DenseBlas

C = alpha · op(A) · op(B) + beta · C (BLAS dgemm), with shapes op(A): m×k, op(B): k×n, C: m×n. beta == 0.0 overwrites c without reading it. workspace reuses any needed transpose packing.

gemm with alpha = 1, beta = 0, into a fresh matrix. A.cols must equal B.rows.

gemm over borrowed column-major panels. c must not overlap either input; disjoint panels may share a backing buffer. Implementations must preserve each physical leading dimension without copying.

gemm over borrowed panels into a fresh owned matrix.

C = alpha · op(A) · op(B) + beta · C in only the selected triangle (Netlib GEMMTR, commonly exposed as gemmt). op(A) is n×k, op(B) is k×n, and c is n×n. The opposite triangle is neither read nor written. alpha == 0.0 does not read either input and beta == 0.0 does not read selected destination entries. If c shares either input buffer, workspace supplies reusable staging.

y = alpha · op(A) · x + beta · y (BLAS dgemv), with op(A) being Aᵀ when transpose. beta == 0.0 overwrites y without reading it.

gemv with alpha = 1, beta = 0, into a fresh result.

gemv over borrowed strided storage. The destination must not overlap a or x; disjoint views may share one backing buffer. Implementations may pass offsets, strides, and leading dimensions directly to BLAS and must not materialize a contiguous copy. Like BLAS dgemv, a zero row or column count returns without reading or changing y.

gemv over borrowed storage into a fresh owned array.

A = A + alpha · x · yᵀ (BLAS dger), the dense form a backend can dispatch. The free ger accepts VectorStorage operands and takes a sparse fast path.

C = alpha · A · B + beta · C, or C = alpha · B · A + beta · C when right (BLAS dsymm). Only the lower triangle of a is read; beta == 0.0 overwrites c without reading it. workspace reuses the packed operand panels and edge tile.

y = alpha · A · x + beta · y for a symmetric a (BLAS dsymv). Only the lower triangle is read, diagonal included; beta == 0.0 overwrites y without reading it.

A += alpha · x · xᵀ (BLAS dsyr), writing only the lower or upper triangle.

A += alpha · (x · yᵀ + y · xᵀ) (BLAS dsyr2), writing only the lower or upper triangle.

C = alpha · (op(A) · op(B)ᵀ + op(B) · op(A)ᵀ) + beta · C (BLAS dsyr2k), where op transposes when transpose. Writes only the lower or upper triangle; beta == 0.0 overwrites it without reading.

In the non-transposed form, a rank step is skipped only when both output-column coefficients are zero, following Netlib dsyr2k; the transposed form evaluates both products. Pass a workspace to reuse the packed panels and diagonal tile.

C = alpha · A·Aᵀ + beta · C, or alpha · Aᵀ·A + beta · C when transpose (BLAS dsyrk). Only the lower or upper triangle is written; beta == 0.0 overwrites it without reading.

In the non-transposed form, a zero entry used as the rank-one multiplier is skipped before it can multiply an infinity, following Netlib dsyrk; the transposed dot-product form evaluates that product. Pass a workspace to reuse the packed panels and diagonal tile.

Fresh transposed a. For a product prefer the transpose flags on gemv and gemm, which avoid a caller-visible intermediate; this is for a caller that means to hold the transpose.

On the seam rather than beside the other whole-matrix operations because a library has its own routine for it, omatcopy in the BLAS-like extensions, where the standard has none.

B = alpha · op(T) · B, or B = alpha · B · op(T) when right (BLAS dtrmm), the counterpart of trsm. workspace reuses portable staging.

x = op(T) · x in place (BLAS dtrmv), the product counterpart of trsv.

B = alpha · op(T)⁻¹ · B in place, or B = alpha · B · op(T)⁻¹ when right (BLAS dtrsm). Flags follow trsv; the right-hand sides are the columns of b from the left and its rows from the right. workspace reuses portable staging.

Solve op(T) · x = b in place (BLAS dtrsv) for the lower or upper triangle of the square a, op transposing when transpose and unitDiag taking the diagonal as 1. x carries b in and x out.

The diagonal is divided by, not tested: dtrsv carries no info and reports nothing, so a singular triangle yields infinities or NaNs and the caller who needs the distinction tests the diagonal first. The sparse com.eignex.koblas.sparse.SparseBlas.trsv follows the same rule.