PersistenceResult

Bottleneck distance (.claude/WORKLOG-mainstream-feature-gap-analysis.md item 4) between this result's and other's dimension-dimension bars, under the L-infinity ground norm -- see barcode.BarcodeDistance for the full matching/essential-bar policy this implements. Double.PositiveInfinity back means the two diagrams have different numbers of essential (never-dying) classes in this dimension, so no finite matching exists; that is a real answer, not a failure.

As the two-argument bottleneckDistance, under an explicit ground norm (see toGroundNorm's own doc for the Double.PositiveInfinity-means-L-infinity convention).

Column indices parallel to boundaryRows -- see that method's own doc.

Row indices of the boundary matrix's nonzero entries (0-based, parallel to boundaryCols/boundaryValues): row i/column j means cell j's boundary includes cell i with coefficient boundaryValues()(k). Every complex/engine combination TDA4j supports populates this (see that class's buildBoundaryMatrix) -- rebuild in MATLAB as sparse(rows()+1, cols()+1, values(), n, n) (MATLAB's sparse is 1-based; every index in this facade, including this one, is 0-based, matching cycleVertices's own convention).

Coefficients parallel to boundaryRows/boundaryCols, reported as double the same way cycleCoefficients is (the representative-integer value cast to double for a finite field, the value itself for the default real-valued field).

The homological dimension of boundary-matrix column j (0 until numCells) -- the same cell ordering boundaryRows/boundaryCols index into, NOT a bar index (there are generally far more cells than bars).

Column j's own filtration value -- the same quantity birth/death above report per bar, but per CELL here. Needed for anything that truncates the complex to a sub-level set K_r (e.g. circular coordinates: pick r in a target bar's [birth, death), keep only columns/rows with columnFiltrationValue <= r).

Column j's own cell identity, in the same per-complex-type shape cycleVertices documents (a sorted vertex array for Simplex[Int]-based complexes, a doubled-coordinate Cube encoding for cubical ones) -- lets a MATLAB caller relate a solved linear-algebra result (e.g. a cocycle from boundaryValues-derived harmonic smoothing) back to actual cells.

Coefficients parallel to cycleVertices(i). Reported as double regardless of the underlying coefficient field -- for a finite field Z/pZ this is the representative integer value cast to double, for the default real-valued field it's the value itself. See cycleVertices for the exceptions this can throw.

The cells making up bar i's representative chain, each as an int[] identifying that cell -- the array's own meaning depends on which complex this result came from, since the underlying cell type differs:

• complex="vr"/"alpha"/"cech" (a Simplex[Int]): the simplex's sorted vertex array (0-based, matching the row indices of whatever point/distance matrix was passed to TDA4j).
• complex="cubical" (a Cube): the cell's own doubled-coordinate encoding (Cube.encoded, see Cubical.scala) -- NOT vertex indices. Axis k's entry is 2*a for a degenerate (point) factor at lattice coordinate a, or 2*a+1 for a non-degenerate (unit-interval) factor spanning [a, a+1]; decode coordinate k as a = v(k)/2 (integer division) plus, when v(k) is odd, a unit interval starting there.

Throws UnsupportedOperationException if this specific bar has no recorded representative. Every engine records one for every bar, at every dimension, for every complex type above, so this indicates an engine bug rather than an expected gap -- see .claude/CLAUDE.md's coefficients-and-representatives design principle for why this matters.

The first numLevels persistence landscape functions (Bubenik 2013, .claude/WORKLOG-mainstream-feature-gap- analysis.md item 8) of this result's dimension-dimension bars, sampled at resolution evenly-spaced points across [tMin, tMax] -- see barcode.Vectorization.landscape for the exact sampling convention, the closed-form check it satisfies, and why an essential (never-dying) bar needs no special handling here. Returns levels(k)(j): level k (0 = the outer envelope) at the j-th sample point.

The number of cells (matrix columns/rows) in the full complex this result was computed from -- pass this as n to MATLAB's own sparse(rows()+1, cols()+1, values(), n, n) (see boundaryRows's own doc for the +1).

The persistence image (Adams et al. 2017, .claude/WORKLOG-mainstream-feature-gap-analysis.md item 8) of this result's dimension-dimension bars, with the weight cap defaulted to that diagram's own maximum finite persistence (the paper's suggested default) -- see the eight-argument overload to pass one explicitly, and barcode.Vectorization.persistenceImage for the exact construction (isotropic Gaussian bumps in birth-persistence coordinates, exact per-pixel integration, piecewise-linear weighting) and why essential (never-dying) bars are dropped rather than given a special-cased value. Returns image(r)(c): r indexes birthResolution pixels spanning [birthMin, birthMax], c indexes persistenceResolution pixels spanning [persistenceMin, persistenceMax].

As the eight-argument persistenceImage, with an explicit weight cap (the persistence value at and beyond which barcode.Vectorization's piecewise-linear weighting saturates to 1.0) instead of the diagram's own maximum finite persistence.

The whole barcode as one N-by-3 matrix: column 0 is dimension, column 1 is birth, column 2 is death (+Inf for an essential class). This is the primary, MATLAB-idiomatic way to consume a result -- immediately plottable, sortable, filterable with ordinary MATLAB matrix operations.

Wasserstein distance, order 1.0, L-infinity ground norm -- see bottleneckDistance and barcode.BarcodeDistance for the shared essential-bar policy and ground-norm convention.

As the two-argument wassersteinDistance, under an explicit order (must be finite and >= 1.0 -- pass Double.PositiveInfinity to bottleneckDistance directly instead, rather than here).

As the two-argument wassersteinDistance, under an explicit order and ground norm.