Lodestar.Decomposition 0.2.0. 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.

PowerIterationNormalizer

What a power iteration does to its block between the two products, and therefore part of the answer rather than an implementation detail.

A power iteration multiplies the probe block by A and then by Aᵀ, which sharpens the spectrum — and, left alone, collapses every column of the block onto the leading singular vector, in double precision within a handful of iterations. Re-orthogonalizing between the products is what stops that. Which factorization does the re-orthogonalizing changes the numbers that come out, so it is a setting on TruncatedSvdOptions and never a decision the implementation makes quietly.

Members

Member	Value	What it does
Auto	0	None below three power iterations, Lu at or above. scikit-learn's rule, and — since its own default is five iterations — the reason the default path is the LU one.
None	1	Nothing between the products. Cheapest, and adequate only for one or two iterations.
Qr	2	An economic QR, by Householder reflections. The most accurate and the most expensive.
Lu	3	LU with partial pivoting, keeping P L. Its columns are not orthonormal, which is the accuracy it trades away for being cheaper.

None past two iterations is not a saving, it is a wrong answer: the block loses rank to rounding and the components it produces are approximately parallel. If five iterations are too slow, lower PowerIterations rather than turning the normalizer off.