org.ejml.interfaces.decomposition

Interface QRDecomposition<T extends Matrix64F>

All Superinterfaces:

DecompositionInterface<T>

All Known Subinterfaces:

QRPDecomposition<T>

All Known Implementing Classes:

QRColPivDecompositionHouseholderColumn_D64, QRDecomposition_B64_to_D64, QRDecompositionHouseholder_B64, QRDecompositionHouseholder_D64, QRDecompositionHouseholderColumn_D64, QRDecompositionHouseholderTran_D64

public interface QRDecomposition<T extends Matrix64F>
extends DecompositionInterface<T>

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 AdjLinearSolverQr

Orthogonal matrices have the following properties:

• QQ^T=I
• Q^T=Q^-1

Author:

Peter Abeles

See Also:

QRDecompositionHouseholder_D64, QRDecompositionHouseholderColumn_D64

Method Summary

Methods

Modifier and Type	Method and Description
T	getQ(T Q, boolean compact) Returns the Q matrix from the decomposition.
T	getR(T R, boolean compact) Returns the R matrix from the decomposition.

Methods inherited from interface org.ejml.interfaces.decomposition.DecompositionInterface

decompose, inputModified

Method Detail

getQ

T getQ(T Q,
     boolean compact)

Returns the Q matrix from the decomposition. Should only be called after DecompositionInterface.decompose(org.ejml.data.Matrix64F) has been called.

If parameter Q is not null, then that matrix is used to store the Q matrix. Otherwise a new matrix is created.

Parameters:

Q - If not null then the Q matrix is written to it. Modified.

compact - If true an m by n matrix is created, otherwise n by n.

Returns:

The Q matrix.

getR

T getR(T R,
     boolean compact)

Returns the R matrix from the decomposition. Should only be called after DecompositionInterface.decompose(org.ejml.data.Matrix64F) has been.

If setZeros is true then an n × m matrix is required and all the elements are set. If setZeros is false then the matrix must be at least m × m and only the upper triangular elements are set.

If parameter R is not null, then that matrix is used to store the R matrix. Otherwise a new matrix is created.

Parameters:

R - If not null then the R matrix is written to it. Modified.

compact - If true only the upper triangular elements are set

Returns:

The R matrix.