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ScaleInvariantAnalysis

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This package computes covers of matrices: non-negative vectors a (and b) such that a[i] * b[j] >= abs(A[i, j]) for all i, j. Covers are the natural scale-covariant representation of a matrix — under row/column diagonal scaling they transform exactly as the matrix entries do — making them a useful building block for scale-invariant numerical analysis.

Fast O(mn) heuristics (symcover, cover) are provided for everyday use, along with soft covers (soft_symcover, soft_cover) that penalize under-coverage rather than forbid it. Objective-minimal hard covers (symcover_min, cover_min) minimize a penalty subject to the coverage constraint: the default squared-log-excess penalty is solved natively, with no external solver, while the other penalties are available when JuMP and HiGHS (or Ipopt) are loaded.

See the documentation for motivation, examples, and a full API reference.

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Tools for for scale-invariant numerical analysis

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