[henrikjacobsenfys]

A user reported that StretchedExponential is very slow. Profiling showed that ~95% of fit time went into _kww_shape, the quadrature that evaluates the transform at every energy point. With a resolution convolution, a single-Q fit took 1.37 s, compared with 0.03 s for a Lorentzian.

This PR makes it about 14× faster, in two commits.

1. Faster quadrature (results unchanged)

• Cache-sized blocks: the quadrature was memory bound. It now runs in blocks of 2^15 elements (256 kB temporaries, small enough to stay in cache) instead of 2M, with in-place operations.
• Dropped nodes: nodes where exp(-P) provably underflows to exactly 0 are removed, since P ≥ min(s, s^β) on the rescaled grid. That is about a quarter of the grid for β ≳ 0.5.
• Results match the old code to rounding, and are still bitwise independent of block boundaries (reduction via einsum, not BLAS).
• Speedup: 3–4×.

2. interpolate flag, default True

• What it does: builds a cubic-spline table of log(G/G(0)) against y = asinh(w / w_ref) and interpolates from it. w_ref sits where the profile has dropped by 1e-6, which happens many decades below the half width at small β.
• Caching: tables are cached per β. Steps in area, center and τ, and all Q values that share β, reuse them.
• Smooth for fitting: nodes sit on a fixed lattice and the table grows in fixed steps, so the model stays smooth under the small parameter steps lmfit takes for its Jacobian. Finite differences match the quadrature to 1e-5.
• Accuracy:
  • Within 1.2e-7 of the peak for all β in [0.05, 2].
  • For β ≤ 1, within ~1e-6 at every point, including the far tail, which holds most of the area at small β.
  • For β > 1, the profile is cut to 0 below 1e-14 of the peak, where the quadrature is already rounding noise.
• interpolate=False keeps the ~1e-11 quadrature.

Timings

	before	after (quadrature)	after (interpolate=True)
1505 points	~17 ms	~4.5 ms	~1.3 ms (0.03 ms cached)
Single-Q fit with resolution	1.37 s	0.41 s	0.10 s

Fitted values and errors are identical to 5 digits with and without interpolation.

Notes for review

• interpolate is placed right after beta in the constructor, so code passing x_unit or later arguments by position would break.
• Tests that check the quadrature against the exact Lorentzian/Gaussian to 1e-10 now pin interpolate=False. The interpolated path has its own tests: agreement relative to the peak across 40 β values, pointwise agreement for β ≤ 1, the β>1 cutoff, independence from table length, and smoothness under finite differences.

🤖 Generated with Claude Code

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 98.17%. Comparing base (762b081) to head (c605276).
⚠️ Report is 6 commits behind head on develop.

Additional details and impacted files

@@             Coverage Diff             @@
##           develop     #268      +/-   ##
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+ Coverage    98.15%   98.17%   +0.01%     
===========================================
  Files           60       60              
  Lines         6066     6123      +57     
  Branches      1022     1027       +5     
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+ Hits          5954     6011      +57     
  Misses          58       58              
  Partials        54       54              

Flag	Coverage Δ
unittests	98.17% <100.00%> (+0.01%)	⬆️

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Files with missing lines	Coverage Δ
...s/sample_model/components/stretched_exponential.py	100.00% <100.00%> (ø)

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