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MikaelSlevinsky / FastTransforms

:bullettrain_front: Fast orthogonal polynomial transforms :surfer:

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Combine DCTs (DSTs) and connection coefficients for faster (alternative) synthesis and analysis

MikaelSlevinsky opened this issue · comments

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Using an O(n2 log n) instead of O(n2) precomputation, the colatitudinal DCTs and DSTs can be applied to the Legendre to Chebyshev connection coefficients to reduce the overall spherical harmonic synthesis and analysis to execute_sph_hi2lo followed by a sequence of cblas_dgemm and one longitudinal FFTW_HC2R.

Contrast this with the current four-step approach of execute_sph_hi2lo followed by a sequence of cblas_dtrmm and a sequence of FFTW_REDFT01 and FFTW_RODFT01, and finally the longitudinal FFTW_HC2R.