org.ejml.dense.row.decomposition.qr

Class QRColPivDecompositionHouseholderColumn_DDRM

java.lang.Object

org.ejml.dense.row.decomposition.qr.QRDecompositionHouseholderColumn_DDRM

org.ejml.dense.row.decomposition.qr.QRColPivDecompositionHouseholderColumn_DDRM

All Implemented Interfaces:

org.ejml.interfaces.decomposition.DecompositionInterface<org.ejml.data.DMatrixRMaj>, org.ejml.interfaces.decomposition.QRDecomposition<org.ejml.data.DMatrixRMaj>, org.ejml.interfaces.decomposition.QRPDecomposition<org.ejml.data.DMatrixRMaj>, org.ejml.interfaces.decomposition.QRPDecomposition_F64<org.ejml.data.DMatrixRMaj>

public class QRColPivDecompositionHouseholderColumn_DDRM
extends QRDecompositionHouseholderColumn_DDRM
implements org.ejml.interfaces.decomposition.QRPDecomposition_F64<org.ejml.data.DMatrixRMaj>

Performs QR decomposition with column pivoting. To prevent overflow/underflow the whole matrix is normalized by the max value, but columns are not normalized individually any more. To enable code reuse it extends QRDecompositionHouseholderColumn_DDRM and functions from that class are used whenever possible. Columns are transposed into single arrays, which allow for fast pivots.

Decomposition: A*P = Q*R

Based off the description in "Fundamentals of Matrix Computations", 2nd by David S. Watkins.

Field Summary

Fields

Modifier and Type	Field and Description
protected double[]	normsCol
protected int[]	pivots
protected int	rank
protected double	singularThreshold

Fields inherited from class org.ejml.dense.row.decomposition.qr.QRDecompositionHouseholderColumn_DDRM

dataQR, error, gamma, gammas, minLength, numCols, numRows, tau, v

Constructor Summary

Constructors

Constructor and Description
QRColPivDecompositionHouseholderColumn_DDRM()
QRColPivDecompositionHouseholderColumn_DDRM(double singularThreshold) Configure parameters.

Method Summary

Modifier and Type	Method and Description
boolean	decompose(org.ejml.data.DMatrixRMaj A) To decompose the matrix 'A' it must have full rank.
org.ejml.data.DMatrixRMaj	getColPivotMatrix(org.ejml.data.DMatrixRMaj P)
int[]	getColPivots()
org.ejml.data.DMatrixRMaj	getQ(org.ejml.data.DMatrixRMaj Q, boolean compact) Computes the Q matrix from the information stored in the QR matrix.
int	getRank()
protected boolean	householderPivot(int j) Computes the householder vector "u" for the first column of submatrix j.
void	setExpectedMaxSize(int numRows, int numCols)
void	setSingularThreshold(double threshold)
protected void	setupPivotInfo() Sets the initial pivot ordering and compute the F-norm squared for each column
protected void	swapColumns(int j) Finds the column with the largest normal and makes that the first column
protected void	updateNorms(int j) Performs an efficient update of each columns' norm

Methods inherited from class org.ejml.dense.row.decomposition.qr.QRDecompositionHouseholderColumn_DDRM

convertToColumnMajor, getGammas, getQR, getR, householder, inputModified, updateA

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

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

getR

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

inputModified

Field Detail

pivots

protected int[] pivots

normsCol

protected double[] normsCol

singularThreshold

protected double singularThreshold

rank

protected int rank

Constructor Detail

QRColPivDecompositionHouseholderColumn_DDRM

public QRColPivDecompositionHouseholderColumn_DDRM(double singularThreshold)

Configure parameters.

Parameters:

singularThreshold - The singular threshold.

QRColPivDecompositionHouseholderColumn_DDRM

public QRColPivDecompositionHouseholderColumn_DDRM()

Method Detail

setSingularThreshold

public void setSingularThreshold(double threshold)

Specified by:

setSingularThreshold in interface org.ejml.interfaces.decomposition.QRPDecomposition_F64<org.ejml.data.DMatrixRMaj>

setExpectedMaxSize

public void setExpectedMaxSize(int numRows,
                               int numCols)

Overrides:

setExpectedMaxSize in class QRDecompositionHouseholderColumn_DDRM

getQ

public org.ejml.data.DMatrixRMaj getQ(org.ejml.data.DMatrixRMaj Q,
                                      boolean compact)

Computes the Q matrix from the information stored in the QR matrix. This operation requires about 4(m²n-mn²+n³/3) flops.

Specified by:

getQ in interface org.ejml.interfaces.decomposition.QRDecomposition<org.ejml.data.DMatrixRMaj>

Overrides:

getQ in class QRDecompositionHouseholderColumn_DDRM

Parameters:

Q - The orthogonal Q matrix.

decompose

public boolean decompose(org.ejml.data.DMatrixRMaj A)

To decompose the matrix 'A' it must have full rank. 'A' is a 'm' by 'n' matrix. It requires about 2n*m²-2m²/3 flops.

The matrix provided here can be of different dimension than the one specified in the constructor. It just has to be smaller than or equal to it.

Specified by:

decompose in interface org.ejml.interfaces.decomposition.DecompositionInterface<org.ejml.data.DMatrixRMaj>

Overrides:

decompose in class QRDecompositionHouseholderColumn_DDRM

setupPivotInfo

protected void setupPivotInfo()

Sets the initial pivot ordering and compute the F-norm squared for each column

updateNorms

protected void updateNorms(int j)

Performs an efficient update of each columns' norm

swapColumns

protected void swapColumns(int j)

Finds the column with the largest normal and makes that the first column

Parameters:

j - Current column being inspected

householderPivot

protected boolean householderPivot(int j)

Computes the householder vector "u" for the first column of submatrix j. The already computed norm is used and checks to see if the matrix is singular at this point.

Q = I - γuu^T

This function finds the values of 'u' and 'γ'.

Parameters:

j - Which submatrix to work off of.

Returns:

false if it is degenerate

getRank

public int getRank()

Specified by:

getRank in interface org.ejml.interfaces.decomposition.QRPDecomposition<org.ejml.data.DMatrixRMaj>

getColPivots

public int[] getColPivots()

Specified by:

getColPivots in interface org.ejml.interfaces.decomposition.QRPDecomposition<org.ejml.data.DMatrixRMaj>

getColPivotMatrix

public org.ejml.data.DMatrixRMaj getColPivotMatrix(org.ejml.data.DMatrixRMaj P)

Specified by:

getColPivotMatrix in interface org.ejml.interfaces.decomposition.QRPDecomposition<org.ejml.data.DMatrixRMaj>