# Help me to understand the input/output strides, number of transforms and input/output distance of 2D/3D data to perform DFT with oneAPI MLK libs

The computed excitation vectors of each basis function $$m$$ at level $$\ell$$ are just the samples on the sphere represented as $$\zeta_m^\ell(\phi_i,\theta_j)$$.

These samples are interpolated to get samples $$\zeta_m^{\ell-1}(\phi_\tilde{i},\theta_\tilde{j})$$ at level $$\ell-1$$

Fast Spherical Filter is one of the algorithm that starts the interpolation process by taking Fourier transform of samples $$\zeta_m^\ell(\phi_i,\theta_j)$$ in $$\phi$$ direction at first and continues$$\dots$$

Right now I perform this interpolation for each basis which is very slow.

$$\mathrm{FT}\left[\zeta_{m=0}^\ell(\phi_i,\theta_j),\,\zeta_{m=1}^\ell(\phi_i,\theta_j),\dots,\,\zeta_{m=\mathrm{M-1}}^\ell(\phi_i,\theta_j)\right]$$
• Further, what are number of transforms and in the current context $\mathrm{M}$ be number of transforms and the distance is $\mathrm{M}*i*j$? May 14 at 12:23