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Added mapping of points to deal with general Rays #12

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Merged
merged 5 commits into from
Nov 27, 2019

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tomtrogdon
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A small change to make the Laguerre code work for general rays.

@dlfivefifty
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Can you add a unit test for this, please?

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codecov bot commented Nov 12, 2019

Codecov Report

Merging #12 into master will increase coverage by 0.34%.
The diff coverage is 100%.

Impacted file tree graph

@@            Coverage Diff             @@
##           master      #12      +/-   ##
==========================================
+ Coverage   55.53%   55.87%   +0.34%     
==========================================
  Files          26       26              
  Lines        2058     2058              
==========================================
+ Hits         1143     1150       +7     
+ Misses        915      908       -7
Impacted Files Coverage Δ
src/Spaces/Laguerre/Laguerre.jl 60.16% <100%> (ø) ⬆️
src/Domains/Ray.jl 43.13% <0%> (+13.72%) ⬆️

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@tomtrogdon
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The biggest functional change is that adaptivity works for Laguerre spaces now. The addtional scale parameter will be useful for Fourier transform of Laurent{PeriodicLine}.

@dlfivefifty
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Cool! I had a similar issue with underflow/overflow in Hermite transforms which I managed to fix by factoring out an exponential term in the weights: that is, in

https://github.com/JuliaApproximation/FastGaussQuadrature.jl/blob/master/src/gausshermite.jl#L1

the unweightedgausshermite function calculates the Gauss--Hermite weights w_k as w_k * exp(x_k^2), thus avoiding underflow. These "unweighted" Gauss points are used in hermitetransform here:

https://github.com/JuliaApproximation/FastTransforms.jl/blob/master/src/hermite.jl

Note that there is also underflow/overflow in the recurrence relationship defining the polynomials, but if we incorporate the weight during the recurrence we can avoid this:

https://github.com/JuliaApproximation/FastGaussQuadrature.jl/blob/a81140c0b642193625837fb9afb58dfe251987ad/src/gausshermite.jl#L83

This might be useful here...

@dlfivefifty dlfivefifty merged commit 5867548 into JuliaApproximation:master Nov 27, 2019
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2 participants