Development build. This page describes main, not a released package. The latest published Lodestar.Abstractions is 0.2.0 — read its documentation.

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 O(RowCount + 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.

A NaN or infinite value, stored or in the operand, is carried through, not refused — and a stored zero times an infinity is NaN, as it is in scipy's product. One in the operand reaches the result only where a row stores that column — the vector's entry, or the block's row, is otherwise never read — so a row storing 1 at column 0 and nothing else, times [2, NaN], is 2, as in scipy.

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.

Before .NET 6 the cap is lower. The bound is the running runtime's largest array: .NET 6's Array.MaxLength, or 0x7FEFFFFF elements earlier, where a result between the two is refused as past it rather than failing in the allocation (#1614). .NET Framework also refuses a double array past 2 GB without gcAllowVeryLargeObjects, with its own out-of-memory error.

Applies to — net10.0, netstandard2.0.

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