Multiple Period Fitting

[dwysocki]

We should be able to fit a Fourier series with more than one period. This is going to break API backwards compatibility pretty badly, and change some of the command line options. Although most previous command line behaviour should not be difficult to achieve by default.

Library Changes

• (almost) Any place we pass a single period, we should now accept either a single period, or a 1 dimensional array-like of periods.
• The Fourier.design_matrix function must now return a generalization of the design matrix for any number of periods. In the special case of 1 period, it will simplify to the current behaviour
  • This should also now take times instead of phases, as they need to be phased by a different period in different parts of the matrix

Command Line Changes

• The --period command line argument, which takes a float, should now be replaced with a --periods command line argument, taking 1 or more floats.
• The --parameters file should now, instead of looking for the column labeled "Period", look for any column prefixed with "Period" and suffixed with a number.
  • Somehow impose a consistent ordering on them, either by enforcing that they be followed by an integer (probably the simplest, especially when considering the output table), or some more general rule.
  • We need to support NaNs as representations of missing periods, as some stars may have more periods than others. _process_star may just have to drop the NaNs, although that may cause inconsistencies between input/output tables if there are NaNs in-between two periods for some stars.

Overarching Changes

• We need to fundamentally reconsider how we handle phased plots, as multi-periodic stars cannot be phased, but we need an approach which can generalize the current behaviour of phasing singly periodic stars
• Printing fitted magnitudes in the output table will have to be off by default, as it is problematic when considering the number of points needed for a multiperiodic star

[dwysocki]

I wanted to add an update, since we're finally making progress on multiple period support.

As of 6819788, Fourier coefficients are being output in a way which is compatible with multiple periods. The current output is actually identical to the special case of single periods, once multiple period support is added. The format is

k	A_k	Phi_k	dA_k	dPhi_k
0	A_0	Phi_0	dA_0	dPhi_0
...	...	...	...	...
n	A_n	Phi_n	dA_n	dPhi_n

In the case of multiple periods, we will simply have multiple k columns, i.e. k_1, ..., k_p.