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Gauss–Kronrod weights for arbitrary weight functions #83

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merged 36 commits into from
Jul 25, 2023

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@stevengj stevengj commented Jul 18, 2023

The goal of this PR is to implement arbitrary-precision Gauss–Kronrod weights for arbitrary Jacobi matrices, corresponding to arbitrary weight functions. This involves:

  • generalizing our tridiagonal eigensolvers to nonzero diagonals (but still optimizing the zero-diagonal case)
  • generalizing gauss(J) to take an arbitrary tridiagonal Jacobi matrix J
  • generalizing the kronrod code to the original form of Laurie (1997) to handle arbitrary J
  • more tests
  • documentation

(It's a large PR, but it's mostly docs and tests. The actual amount of new code is relatively small.)

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codecov bot commented Jul 18, 2023

Codecov Report

Patch coverage: 98.37% and project coverage change: +0.53% 🎉

Comparison is base (d20d07a) 97.33% compared to head (5c6c1c6) 97.87%.

Additional details and impacted files
@@            Coverage Diff             @@
##           master      #83      +/-   ##
==========================================
+ Coverage   97.33%   97.87%   +0.53%     
==========================================
  Files           5        5              
  Lines         338      471     +133     
==========================================
+ Hits          329      461     +132     
- Misses          9       10       +1     
Files Changed Coverage Δ
src/gausskronrod.jl 98.37% <98.25%> (+0.89%) ⬆️
src/weightedgauss.jl 100.00% <100.00%> (ø)

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@stevengj stevengj merged commit 4b4a82f into master Jul 25, 2023
@stevengj stevengj deleted the general_gauss branch July 25, 2023 04:45
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