Package org.flag4j.linalg.decompositions.svd

Class ComplexSVD

java.lang.Object

org.flag4j.linalg.decompositions.svd.SVD<CMatrix>

org.flag4j.linalg.decompositions.svd.ComplexSVD

All Implemented Interfaces:

Decomposition<CMatrix>

public class ComplexSVD
extends SVD<CMatrix>

Instances of this class can be used to compute the singular value decomposition (SVD) of a real dense matrix. That is, decompose a rectangular matrix M as M=USV<sup>H</sup> where U and V are unitary matrices whose columns are the left and right singular vectors of M and S is a rectangular diagonal matrix containing the singular values of M.

Field Summary

Fields inherited from class org.flag4j.linalg.decompositions.svd.SVD

computeUV, rank, reduced, S, U, V

Constructor Summary

Constructors

Constructor	Description
ComplexSVD()	Creates a decomposer to compute the singular value decomposition of a real matrix.
ComplexSVD(boolean computeUV)	Creates a decomposer to compute the Schur decomposition.
ComplexSVD(boolean computeUV, boolean reduced)	Creates a decomposer to compute the singular value decomposition of a real matrix.

Method Summary

Modifier and Type	Method	Description
protected void	extractNormalizedCols(CMatrix singularVecs, int j)	Extracts the singular vectors, normalizes them and sets the columns of U and V to be the left/right singular vectors.
protected void	initUV(Shape src, int cols)	Initializes the unitary U and V matrices for the SVD.
protected CMatrix	invDirectSum(CMatrix src)	Computes the inverse direct sum of a matrix and its hermitian transpose.
protected CMatrix	makeEigenPairs(CMatrix B, double[] eigVals)	Gets the eigen values and vectors of symmetric the block matrix which corresponds to the singular values and vectors of the matrix being decomposed.
protected void	makeEigenVals(CMatrix B, double[] eigVals)	Gets the eigen values of the symmetric block matrix which corresponds to the singular values of the matrix being decomposed.

Methods inherited from class org.flag4j.linalg.decompositions.svd.SVD

computeRank, decompose, getRank, getS, getU, getV

Methods inherited from class java.lang.Object

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

Constructor Details

ComplexSVD

public ComplexSVD()

Creates a decomposer to compute the singular value decomposition of a real matrix. The left and right singular vectors will be computed.

ComplexSVD

public ComplexSVD(boolean computeUV)

Creates a decomposer to compute the Schur decomposition.

Parameters:

computeUV - A flag which indicates if the unitary matrices Q and V should be computed (i.e. the singular vectors). By default, this is true.
- If true, the Q and V matrices will be computed.
- If false, the Q and V matrices will not be computed. If it is not needed, this may provide a performance improvement.

ComplexSVD

public ComplexSVD(boolean computeUV,
 boolean reduced)

Creates a decomposer to compute the singular value decomposition of a real matrix.

Parameters:

computeUV - A flag which indicates if the orthogonal matrices Q and V should be computed (i.e. the singular vectors). By default, this is true.
- If true, the Q and V matrices will be computed.
- If false, the Q and V matrices will not be computed. If they are not needed, this may provide a performance improvement.

reduced - Flag which indicates if the reduced (or full) SVD should be computed. This is false by default.
- If true, reduced SVD is computed. - If false, the full SVD is computed.

Method Details

invDirectSum

protected CMatrix invDirectSum(CMatrix src)

Computes the inverse direct sum of a matrix and its hermitian transpose.

Specified by:

invDirectSum in class SVD<CMatrix>

Parameters:

src - Matrix to inverse direct add with its hermitian transpose.

Returns:

The inverse direct sum of the src matrix with its hermitian transpose.

makeEigenPairs

protected CMatrix makeEigenPairs(CMatrix B,
 double[] eigVals)

Gets the eigen values and vectors of symmetric the block matrix which corresponds to the singular values and vectors of the matrix being decomposed.

Specified by:

makeEigenPairs in class SVD<CMatrix>

Parameters:

B - Symmetric block matrix to compute the eigenvalues of.

eigVals - Storage for eigenvalues.

Returns:

The eigenvalues and eigenvectors of the symmetric block matrix which corresponds to the singular values and vectors of the matrix being decomposed.

makeEigenVals

protected void makeEigenVals(CMatrix B,
 double[] eigVals)

Gets the eigen values of the symmetric block matrix which corresponds to the singular values of the matrix being decomposed.

Specified by:

makeEigenVals in class SVD<CMatrix>

Parameters:

B - Symmetric block matrix to compute the eigenvalues of.

eigVals - Storage for eigenvalues.

initUV

protected void initUV(Shape src,
 int cols)

Initializes the unitary U and V matrices for the SVD.

Specified by:

initUV in class SVD<CMatrix>

Parameters:

src - Shape of the source matrix being decomposed.

cols - The number of columns for U and V.

extractNormalizedCols

protected void extractNormalizedCols(CMatrix singularVecs,
 int j)

Extracts the singular vectors, normalizes them and sets the columns of U and V to be the left/right singular vectors.

Specified by:

extractNormalizedCols in class SVD<CMatrix>

Parameters:

singularVecs - Computed left and right singular vectors.

j - Index of the column of U and V to set.