Class BidiagonalDecompositionTall_FDRM

All Implemented Interfaces:
BidiagonalDecomposition<FMatrixRMaj>, BidiagonalDecomposition_F32<FMatrixRMaj>, DecompositionInterface<FMatrixRMaj>

public class BidiagonalDecompositionTall_FDRM
extends Object
implements BidiagonalDecomposition_F32<FMatrixRMaj>

BidiagonalDecomposition_F32 specifically designed for tall matrices. First step is to perform QR decomposition on the input matrix. Then R is decomposed using a bidiagonal decomposition. By performing the bidiagonal decomposition on the smaller matrix computations can be saved if m/n > 5/3 and if U is NOT needed.

A = [Q1 Q2][U1 0; 0 I] [B1;0] VT
U=[Q1*U1 Q2]
A = U*B*VT

A QRP decomposition is used internally. That decomposition relies an a fixed threshold for selecting singular values and is known to be less stable than SVD. There is the potential for a degregation of stability by using BidiagonalDecompositionTall instead of BidiagonalDecomposition_F32. A few simple tests have shown that loss in stability to be insignificant.

See page 404 in "Fundamentals of Matrix Computations", 2nd by David S. Watkins.