[michakraus]

Summary

• Rename the internal _deim_indices(Ψ) to get_DEIM_indices(Ψ) and export it beside get_DEIM_interpolation_matrix.
• The docstring describes it as public API: it returns the k rows that greedy DEIM selects, and it is the index form of get_DEIM_interpolation_matrix, Π' * A == A[p, :] for p = get_DEIM_indices(Ψ) and a finite A.
• Update every use: get_DEIM_interpolation_matrix, the SymplecticDEIM constructor and its two docstring @refs, and both DEIM test files. The using ReducedBasisMethods: _deim_indices lines go, because the name is now exported.
• New testset: get_DEIM_interpolation_matrix(Ψ)' * A == A[get_DEIM_indices(Ψ), :] on a random orthonormal basis, in Float32 and Float64.
• CHANGELOG: one New Features bullet under [Unreleased]. No version bump; not breaking, because the old name was internal.
• Docs: library.md uses @autodocs, so the new export appears with no page change.

Tests

• test/algorithms/deim.jl, test/algorithms/symplectic_deim.jl and test/quality/aqua.jl: 397/397 pass.
• JuliaFormatter (sciml) passes on the changed .jl files.

Pre-PR verification

Fixed

• get_DEIM_indices docstring (src/algorithms/deim.jl): the identity Π' * A == A[p, :] was stated "for every N-row matrix A". It now says "finite". With an Inf or NaN in an unselected row of A, Π' * A has a column that is all NaN (0 * Inf), while A[p, :] stays finite. The comment of the new testset in test/algorithms/deim.jl has the same correction.

Unresolved

• None.

Pre-existing / sequencing

• This branch conflicts with P33: the CairoMakie extension, Aqua, docs and CHANGELOG of ReducedBasisMethods #56 in CHANGELOG.md and src/algorithms/deim.jl (checked with git merge-tree). The one that merges second must resolve the conflict. In the resolution, the @ref next to P33: the CairoMakie extension, Aqua, docs and CHANGELOG of ReducedBasisMethods #56's new jldoctest must name get_DEIM_indices, not _deim_indices.

Checked and clean

• Callers: no use of the old name is left. _deim_indices is undefined after load, and get_DEIM_indices is public.
• Type piracy: Aqua test_piracies passes.
• Type stability: get_DEIM_indices infers Vector{Int64} for Float64, Float32, Int32 and reshaped inputs. get_DEIM_interpolation_matrix follows the element type. No Any originates at a changed line.
• Allocations: fatou lint is clean on the changed files. The diff adds no allocating construct.
• Comments: all comments and docstrings near the hunks are current and in the present tense. No history outside CHANGELOG.md.
• The affected test files pass (algorithms/deim.jl, algorithms/symplectic_deim.jl, quality/aqua.jl: 397/397). JuliaFormatter passes.

Not checked

• The full documentation build (makedocs).
• Behaviour on the compat floor Julia version (checked on 1.13 only).

🤖 Generated with Claude Code

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 91.56%. Comparing base (882eeb2) to head (4816230).

Additional details and impacted files

@@           Coverage Diff           @@
##             main      #57   +/-   ##
=======================================
  Coverage   91.56%   91.56%           
=======================================
  Files          10       10           
  Lines         332      332           
=======================================
  Hits          304      304           
  Misses         28       28           

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