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Max-balance dense blocks with an adjacency-matrix tree - #97
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`_maxbalance` holds a block with more than `n²/8` arcs in a
`DenseParametricTree`: two `n×n` weight matrices with parallel arcs
merged into the heaviest, and an indexed heap over nodes keyed by the
best candidate arc entering each, rescanned lazily when a key may
have fallen. A node whose depth changes then costs one pass over the
live nodes instead of a heap update for each incident arc on a heap
of `n²` entries. Sparser blocks keep the arc-list `ParametricTree`;
the keyword `dense` selects the representation explicitly. The
initial tree and the summation of the contraction chains are shared.
On dense random lognormal matrices, `cover_transversal(PowerMean{2}(),
A; maxbalance=true)` takes 0.8 s at n = 1600 and 20 s at n = 6400,
and the shifts agree with the arc-list path to roundoff.
Assisted-by: Claude Opus 5.5 and Claude Fable 5.1 <noreply@anthropic.com>
Codecov Report✅ All modified and coverable lines are covered by tests. Additional details and impacted files@@ Coverage Diff @@
## main #97 +/- ##
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+ Coverage 98.71% 98.74% +0.02%
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Files 25 25
Lines 7240 7406 +166
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+ Hits 7147 7313 +166
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_maxbalanceholds a block with more thann²/8arcs in aDenseParametricTree: twon×nweight matrices with parallel arcs merged into the heaviest, and an indexed heap over nodes keyed by the best candidate arc entering each, rescanned lazily when a key may have fallen. A node whose depth changes then costs one pass over the live nodes instead of a heap update for each incident arc on a heap ofn²entries. Sparser blocks keep the arc-listParametricTree; the keyworddenseselects the representation explicitly. The initial tree and the summation of the contraction chains are shared.On dense random lognormal matrices,
cover_transversal(PowerMean{2}(), A; maxbalance=true)takes 0.8 s at n = 1600 and 20 s at n = 6400, and the shifts agree with the arc-list path to roundoff.Assisted-by: Claude Opus 5.5 and Claude Fable 5.1 noreply@anthropic.com