mikera.matrixx.decompose.impl.qr

Interface QRDecomposition

All Known Implementing Classes:

HouseholderColQR, HouseholderQR

public interface QRDecomposition

QR decompositions decompose a rectangular matrix 'A' such that 'A=QR'. Where A ∈ ℜ ^{n × m} , n ≥ m, Q ∈ ℜ ^{n × n} is an orthogonal matrix, and R ∈ ℜ ^{n × m} is an upper triangular matrix. Some implementations of QR decomposition require that A has full rank.

Some features of QR decompositions:

• Can decompose rectangular matrices.
• Numerically stable solutions to least-squares problem, but not as stable as SVD
• Can incrementally add and remove columns from the decomposed matrix. See org.ejml.alg.dense.linsol.qr.AdjLinearSolverQr

Orthogonal matrices have the following properties:

• QQ^T=I
• Q^T=Q^-1

Author:

Peter Abeles

Method Summary

Modifier and Type	Method and Description
IQRResult	decompose(AMatrix A)

Method Detail

decompose

IQRResult decompose(AMatrix A)