conv

convolution of an SO3FunRBF with another SO3FunRBF or an SO3Kernel

There are two SO3Funs \(f: {S_f^L\backslash}SO(3){/S_f^R} \to \mathbb{C}\) where \(S_f^L\) is the Left symmetry and \(S_f^R\) is the Right symmetry and \(g: {S_g^L\backslash}SO(3){/S_g^R} \to \mathbb{C}\) given. Then the convolution \( f *L g : _{S_f^L\backslash}SO(3){/S_g^R} \to \mathbb{C}\) is defined by

\[ (f *L g)(R) = \frac1{8\pi^2} \int{SO(3)} f(q) \cdot g(q^{-1}\,R) \, dq \]

and the convolution \( f *R g : _{S_g^L\backslash}SO(3){/S_f^R} \to \mathbb{C}\) is defined by

\[ (f *R g)(R) = \frac1{8\pi^2} \int{SO(3)} f(q) \cdot g(R\,q^{-1}) \, dq \].

with \(vol(SO(3)) = \int_{SO(3)} 1 \, dR = 8\pi^2\). The convolution \(*_L\) is used as default. The convolution of matrices of SO3Functions with matrices of SO3Functions works elementwise.

Syntax

SO3F = conv(SO3F1,SO3F2)
SO3F = conv(SO3F1,SO3F2,'noFourier')
SO3F = conv(SO3F1,psi)

Input

Output

See also

SO3FunHarmonic.conv SO3Kernel.conv S2FunHarmonic.conv S2Kernel.conv