SparseMatrix

A sparse matrix in compressed-sparse-column (CSC) form: column j occupies rowIdx[colPtr[j] until colPtr[j + 1]] with the parallel nonzero values in values, row indices strictly ascending within a column — validated by the constructor, since get relies on the ordering. colPtr has length cols + 1 with colPtr[0] == 0 and colPtr[cols] == values.size. CSC is the layout sparse solvers and column-oriented sweeps (matrix–vector products, LU factorization) consume directly — and, since DenseMatrix became column-major, the axis both storages agree is contiguous.

The invariants are not arbitrary: they are what a host sparse solver requires. UMFPACK states them verbatim — Ap[0] zero, Ap[j] <= Ap[j+1], row indices ascending within a column with no duplicates, 0-based and in range — so this backing passes to umfpack_di_* with no repacking. KLU takes the same (n, Ap, Ai) with int32_t arrays. CHOLMOD wraps it as a cholmod_sparse with packed = 1, sorted = 1, stype = 0 (both triangles stored, which is what koblas does) and itype = CHOLMOD_INT. Checked against the 7.x headers rather than remembered.

Two mismatches remain for a future binding, neither structural. A library built for 64-bit indices wants the umfpack_dl_* family and a widening copy, the sparse counterpart of the LP64/ILP64 split the dense backend already documents. And an explicitly stored zero is part of the value here — equality distinguishes it — where a host library may drop it, so a round-trip through one can lose pattern.

Arithmetic lives on the sparse seam rather than here, as it does for DenseMatrix: the products are com.eignex.koblas.sparse.SparseBlas methods, reachable as gemv/lu extensions, so a container stays storage and does not depend on which backend is installed.

A MatrixView like the dense one, so anything written against the view contract accepts either. The two access costs differ though, and the difference is not small: get searches a column rather than indexing, and toArray densifies. Code that wants the sparsity should reach for forEachInColumn.

Serializes through its CSC arrays rather than a readable 2D form, unlike DenseMatrix. The flat dense backing is an implementation detail worth hiding behind a nicer wire shape; CSC is the format, and writing a sparse matrix out densely would cost the rows × cols the representation exists to avoid.