Fresh CSC matrix holding A + alpha * x * xT in its lower or upper triangle. The other triangle is copied unchanged. Unlike dense com.eignex.koblas.dense.DenseBlas.syr, this is not in place: a rank update can introduce entries that the source CSC pattern has no room to store.

Existing explicit zeros survive. A coordinate reached by nonzero vector support is stored even when its arithmetic cancels or underflows to zero, so the returned matrix never silently drops discovered fill. Zero vector entries are skipped, including with non-finite operands; dense NaN propagation is not guaranteed. The result owns independent structural and value arrays, and its rows ascend within every column.

Fresh CSC matrix holding A + alpha * (x * yT + y * xT) in its lower or upper triangle. The other triangle is copied unchanged. This structural counterpart of dense com.eignex.koblas.dense.DenseBlas.syr2 never mutates its source, because newly nonzero entries may require CSC fill.

Existing explicit zeros survive. A coordinate reached by nonzero vector support is stored even when its two terms cancel or underflow to zero. Zero vector entries are skipped as in SparseMatrix.syr. The result has independent arrays and canonical ascending CSC rows.