Implement gausslobatto / gaussradau and Monic

[DanielVandH]

Implements gaussradau and gausslobatto for computing quadrature weights using Gauss-Radau or Gauss-Lobatto quadrature, respectively.

Is there a proper way I should be getting the monic polynomials? Or are my loops fine?

[dlfivefifty]

There is a routine forwardrecurrence! that builds OPs fast. The benefit over the for-loop is it special cases Zeros, Vcat, etc. to get high-efficiency. Whereas your for-loop will need to do slow checks.

But the cost of building the OPs is so fast compared to computing eigenvalues it wouldn't matter anyways.

Though perhaps its worth making a Monic type a la Normalized to just abstract away this step?

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 91.06%. Comparing base (cc668ce) to head (dcb37b7).

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #199      +/-   ##
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+ Coverage   90.75%   91.06%   +0.31%     
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  Files          17       18       +1     
  Lines        1936     1992      +56     
==========================================
+ Hits         1757     1814      +57     
+ Misses        179      178       -1     

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[DanielVandH]

Would you prefer I rewrite it using forwardrecurrence!? I didn't know about that function I forgot it can be used for that. Is it still as fast if I need to store pn and pn-1? If not maybe coming back to Monic eventually and rewriting this would be a good approach too.

[dlfivefifty]

I think making a type for Monic and just using your for loop implementation for getindex with a comment about rewriting in the future would be good. This way if we need monic OPs for something in the future we remember that code is there!

[DanielVandH]

Alright. I'll add Monic to this PR (or I can make a second PR if you prefer?) and reuse it, good idea.

[DanielVandH]

Now added Monic. Just added the basics for now and I guess if/when another need for it comes up we can figure out the details a bit better

[DanielVandH]

Anything left to do here?

[dlfivefifty]

Does this actually benefit from requiring normalized OPs?

[DanielVandH]

Makes the code for getting the recurrence coefficients simpler I think