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CsrMatrix.RowL2Norm

The Euclidean length of one row.

public double RowL2Norm(int row)

Parameters — row is the zero-based row index.

Returns — double, the square root of the sum of the squares of that row's stored cells. Zero for an empty row.

Exceptions — IndexOutOfRangeException when row is negative or not below RowCount. The index reaches the backing array directly, so the array's own exception is what surfaces rather than a re-wrapped one.

Example — three ones give √3; the third row's repeated the makes it longer.

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 first = counts.RowL2Norm(0);   // => 1.7320508075688772
double third = counts.RowL2Norm(2);   // => 2.6457513110645907

Remarks — this is the norm that matters for similarity. Two rows divided by their L2 norms have a dot product equal to their cosine similarity, which is why TfidfOptions normalizes by it and why NormalizeRows(SparseNorm.L2) is the usual call before comparing documents.

A matrix straight out of TfidfVectorizer is already L2-normalized, so every row's norm is 1 and calling this on one is a way to confirm that rather than to learn something new.

A stored NaN or infinity is carried into the norm, not refused: the row's norm is then NaN or +∞. The squares are summed as they are, unscaled, so a finite row whose sum of squares overflows — any value past about 1.34e154, such as [1e200] — reads +∞ although its true norm is finite.

Applies to — net10.0, netstandard2.0.

See also — CsrMatrix.RowL1Norm, CsrMatrix.NormalizeRows, SparseNorm.