Home › Abstractions › The shared sparse primitive

The matrix times a dense vector, or times a dense block, in one pass over the stored cells.

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

Parameters — vector is the dense vector to multiply by, and must hold exactly ColumnCount values. The second overload takes block, a row-major dense operand of ColumnCount rows and columnCount columns, so its length is the product of the two.

Returns — double[]. From the first overload, RowCount entries, each the dot product of that row with vector. From the second, RowCount × columnCount entries, row-major.

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

Example — multiplying by all ones totals each row, which is that document's term count.

using Lodestar.Abstractions;
using Lodestar.Text.Vectorization;

string[] docs = ["the cat eats", "the dog eats", "the cat and the dog"];
CsrMatrix counts = new CountVectorizer().FitTransform(docs);

double[] totals = counts.Multiply([1, 1, 1, 1, 1]);

double first = totals[0];   // => 3
double third = totals[2];   // => 5

Remarks — the cost is NonZeroCount, not RowCount × ColumnCount, which is the whole reason to keep the matrix sparse. The third document totals 5 rather than 4 because the appears twice in it and the count is a count.

This is the operation behind scoring a corpus against a linear model: the weights are the vector, and each row's dot product is that document's score.

The block overload is not a loop over the vector one. It makes one pass over the non-zeros rather than columnCount passes: each column index is read once and the inner loop walks contiguous memory on both sides. That is the operation a randomized SVD's power iteration spends its time in — A Ω for a thin dense Ω — and TransposeMultiply is its other half.

Applies to — net10.0, netstandard2.0.

See also — CsrMatrix.TransposeMultiply, CsrMatrix, CsrMatrix.ToDense.