Speed up Thiele construction by using array evaluatoin, and add barycentric array evaluation

[tobydriscoll]

No description provided.

[codecov]

Codecov Report

❌ Patch coverage is 41.66667% with 21 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
src/barycentric.jl	0.00%	20 Missing ⚠️
src/thiele.jl	93.75%	1 Missing ⚠️

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[github-actions]

Benchmark Results

Ratios above 1 mean this PR is slower than main.

	main	4930bb1...	main / 4930bb1...
approximate/aaa/abs_circle	0.0503 ± 0.0047 s	0.051 ± 0.0045 s	0.987 ± 0.13
approximate/aaa/exp_interval	0.159 ± 0.076 ms	0.156 ± 0.023 ms	1.01 ± 0.51
approximate/aaa/tanh_steep	1.81 ± 0.078 ms	1.81 ± 0.059 ms	0.998 ± 0.054
approximate/thiele/abs_circle	13.5 ± 0.15 ms	13.5 ± 0.19 ms	0.994 ± 0.017
approximate/thiele/exp_interval	0.32 ± 0.014 ms	0.259 ± 0.017 ms	1.24 ± 0.097
approximate/thiele/tanh_steep	1.18 ± 0.021 ms	1.01 ± 0.021 ms	1.16 ± 0.032
approximate_discrete/aaa/abs_shift	4.74 ± 0.5 ms	4.73 ± 0.13 ms	1 ± 0.11
approximate_discrete/aaa/sin_recip	1.52 ± 0.056 ms	1.52 ± 0.038 ms	1 ± 0.045
approximate_discrete/aaa/tanh_steep	15.1 ± 1.4 ms	14.8 ± 0.9 ms	1.02 ± 0.11
approximate_discrete/thiele/abs_shift	3.25 ± 0.088 ms	0.266 ± 0.022 ms	12.2 ± 1.1
approximate_discrete/thiele/sin_recip	1.96 ± 0.031 ms	0.142 ± 0.014 ms	13.8 ± 1.3
approximate_discrete/thiele/tanh_steep	8.37 ± 1.2 ms	0.92 ± 0.057 ms	9.1 ± 1.4
evaluate/bary_vector	0.167 ± 0.01 ms	0.166 ± 0.0087 ms	1 ± 0.082
evaluate/thiele_vector	0.15 ± 0.009 ms	0.14 ± 0.0095 ms	1.08 ± 0.098
poles/thiele	0.457 ± 0.016 ms	0.456 ± 0.013 ms	1 ± 0.044
time_to_load	0.933 ± 0.014 s	0.954 ± 0.0059 s	0.978 ± 0.016

Benchmark Plots

Plots have been uploaded as an artifact to this workflow run
("Actions" -> this run -> "Artifacts" at the bottom).