Decide what arithmetic operations are allowed on spectra

[brechmos-stsci]

Need to be able to do arithmetic calculations and operations on Spectrum1D objects and on multiple Spectrum1D objects. Maybe easiest to start out with simple arithmetic operations.

[SaOgaz]

What arithmetic stuff do we want here? @brechmos-stsci and I have brainstormed addition, subtraction, some stats (mean, median, standard deviation), integrated flux

Do any of these make sense for spectra:
multiplication, division, power

Any others I don't have?

@nmearl @stscicrawford

[nmearl]

Even though we only have an arithmetic test that tests addition -- subtraction, division, and multiplication should work.

Currently, those are the only operator overloads implemented. You'd have to override __pow__ to get exponentials. You can see how it's currently implemented here.

[brechmos-stsci]

@SaOgaz and I were just talking about some of the implementation details and there are a couple of questions... For example, with addition, and assuming s1 and s2 are Spectrum1D objects, would you like:

1. s1.add(s2) so s2 is added into s1

2. s3 = s1.add(2) (probably doesn't make as much sense)

3. s3 = s1 + s2 (the obvious)

4. s3 = spec_arith.add(s1, s2) (not necessarily for adding but maybe spec_arith.mean(s1) ?)

Then.... given an answer there, there are a few options on implementation whether some functionality should be added to the Spectrum1D class, or as a Mixin or in a separate arithmetic type of class.

[crawfordsm]

There is also the read the docs page here:
http://specutils.readthedocs.io/en/latest/arithmetic.html

[nmearl]

Note that the arithmetic operations are implemented in the NDArithmeticMixin. More operations would have to be implemented there. Although, "old" specviz did not support these other operations, so we can certainly punt this to a later sprint.

[nmearl]

@brechmos-stsci 2. and 3. are already supported. See @crawfordsm's link to the docs.

[brechmos-stsci]

Cool. @SaOgaz is going to look through the arithmetic operations and will get back here to see if we want any others in the short term. She will also look at the tests and make sure they are complete. If everything is done, then we can close this and move on.

[brechmos-stsci]

(you guys will have to be slightly patient as we come up to speed with what is here and all :) )

[SaOgaz]

Okay, I've gone over the current arithmetic stuff and have a decent handle on the operator stuff and what's happening with the WCS. So once we have the test data setup (as discussed in the tag up) I can go ahead an add some tests for the other operators etc. I don't see anything else when it comes to the already existing basic operators that needs to be done.

[eteq]

@SaOgaz - so do you think this can be closed, then? Or should we leave this open but re-name it "document more clearly how to do arithmetic operations" or something like that?

[SaOgaz]

I'd like to leave it open at least until the tests are done. Maybe then we can rename it to documentation.

[SaOgaz]

Current support for arithmetic consists of the four basic algebra operators: addition, subtraction, division, multiplication.