Add (scalar) spherical harmonic transforms #68
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jmert
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...by actually making use of the symmetry over the equator. The loop was incorrectly running over all rings rather than only the northern half.
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`.
Part 1 just adds very basic analytical checks of the reference implementation.
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.
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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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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