Improve FFT interpolation (1/2)

[unalmis]

This is the first of two pull requests to improve the FFT interpolation.

4 goals are achieved by this PR.

• The real FFT is now used where possible. This is especially useful for 2D transforms. Resolves Use real fft in interpolation #75 .
• Double the width of the Fourier spectrum is now preserved when interpolating to a less dense grid, at no additional cost. Previously, when the number of requested output samples $n_{\text{out}}$ was less than the number of input samples $n_{\text{in}}$, the interpolation would neglect the $n_{\text{in}} - n_{\text{out}}$ highest frequency spectral coefficients, resulting in lossy interpolation. Now the interpolation is lossless for all $n_{\text{out}} >= \lfloor n_{\text{in}} / 2 \rfloor + 1$. Likewise, if $n_{\text{out}} < \lfloor n_{\text{in}} / 2 \rfloor + 1$, then only the $\lfloor n_{\text{in}} / 2 \rfloor + 1 - n_{\text{out}}$ highest frequency spectral coefficients will be neglected.
• In the 2D upsampling case, the second transform is now padded only after computing the first transform. This reduces the size of the problem, so the computation is less expensive.
• In the 2D downsampling case, the second transform is now truncated prior to computing the first transform. This reduces the size of the problem, so the computation is less expensive.

[f0uriest]

doesn't this truncation mean that we're still interpolating the band limited signal, not the full one?

[unalmis]

c.shape[0] has size f.shape[0]//2 + 1. so our band limited signal can preserve double the width of the fourier spectrum than before

[f0uriest]

can you explain this part? Isn't this just multiplying the output by exp(i*n*x)?

[unalmis]

we transform sum_n^N c_n e^(i n x) for n>=0 to e^iNx//2 sum_k c_n e^(ikx) where k now includes the relevant negative values (that result from pulling the highest frequency outside the sum)

[unalmis]

https://github.com/PlasmaControl/DESC/blob/82d2fe6221976e93c54415195e32e62bfe07d1a7/tests/test_integrals.py#L584