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org.apache.commons.math3.linear

pack-priv Class TriDiagonalTransformer

Class Inheritance

extends Object

java.lang.Object
org.apache.commons.math3.linear.TriDiagonalTransformer

Imports

java.util.Arrays, org.apache.commons.math3.util.FastMath

Class transforming a symmetrical matrix to tridiagonal shape.

A symmetrical m × m matrix A can be written as the product of three matrices: A = Q × T × Q^T with Q an orthogonal matrix and T a symmetrical tridiagonal matrix. Both Q and T are m × m matrices.

This implementation only uses the upper part of the matrix, the part below the diagonal is not accessed at all.

Transformation to tridiagonal shape is often not a goal by itself, but it is an intermediate step in more general decomposition algorithms like eigen decomposition. This class is therefore intended for internal use by the library and is not public. As a consequence of this explicitly limited scope, many methods directly returns references to internal arrays, not copies.

Since: 2.0

Field Summary

Modifier and Type	Field and Description
private RealMatrix	cachedQ Cached value of Q.
private RealMatrix	cachedQt Cached value of Qt.
private RealMatrix	cachedT Cached value of T.
private final double[][]	householderVectors Householder vectors.
private final double[]	main Main diagonal.
private final double[]	secondary Secondary diagonal.

Constructor Summary

Access	Constructor and Description
pack-priv	TriDiagonalTransformer(RealMatrix Symmetrical matrix to transform. matrix) Build the transformation to tridiagonal shape of a symmetrical matrix.

Method Summary

Modifier and Type	Method and Description
pack-priv double[][]	Returns: the main diagonal elements of the B matrix getHouseholderVectorsRef() Get the Householder vectors of the transform.
pack-priv double[]	Returns: the main diagonal elements of the T matrix getMainDiagonalRef() Get the main diagonal elements of the matrix T of the transform.
public RealMatrix	Returns: the Q matrix getQ() Returns the matrix Q of the transform.
public RealMatrix	Returns: the Q matrix getQT() Returns the transpose of the matrix Q of the transform.
pack-priv double[]	Returns: the secondary diagonal elements of the T matrix getSecondaryDiagonalRef() Get the secondary diagonal elements of the matrix T of the transform.
public RealMatrix	Returns: the T matrix getT() Returns the tridiagonal matrix T of the transform.
private void	transform() Transform original matrix to tridiagonal form.

Inherited from java.lang.Object:: clone equals finalize getClass hashCode notify notifyAll toString wait wait wait

Field Detail

cachedQ	back to summary
private RealMatrix cachedQ Cached value of Q.

cachedQt	back to summary
private RealMatrix cachedQt Cached value of Qt.

cachedT	back to summary
private RealMatrix cachedT Cached value of T.

householderVectors	back to summary
private final double[][] householderVectors Householder vectors.

main	back to summary
private final double[] main Main diagonal.

secondary	back to summary
private final double[] secondary Secondary diagonal.

Constructor Detail

TriDiagonalTransformer	back to summary
pack-priv TriDiagonalTransformer(RealMatrix matrix) Build the transformation to tridiagonal shape of a symmetrical matrix. The specified matrix is assumed to be symmetrical without any check. Only the upper triangular part of the matrix is used. Parameters matrix:RealMatrix Symmetrical matrix to transform. Exceptions NonSquareMatrixException: if the matrix is not square.

TriDiagonalTransformer

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pack-priv TriDiagonalTransformer(RealMatrix matrix)

Build the transformation to tridiagonal shape of a symmetrical matrix.

The specified matrix is assumed to be symmetrical without any check. Only the upper triangular part of the matrix is used.

Parameters

matrix:RealMatrix: Symmetrical matrix to transform.

Exceptions

NonSquareMatrixException:: if the matrix is not square.

Method Detail

getHouseholderVectorsRef	back to summary
pack-priv double[][] getHouseholderVectorsRef() Get the Householder vectors of the transform. Note that since this class is only intended for internal use, it returns directly a reference to its internal arrays, not a copy. Returns:double[][] the main diagonal elements of the B matrix

getHouseholderVectorsRef

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pack-priv double[][] getHouseholderVectorsRef()

Get the Householder vectors of the transform.

Note that since this class is only intended for internal use, it returns directly a reference to its internal arrays, not a copy.

Returns:double[][]: the main diagonal elements of the B matrix

getMainDiagonalRef	back to summary
pack-priv double[] getMainDiagonalRef() Get the main diagonal elements of the matrix T of the transform. Note that since this class is only intended for internal use, it returns directly a reference to its internal arrays, not a copy. Returns:double[] the main diagonal elements of the T matrix

getMainDiagonalRef

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pack-priv double[] getMainDiagonalRef()

Get the main diagonal elements of the matrix T of the transform.

Note that since this class is only intended for internal use, it returns directly a reference to its internal arrays, not a copy.

Returns:double[]: the main diagonal elements of the T matrix

getQ	back to summary
public RealMatrix getQ() Returns the matrix Q of the transform. Q is an orthogonal matrix, i.e. its transpose is also its inverse. Returns:RealMatrix the Q matrix

getQ

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public RealMatrix getQ()

Returns the matrix Q of the transform.

Q is an orthogonal matrix, i.e. its transpose is also its inverse.

Returns:RealMatrix: the Q matrix

getQT	back to summary
public RealMatrix getQT() Returns the transpose of the matrix Q of the transform. Q is an orthogonal matrix, i.e. its transpose is also its inverse. Returns:RealMatrix the Q matrix

getQT

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public RealMatrix getQT()

Returns the transpose of the matrix Q of the transform.

Q is an orthogonal matrix, i.e. its transpose is also its inverse.

Returns:RealMatrix: the Q matrix

getSecondaryDiagonalRef	back to summary
pack-priv double[] getSecondaryDiagonalRef() Get the secondary diagonal elements of the matrix T of the transform. Note that since this class is only intended for internal use, it returns directly a reference to its internal arrays, not a copy. Returns:double[] the secondary diagonal elements of the T matrix

getSecondaryDiagonalRef

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pack-priv double[] getSecondaryDiagonalRef()

Get the secondary diagonal elements of the matrix T of the transform.

Note that since this class is only intended for internal use, it returns directly a reference to its internal arrays, not a copy.