org.ejml.alg.dense.decomposition.svd.implicitqr

Class SvdImplicitQrAlgorithm

java.lang.Object

org.ejml.alg.dense.decomposition.svd.implicitqr.SvdImplicitQrAlgorithm

Direct Known Subclasses:

SvdImplicitQrAlgorithmSmart

public class SvdImplicitQrAlgorithm
extends java.lang.Object

Computes the QR decomposition of a bidiagonal matrix. Internally this matrix is stored as two arrays. Shifts can either be provided to it or it can generate the shifts on its own. It optionally computes the U and V matrices. This comparability allows it to be used to compute singular values and associated matrices efficiently.

A = U*S*V^T
where A is the original m by n matrix.

Based off of the outline provided in:

David S. Watkins, "Fundamentals of Matrix Computations," Second Edition. Page 404-411

Note: To watch it process the matrix step by step uncomment commented out code.

Constructor Summary

Constructors

Constructor and Description
SvdImplicitQrAlgorithm()
SvdImplicitQrAlgorithm(boolean fastValues)

Method Summary

Modifier and Type	Method and Description
boolean	_process()
void	exceptionShift() It is possible for the QR algorithm to get stuck in a loop because of symmetries.
double[]	getDiag()
double	getMaxValue()
int	getNumberOfSingularValues()
double[]	getOff()
double	getSingularValue(int index)
double[]	getSingularValues()
DenseMatrix64F	getUt()
DenseMatrix64F	getVt()
void	incrementSteps()
void	initParam(int M, int N)
boolean	isDiagonalZero(int i)
boolean	isOffZero(int i)
boolean	nextSplit() Tells it to process the submatrix at the next split.
void	performImplicitSingleStep(double scale, double lambda, boolean byAngle) Given the lambda value perform an implicit QR step on the matrix.
void	printMatrix()
boolean	process()
boolean	process(double[] values) Perform a sequence of steps based off of the singular values provided.
void	resetSteps()
double	selectWilkinsonShift(double scale) Selects the Wilkinson's shift for BTB.
void	setFastValues(boolean b)
void	setMatrix(int numRows, int numCols, double[] diag, double[] off)
void	setMaxValue(double maxValue)
void	setSubmatrix(int x1, int x2)
void	setUt(DenseMatrix64F ut)
void	setVt(DenseMatrix64F vt)
double[]	swapDiag(double[] diag)
double[]	swapOff(double[] off)

Methods inherited from class java.lang.Object

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

Constructor Detail

SvdImplicitQrAlgorithm

public SvdImplicitQrAlgorithm(boolean fastValues)

SvdImplicitQrAlgorithm

public SvdImplicitQrAlgorithm()

Method Detail

getUt

public DenseMatrix64F getUt()

setUt

public void setUt(DenseMatrix64F ut)

getVt

public DenseMatrix64F getVt()

setVt

public void setVt(DenseMatrix64F vt)

setMatrix

public void setMatrix(int numRows,
                      int numCols,
                      double[] diag,
                      double[] off)

swapDiag

public double[] swapDiag(double[] diag)

swapOff

public double[] swapOff(double[] off)

setMaxValue

public void setMaxValue(double maxValue)

initParam

public void initParam(int M,
                      int N)

process

public boolean process()

process

public boolean process(double[] values)

Perform a sequence of steps based off of the singular values provided.

Parameters:

values -

Returns:

_process

public boolean _process()

incrementSteps

public void incrementSteps()

isOffZero

public boolean isOffZero(int i)

isDiagonalZero

public boolean isDiagonalZero(int i)

resetSteps

public void resetSteps()

nextSplit

public boolean nextSplit()

Tells it to process the submatrix at the next split. Should be called after the current submatrix has been processed.

performImplicitSingleStep

public void performImplicitSingleStep(double scale,
                                      double lambda,
                                      boolean byAngle)

Given the lambda value perform an implicit QR step on the matrix. B^T*B-lambda*I

Parameters:

lambda - Stepping factor.

setSubmatrix

public void setSubmatrix(int x1,
                         int x2)

selectWilkinsonShift

public double selectWilkinsonShift(double scale)

Selects the Wilkinson's shift for B^TB. See page 410. It is guaranteed to converge and converges fast in practice.

Parameters:

scale - Scale factor used to help prevent overflow/underflow

Returns:

Shifting factor lambda/(scale*scale)

exceptionShift

public void exceptionShift()

It is possible for the QR algorithm to get stuck in a loop because of symmetries. This happens more often with larger matrices. By taking a random step it can break the symmetry and finish.

printMatrix

public void printMatrix()

getNumberOfSingularValues

public int getNumberOfSingularValues()

getSingularValue

public double getSingularValue(int index)

setFastValues

public void setFastValues(boolean b)

getSingularValues

public double[] getSingularValues()

getDiag

public double[] getDiag()

getOff

public double[] getOff()

getMaxValue

public double getMaxValue()