org.ejml.alg.dense.decomposition.svd

Class SvdImplicitQrDecompose

java.lang.Object

org.ejml.alg.dense.decomposition.svd.SvdImplicitQrDecompose

All Implemented Interfaces:

DecompositionInterface<DenseMatrix64F>, SingularValueDecomposition<DenseMatrix64F>

public class SvdImplicitQrDecompose
extends Object
implements SingularValueDecomposition<DenseMatrix64F>

Computes the Singular value decomposition of a matrix using the implicit QR algorithm for singular value decomposition. It works by first by transforming the matrix to a bidiagonal A=U*B*V^T form, then it implicitly computing the eigenvalues of the B^TB matrix, which are the same as the singular values in the original A matrix.

Based off of the description provided in:

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

Author:

Peter Abeles

Constructor Summary

Constructors

Constructor and Description
SvdImplicitQrDecompose(boolean compact, boolean computeU, boolean computeV, boolean canUseTallBidiagonal) Configures the class

Method Summary

Methods

Modifier and Type	Method and Description
boolean	decompose(DenseMatrix64F orig) Computes the decomposition of the input matrix.
double[]	getSingularValues() Returns the singular values.
DenseMatrix64F	getU(DenseMatrix64F U, boolean transpose) Returns the orthogonal 'U' matrix.
DenseMatrix64F	getV(DenseMatrix64F V, boolean transpose) Returns the orthogonal 'V' matrix.
DenseMatrix64F	getW(DenseMatrix64F W) Returns a diagonal matrix with the singular values.
boolean	inputModified() Is the input matrix to DecompositionInterface.decompose(org.ejml.data.Matrix64F) is modified during the decomposition process.
boolean	isCompact() If true then compact matrices are returned.
int	numberOfSingularValues() The number of singular values in the matrix.
int	numCols() Number of columns in the decomposed matrix.
int	numRows() Number of rows in the decomposed matrix.

Methods inherited from class java.lang.Object

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

Constructor Detail

SvdImplicitQrDecompose

public SvdImplicitQrDecompose(boolean compact,
                      boolean computeU,
                      boolean computeV,
                      boolean canUseTallBidiagonal)

Configures the class

Parameters:

compact - Compute a compact SVD

computeU - If true it will compute the U matrix

computeV - If true it will compute the V matrix

canUseTallBidiagonal - If true then it can choose to use a tall Bidiagonal decomposition to improve runtime performance.

Method Detail

getSingularValues

public double[] getSingularValues()

Description copied from interface: SingularValueDecomposition

Returns the singular values. This is the diagonal elements of the W matrix in the decomposition. Ordering of singular values is not guaranteed..

Specified by:

getSingularValues in interface SingularValueDecomposition<DenseMatrix64F>

Returns:

Singular values. Note this array can be longer than the number of singular values. Extra elements have no meaning.

numberOfSingularValues

public int numberOfSingularValues()

Description copied from interface: SingularValueDecomposition

The number of singular values in the matrix. This is equal to the length of the smallest side.

Specified by:

numberOfSingularValues in interface SingularValueDecomposition<DenseMatrix64F>

Returns:

Number of singular values in the matrix.

isCompact

public boolean isCompact()

Description copied from interface: SingularValueDecomposition

If true then compact matrices are returned.

Specified by:

isCompact in interface SingularValueDecomposition<DenseMatrix64F>

Returns:

true if results use compact notation.

getU

public DenseMatrix64F getU(DenseMatrix64F U,
                  boolean transpose)

Description copied from interface: SingularValueDecomposition

Returns the orthogonal 'U' matrix.

Internally the SVD algorithm might compute U transposed or it might not. To avoid an unnecessary double transpose the option is provided to select if the transpose is returned.

Specified by:

getU in interface SingularValueDecomposition<DenseMatrix64F>

Parameters:

U - Optional storage for U. If null a new instance or internally maintained matrix is returned. Modified.

transpose - If the returned U is transposed.

Returns:

An orthogonal matrix.

getV

public DenseMatrix64F getV(DenseMatrix64F V,
                  boolean transpose)

Description copied from interface: SingularValueDecomposition

Returns the orthogonal 'V' matrix.

Internally the SVD algorithm might compute V transposed or it might not. To avoid an unnecessary double transpose the option is provided to select if the transpose is returned.

Specified by:

getV in interface SingularValueDecomposition<DenseMatrix64F>

Parameters:

V - Optional storage for v. If null a new instance or internally maintained matrix is returned. Modified.

transpose - If the returned V is transposed.

Returns:

An orthogonal matrix.

getW

public DenseMatrix64F getW(DenseMatrix64F W)

Description copied from interface: SingularValueDecomposition

Returns a diagonal matrix with the singular values. Order of the singular values is not guaranteed.

Specified by:

getW in interface SingularValueDecomposition<DenseMatrix64F>

Parameters:

W - Optional storage for W. If null a new instance or internally maintained matrix is returned. Modified.

Returns:

Diagonal matrix with singular values along the diagonal.

decompose

public boolean decompose(DenseMatrix64F orig)

Description copied from interface: DecompositionInterface

Computes the decomposition of the input matrix. Depending on the implementation the input matrix might be stored internally or modified. If it is modified then the function DecompositionInterface.inputModified() will return true and the matrix should not be modified until the decomposition is no longer needed.

Specified by:

decompose in interface DecompositionInterface<DenseMatrix64F>

Parameters:

orig - The matrix which is being decomposed. Modification is implementation dependent.

Returns:

Returns if it was able to decompose the matrix.

inputModified

public boolean inputModified()

Description copied from interface: DecompositionInterface

Is the input matrix to DecompositionInterface.decompose(org.ejml.data.Matrix64F) is modified during the decomposition process.

Specified by:

inputModified in interface DecompositionInterface<DenseMatrix64F>

Returns:

true if the input matrix to decompose() is modified.

numRows

public int numRows()

Description copied from interface: SingularValueDecomposition

Number of rows in the decomposed matrix.

Specified by:

numRows in interface SingularValueDecomposition<DenseMatrix64F>

Returns:

Number of rows in the decomposed matrix.

numCols

public int numCols()

Description copied from interface: SingularValueDecomposition

Number of columns in the decomposed matrix.

Specified by:

numCols in interface SingularValueDecomposition<DenseMatrix64F>

Returns:

Number of columns in the decomposed matrix.