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Add (scalar) spherical harmonic transforms #68
Commits on Jun 19, 2022
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Do half as much work when synthesizing
...by actually making use of the symmetry over the equator. The loop was incorrectly running over all rings rather than only the northern half.
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Add spherical harmonic analysis routine with computational optimizations
On an equidistant cylindrical projection (ECP) grid, we know several facts about symmetry and locations of pixels, so improve upon the reference implementation with a method that adds optimizations appropriate for isolatitude rings. Completes the symmetry of the existing `synthesize_ecp`.
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Start testing spherical harmonic analysis
Part 1 just adds very basic analytical checks of the reference implementation.
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Move all reference implementations of SHT to test helper file
With increasing infrastructure in the general form (and passing chains of tests building up to generic implementation), move the slow/specific reference functions to the tests file to reduce code compiled into the module itself.
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Commits on Jul 10, 2022
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New buffer manip utils: pack/unpack lower triangles to/from vectors
These are useful in implementing linear algebra-like operations on spherical harmonic coefficients without unnecessarily including nearly half of the always-zero matrix elements above the main diagonal
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Add conjugate gradient solver utility numerical method
This is required to solve for quadrature weights in the spherical harmonic analysis transform of arbitrary pixelizations. Handle null vector and exact initial conditions in C.G. better - Avoid any iteration when initial condition is already sufficiently accurate - Less-than-or-equal tolerance check handles cases when result is exact, and therefore avoids a division by zero in constructing the iterative update
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