Home › Abstractions › The shared sparse primitive

The transposed matrix times a dense block, without ever building the transpose.

public double[] TransposeMultiply(ReadOnlySpan<double> block, int columnCount)

Parameters — block is the dense right operand, row-major, with RowCount rows and columnCount columns, so its length is the product of the two. columnCount is how many columns it holds.

Returns — double[] of ColumnCount × columnCount entries, row-major: one row per column of the matrix.

Exceptions — ArgumentException when block is not RowCount rows of columnCount. ArgumentOutOfRangeException when columnCount is not positive, or when the product would not fit in a single array.

Example — [[1, 0, 2], [0, 3, 0]] against a two-row, two-column block. The matrix has three columns, so the answer has three rows; the middle one is the only one the second row of the matrix reaches.

using Lodestar.Abstractions;

CsrMatrix matrix = new(2, 3, [1.0, 2.0, 3.0], [0, 2, 1], [0, 2, 3]);

double[] product = matrix.TransposeMultiply([1.0, 0.5, 2.0, 1.5], columnCount: 2);

double firstRow = product[0];    // => 1
double middleRow = product[2];   // => 6
double lastRow = product[4];     // => 2

Remarks — materialising the transpose would cost a second matrix of the same size and a pass to build it. Scattering into the result instead reads each non-zero exactly once, which is the same arithmetic for none of the memory: for every stored cell, the row it sits in selects a row of block and its column index selects the row of the result to add into.

Together with Multiply's block overload this is what a randomized SVD's power iteration alternates between — A Ω, then Aᵀ Q — and the pair is the reason both exist rather than a single vector product.

The result is not the transpose of Multiply's. Multiply produces one row per row of the matrix; this produces one per column.

Applies to — net10.0, netstandard2.0.

See also — CsrMatrix.Multiply, CsrMatrix, the Python equivalence table.