Check every ensemble sample against N, not just the first

[michakraus]

Second follow-up to the review of #110, and stacked on it — it targets feature/toda-lattice-handwritten-equations rather than main, because TodaLattice._check_size only exists on that branch. The diff here is just the fix.

The other follow-up, #111, is independent and targets main.

The problem

_check_size asked _nint/_length for the size of the initial condition, and for an ensemble those report on q₀[begin] alone:

_length([q5, q7])                    # 5
_check_size(5, [q5, q7], [p5, p7])   # accepted
_check_size(5, [q5, q5], [p5, p7])   # accepted — ragged momenta too
_check_size(7, [q5, q7], [p5, p7])   # throws: "initial condition has 5 components, expected N = 7"

That last line is the shape of the bug in miniature: the assertion does fire, but it reports on sample 1 while the mismatch is in sample 2. The two-argument forms compound it, since they assert only that q₀ and p₀ hold the same number of samples, not that the samples agree in length.

What a ragged ensemble actually did

Measured, not reasoned about — a [q5, q7] ensemble declared as N = 5, integrated to t = 0.1 with ImplicitMidpoint. Both branches run to completion without complaint, and they fail differently:

Hand-written branch. The fields read N = length(q) off each state, so sample 2 is a bona fide 7-site periodic lattice:

sample sizes 5 and 7;  |sample1 − true 5-site| = 0.0;  |sample2 − true 7-site| = 0.0

The numbers are right. The defect is that you asked for a five-site ensemble and got two different physical systems, with nothing saying so — every cross-sample comparison downstream is then meaningless while looking perfectly well-behaved.

Symbolic branch — the worse one. The generated functions have N = 5 compiled in. Called directly on a seven-component state:

generated f writes 5 of 7 entries; untouched tail = [NaN, NaN]
hand-written f writes 7 of 7

Sites 6 and 7 never receive a force — in the integrator they get whatever the buffer held. The giveaway is how quietly:

|sample2 − true 7-site| = 1.48e-6

after only t = 0.1. Small because the default momentum is zero and the window is short, not because anything is right; it grows with the window. That is the failure mode that survives a casual look.

Either way, this is exactly what the assertion's own comment says it exists to prevent — "an N that disagrees with the initial condition would silently mean two different systems depending on symbolic" — surviving for samples 2…n.

The change

_check_components replaces the single length query: one method for a plain initial condition, one that walks pairs(x) for a vector of samples. Messages now name the array and the sample:

q₀ sample 2 has 7 components, expected N = 5

_nint/_length stay — the two-argument constructors still use them to infer N from the first sample, which is the right behaviour once the rest are checked against it.

Both modules are fixed together. src/linear_wave.jl had the identical first-sample-only shape; they carry the same helper by design, and fixing one alone would leave the next reader wondering which is intentional.

Tests

test/toda_lattice_tests.jl: the size testset goes 14 → 22 assertions. test/linear_wave_tests.jl: 11 → 19. Each covers a ragged q₀, a ragged p₀, both the N-form and the two-argument form, and — as the positive control — a well-formed ensemble in each of the two branches:

@test_throws AssertionError hodeensemble(M, [qM, qM1], [pM, pM])
@test_throws AssertionError hodeensemble(M, [qM, qM], [pM, pM1])
@test_throws AssertionError hodeensemble([qM, qM1], [pM, pM])       # two-argument form
@test hodeensemble(M, [qM, qM .+ 0.1], [pM, pM]) isa HODEEnsemble
@test lodeensemble(M, [qM, qM .+ 0.1], [pM, pM]; symbolic = true) isa LODEEnsemble

linear_wave_tests.jl needed HODEEnsemble/LODEEnsemble added to its imports, having previously used only the problem types.

Full Pkg.test() passes, as does the pre-push hook suite.

🤖 Generated with Claude Code

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Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 75.46%. Comparing base (e289c4d) to head (fb24f98).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #112      +/-   ##
==========================================
+ Coverage   75.22%   75.46%   +0.24%     
==========================================
  Files          43       43              
  Lines        2442     2454      +12     
==========================================
+ Hits         1837     1852      +15     
+ Misses        605      602       -3     

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