[roytsmart]

Adds ndoptimize.models.gaussian_binned, a Gaussian averaged over each bin:

$$f(x_0, x_1) = \frac{1}{x_1 - x_0} \int_{x_0}^{x_1} A \exp\left(-\frac{(x - \mu)^2}{2\sigma^2}\right) dx.$$

It has the same parameters as gaussian (amplitude, center and width), and its two inputs are the lower and upper edges of each bin, x[:, 0] and x[:, 1].

Why

Averaging matters when the bins are about as wide as the line, which is the usual case for a CTIS reconstruction. sun-data/ctis#23 integrates its line profile over each velocity bin for this reason. Averaging over bins of width Δ broadens the line by about Δ²/12 in variance, and a fit of gaussian at the bin centers takes that broadening as part of the line. For bins as wide as the line, the sampled fit comes out 4.2% too wide and 4% too low in amplitude, while gaussian_binned recovers the line exactly.

It's also the model that bin-edge inputs to na.ModelFitFunctionArray will feed (sun-data/named-arrays#271): when a fit axis of a function array holds bin edges, the model gets each bin's lower and upper edge.

Numerics

• The average is a difference of two error functions. In the tails, where both are close to 1 or to -1, it's computed from their complements, erfc, so it stays accurate where the plain difference would cancel to zero. A bin 15σ from the center comes out within 1e-11 of numerical integration, at about 1e-47 of the peak.
• A bin of zero width gives the Gaussian at that point, and its Jacobian.

Tests

• The model against scipy.integrate.quad over bins in both far tails, on either side of the center, and across it, to a relative 1e-11, with its Jacobian against finite differences.
• Zero-width and 1e-6-wide bins against gaussian.
• A fit to bins as wide as the line recovers the truth to 1e-6, while a fit of gaussian at the bin centers comes out more than 2% too wide.

50 tests pass with and without JIT, with models.py 100% covered. ruff, black and pyright 1.1.411 are clean, and the docstring example (the Gaussian next to its bin averages) builds.

Follow-up

The README and documentation list the models in #5. Once both merge, that list should add the binned Gaussian. I left it out here to avoid a conflict.

🤖 Generated with Claude Code

https://claude.ai/code/session_01PZRXiFhGzzrF87vsFg73B9

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 99.65%. Comparing base (61296fd) to head (ef3d9f9).

Additional details and impacted files

@@            Coverage Diff             @@
##             main       #6      +/-   ##
==========================================
+ Coverage   99.61%   99.65%   +0.03%     
==========================================
  Files           8        8              
  Lines         782      861      +79     
==========================================
+ Hits          779      858      +79     
  Misses          3        3              

Flag	Coverage Δ
unittests	99.65% <100.00%> (+0.03%)	⬆️

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