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org.apache.commons.math3.linear

pack-priv Class BiDiagonalTransformer

Class Inheritance

extends Object

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

Imports

org.apache.commons.math3.util.FastMath

Class transforming any matrix to bi-diagonal shape.

Any m × n matrix A can be written as the product of three matrices: A = U × B × V^T with U an m × m orthogonal matrix, B an m × n bi-diagonal matrix (lower diagonal if m < n, upper diagonal otherwise), and V an n × n orthogonal matrix.

Transformation to bi-diagonal shape is often not a goal by itself, but it is an intermediate step in more general decomposition algorithms like Singular Value 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	cachedB Cached value of B.
private RealMatrix	cachedU Cached value of U.
private RealMatrix	cachedV Cached value of V.
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	BiDiagonalTransformer(RealMatrix the matrix to transform. matrix) Build the transformation to bi-diagonal shape of a matrix.

Method Summary

Modifier and Type	Method and Description
public RealMatrix	Returns: the B matrix getB() Returns the bi-diagonal matrix B of the transform.
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 B matrix getMainDiagonalRef() Get the main diagonal elements of the matrix B of the transform.
pack-priv double[]	Returns: the secondary diagonal elements of the B matrix getSecondaryDiagonalRef() Get the secondary diagonal elements of the matrix B of the transform.
public RealMatrix	Returns: the U matrix getU() Returns the matrix U of the transform.
public RealMatrix	Returns: the V matrix getV() Returns the matrix V of the transform.
pack-priv boolean	Returns: true if the matrix is transformed to upper bi-diagonal isUpperBiDiagonal() Check if the matrix is transformed to upper bi-diagonal.
private void	transformToLowerBiDiagonal() Transform original matrix to lower bi-diagonal form.
private void	transformToUpperBiDiagonal() Transform original matrix to upper bi-diagonal form.

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

Field Detail

cachedB	back to summary
private RealMatrix cachedB Cached value of B.

cachedU	back to summary
private RealMatrix cachedU Cached value of U.

cachedV	back to summary
private RealMatrix cachedV Cached value of V.

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

BiDiagonalTransformer	back to summary
pack-priv BiDiagonalTransformer(RealMatrix matrix) Build the transformation to bi-diagonal shape of a matrix. Parameters matrix:RealMatrix the matrix to transform.

BiDiagonalTransformer

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pack-priv BiDiagonalTransformer(RealMatrix matrix)

Build the transformation to bi-diagonal shape of a matrix.

Parameters

matrix:RealMatrix: the matrix to transform.

Method Detail

getB	back to summary
public RealMatrix getB() Returns the bi-diagonal matrix B of the transform. Returns:RealMatrix the B matrix

getB

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public RealMatrix getB()

Returns the bi-diagonal matrix B of the transform.

Returns:RealMatrix: the B matrix

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 B 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

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pack-priv double[] getMainDiagonalRef()

Get the main diagonal elements of the matrix B 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

getSecondaryDiagonalRef	back to summary
pack-priv double[] getSecondaryDiagonalRef() Get the secondary diagonal elements of the matrix B 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 B matrix

getSecondaryDiagonalRef

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pack-priv double[] getSecondaryDiagonalRef()

Get the secondary diagonal elements of the matrix B 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 B matrix

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

getU

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public RealMatrix getU()

Returns the matrix U of the transform.

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

Returns:RealMatrix: the U matrix

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

getV

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public RealMatrix getV()

Returns the matrix V of the transform.

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

Returns:RealMatrix: the V matrix

isUpperBiDiagonal	back to summary
pack-priv boolean isUpperBiDiagonal() Check if the matrix is transformed to upper bi-diagonal. Returns:boolean true if the matrix is transformed to upper bi-diagonal

isUpperBiDiagonal

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pack-priv boolean isUpperBiDiagonal()

Check if the matrix is transformed to upper bi-diagonal.

Returns:boolean: true if the matrix is transformed to upper bi-diagonal

transformToLowerBiDiagonal	back to summary
private void transformToLowerBiDiagonal() Transform original matrix to lower bi-diagonal form. Transformation is done using alternate Householder transforms on rows and columns.

transformToLowerBiDiagonal

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private void transformToLowerBiDiagonal()

Transform original matrix to lower bi-diagonal form.

Transformation is done using alternate Householder transforms on rows and columns.

transformToUpperBiDiagonal	back to summary
private void transformToUpperBiDiagonal() Transform original matrix to upper bi-diagonal form. Transformation is done using alternate Householder transforms on columns and rows.

transformToUpperBiDiagonal

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private void transformToUpperBiDiagonal()

Transform original matrix to upper bi-diagonal form.

Transformation is done using alternate Householder transforms on columns and rows.