Performance of RecurrenceArray

[ioannisPApapadopoulos]

Sometimes RecurrenceArray is slower than getindex when actually assembling the values e.g.

using ClassicalOrthogonalPolynomials
using SingularIntegrals

import ClassicalOrthogonalPolynomials: recurrenecoefficients
import SingularIntegrals: RecurrenceArray

P = Jacobi(1/3,1/3)
xc = range(-1,1; length=10000)
n = 10000

# getindex baseline ~ 1.102867 seconds
@time pp = P[xc,1:n];
# Lazy is fast ~  0.000466 seconds
@time pr = RecurrenceArray(xc, recurrencecoefficients(P), P[xc, 1:2]');
# Actually getting the matrix is "slow" ~ 1.706700 seconds 
@time pr[1:n,1:length(xc)]';

pr ≈ pp

[ioannisPApapadopoulos]

@dlfivefifty just in case you missed this issue you asked me to raise :)

[dlfivefifty]

Your code doesn't run since T̃ is not defined

[ioannisPApapadopoulos]

ah sorry! fixed. It's particularly slow on the first run of @time pr[1:n,1:length(xc)]';

[dlfivefifty]

Note 0.6s is just making a second copy. That is, when you call pr[1:n,1:length(xc)] it first populates a matrix and then copies this data to a new matrix.

On the other hand, P[xc,1:n] populates the returned matrix directly.

So I don't think there's anything obvious that can be done about this. That is, we can't both cache and return a matrix without the overhead of a copy.

[dlfivefifty]

Unless we decide to get rid of caching and only do populating. That is, RecurrenceArray would become completely lazy and not cache any computations. But is it worth the time?

[ioannisPApapadopoulos]

For the paper, I've not used the RecurrenceArrays at all.. probably not worth it for now.