Class BidiagonalDecompositionTall_MT_DDRM

java.lang.Object
org.ejml.dense.row.decomposition.bidiagonal.BidiagonalDecompositionTall_MT_DDRM
All Implemented Interfaces:
BidiagonalDecomposition<DMatrixRMaj>, BidiagonalDecomposition_F64<DMatrixRMaj>, DecompositionInterface<DMatrixRMaj>

@Generated("org.ejml.dense.row.decomposition.bidiagonal.BidiagonalDecompositionTall_DDRM") public class BidiagonalDecompositionTall_MT_DDRM extends Object implements BidiagonalDecomposition_F64<DMatrixRMaj>

BidiagonalDecomposition_F64 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]
B=[B1;0]
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_F64. 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.