Embeddings 0.4.0 vectormath dot

Lodestar.Embeddings 0.4.0. This page is frozen at that release. Read the current documentation for what main says now. A link to a decision or a migration page follows main, and leaves the archive.

VectorMath.Dot

The dot product of two equal-length vectors.

public static float Dot(ReadOnlySpan<float> a, ReadOnlySpan<float> b)

Parameters — a and b are the two vectors. They must be the same length; a float[] converts implicitly, so nothing is allocated to pass one.

Returns — float, the sum of the element-wise products. Order of the arguments does not change it.

Exceptions — ArgumentException when a and b differ in length. There is no silent truncation to the shorter of the two.

Example — the textbook product, and the same call standing in for cosine similarity on unit vectors.

using Lodestar.Embeddings.Search;

float plain = VectorMath.Dot(new float[] { 1f, 2f, 3f }, new float[] { 4f, 5f, 6f });  // => 32
float orthogonal = VectorMath.Dot(new float[] { 1f, 0f }, new float[] { 0f, 1f });  // => 0

Remarks — on two L2-normalized vectors this is cosine similarity: 1 for the same direction, 0 for perpendicular, -1 for opposite. That identity is the whole reason EmbeddingIndex normalizes on insertion — it turns a similarity metric into one multiply-accumulate loop.

On unnormalized vectors it is not a similarity, because length contributes. A long vector scores high against everything.

The accumulation order differs between the two target frameworks, which VectorMath explains: the SIMD path on net10.0 sums lane-wise and the netstandard2.0 scalar loop sums left to right, so long vectors can disagree in the last bits.

Applies to — net10.0, netstandard2.0.

See also — VectorMath.L2Norm, EmbeddingIndex.Search, the search index.