d\my(v)≈M∑m=1ωmf(vm)¯Ykn(vm),
for all n=0,…,N and k=−n,…,n.
Therefore this method evaluates the given S2Fun on the quadrature grid. Afterwards it uses the adjoint NFSFT (nonequispaced fast spherical Fourier transform) to quickly compute the above sums.
Syntax
sF = S2FunHarmonic.quadrature(nodes,values,'weights',w)
sF = S2FunHarmonic.quadrature(f)
sF = S2FunHarmonic.quadrature(f, 'bandwidth', bandwidth)Input
| values | double (first dimension has to be the evaluations) |
| nodes | vector3d |
| f | function handle in vector3d (first dimension has to be the evaluations) |
Output
| sF | S2FunHarmonic |
Options
| bandwidth | minimal degree of the spherical harmonic (default: 128) |