Calculates the Cholesky decomposition of a matrix.

The Cholesky decomposition of a real symmetric positive-definite matrix A consists of a lower triangular matrix L with same size such that: A = LL^T. In a sense, this is the square root of A.

This class is based on the class with similar name from the JAMA library, with the following changes:

a getLT method has been added,
the isspd method has been removed, since the constructor of this class throws a NonPositiveDefiniteMatrixException when a matrix cannot be decomposed,
a getDeterminant method has been added,
the solve method has been replaced by a getSolver method and the equivalent method provided by the returned DecompositionSolver.

Nested and Inner Type Summary

Modifier and Type	Class and Description
private static class	CholeskyDecomposition.Solver Specialized solver.

Field Summary

Modifier and Type	Field and Description
private RealMatrix	cachedL Cached value of L.
private RealMatrix	cachedLT Cached value of LT.
public static final double	DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD Default threshold below which diagonal elements are considered null and matrix not positive definite.
public static final double	DEFAULT_RELATIVE_SYMMETRY_THRESHOLD Default threshold above which off-diagonal elements are considered too different and matrix not symmetric.
private double[][]	lTData Row-oriented storage for L^T matrix data.

Access	Constructor and Description
public	CholeskyDecomposition(final RealMatrix the matrix to decompose matrix) Calculates the Cholesky decomposition of the given matrix.
public	CholeskyDecomposition(final RealMatrix the matrix to decompose matrix, final double threshold above which off-diagonal elements are considered too different and matrix not symmetric relativeSymmetryThreshold, final double threshold below which diagonal elements are considered null and matrix not positive definite absolutePositivityThreshold) Calculates the Cholesky decomposition of the given matrix.

Method Summary

Modifier and Type	Method and Description
public double	Returns: determinant of the matrix getDeterminant() Return the determinant of the matrix
public RealMatrix	Returns: the L matrix getL() Returns the matrix L of the decomposition.
public RealMatrix	Returns: the transpose of the matrix L of the decomposition getLT() Returns the transpose of the matrix L of the decomposition.
public DecompositionSolver	Returns: a solver getSolver() Get a solver for finding the A × X = B solution in least square sense.

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

Field Detail

cachedL	back to summary
private RealMatrix cachedL Cached value of L.

cachedLT	back to summary
private RealMatrix cachedLT Cached value of LT.

DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD	back to summary
public static final double DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD Default threshold below which diagonal elements are considered null and matrix not positive definite.

DEFAULT_RELATIVE_SYMMETRY_THRESHOLD	back to summary
public static final double DEFAULT_RELATIVE_SYMMETRY_THRESHOLD Default threshold above which off-diagonal elements are considered too different and matrix not symmetric.

lTData	back to summary
private double[][] lTData Row-oriented storage for L^T matrix data.

Constructor Detail

CholeskyDecomposition back to summary

CholeskyDecomposition	back to summary
public CholeskyDecomposition(final RealMatrix matrix) Calculates the Cholesky decomposition of the given matrix. Calling this constructor is equivalent to call `CholeskyDecomposition(RealMatrix, double, double)` with the thresholds set to the default values `DEFAULT_RELATIVE_SYMMETRY_THRESHOLD` and `DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD` Parameters matrix:RealMatrix the matrix to decompose Exceptions NonSquareMatrixException: if the matrix is not square. NonSymmetricMatrixException: if the matrix is not symmetric. NonPositiveDefiniteMatrixException: if the matrix is not strictly positive definite. See Also `CholeskyDecomposition(RealMatrix, double, double)`, `DEFAULT_RELATIVE_SYMMETRY_THRESHOLD`, `DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD`

public CholeskyDecomposition(final RealMatrix matrix)

Calculates the Cholesky decomposition of the given matrix.

Calling this constructor is equivalent to call CholeskyDecomposition(RealMatrix, double, double) with the thresholds set to the default values DEFAULT_RELATIVE_SYMMETRY_THRESHOLD and DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD

Parameters

matrix:RealMatrix: the matrix to decompose

Exceptions

NonSquareMatrixException:: if the matrix is not square.
NonSymmetricMatrixException:: if the matrix is not symmetric.
NonPositiveDefiniteMatrixException:: if the matrix is not strictly positive definite.

CholeskyDecomposition back to summary

CholeskyDecomposition	back to summary
public CholeskyDecomposition(final RealMatrix matrix, final double relativeSymmetryThreshold, final double absolutePositivityThreshold) Calculates the Cholesky decomposition of the given matrix. Parameters matrix:RealMatrix the matrix to decompose relativeSymmetryThreshold:double threshold above which off-diagonal elements are considered too different and matrix not symmetric absolutePositivityThreshold:double threshold below which diagonal elements are considered null and matrix not positive definite Exceptions NonSquareMatrixException: if the matrix is not square. NonSymmetricMatrixException: if the matrix is not symmetric. NonPositiveDefiniteMatrixException: if the matrix is not strictly positive definite. See Also `CholeskyDecomposition(RealMatrix)`, `DEFAULT_RELATIVE_SYMMETRY_THRESHOLD`, `DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD`

public CholeskyDecomposition(final RealMatrix matrix, final double relativeSymmetryThreshold, final double absolutePositivityThreshold)

Calculates the Cholesky decomposition of the given matrix.

Parameters

matrix:RealMatrix: the matrix to decompose
relativeSymmetryThreshold:double: threshold above which off-diagonal elements are considered too different and matrix not symmetric
absolutePositivityThreshold:double: threshold below which diagonal elements are considered null and matrix not positive definite

Exceptions

NonSquareMatrixException:: if the matrix is not square.
NonSymmetricMatrixException:: if the matrix is not symmetric.
NonPositiveDefiniteMatrixException:: if the matrix is not strictly positive definite.

Method Detail

getDeterminant	back to summary
public double getDeterminant() Return the determinant of the matrix Returns:double determinant of the matrix

getDeterminant

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public double getDeterminant()

Return the determinant of the matrix

Returns:double: determinant of the matrix

getL	back to summary
public RealMatrix getL() Returns the matrix L of the decomposition. L is an lower-triangular matrix Returns:RealMatrix the L matrix

getL

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public RealMatrix getL()

Returns the matrix L of the decomposition.

L is an lower-triangular matrix

Returns:RealMatrix: the L matrix

getLT	back to summary
public RealMatrix getLT() Returns the transpose of the matrix L of the decomposition. L^T is an upper-triangular matrix Returns:RealMatrix the transpose of the matrix L of the decomposition

getLT

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public RealMatrix getLT()

Returns the transpose of the matrix L of the decomposition.

L^T is an upper-triangular matrix

Returns:RealMatrix: the transpose of the matrix L of the decomposition

getSolver	back to summary
public DecompositionSolver getSolver() Get a solver for finding the A × X = B solution in least square sense. Returns:DecompositionSolver a solver

getSolver

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public DecompositionSolver getSolver()

Get a solver for finding the A × X = B solution in least square sense.

Returns:DecompositionSolver: a solver

org.apache.commons.math3.linear back to summary

private Class CholeskyDecomposition.Solver

Class Inheritance

extends Object
implements DecompositionSolver

java.lang.Object
org.apache.commons.math3.linear.CholeskyDecomposition.Solver

All Implemented Interfaces

org.apache.commons.math3.linear.DecompositionSolver

Specialized solver.

Field Summary

Modifier and Type	Field and Description
private final double[][]	lTData Row-oriented storage for L^T matrix data.

Constructor Summary

Access	Constructor and Description
private	Solver(final double[][] row-oriented storage for L^T matrix data lTData) Build a solver from decomposed matrix.

Method Summary

Modifier and Type	Method and Description
public RealMatrix	Returns: the inverse matrix. getInverse() Implements org.apache.commons.math3.linear.DecompositionSolver.getInverse. Get the inverse of the decomposed matrix.
public boolean	isNonSingular() Implements org.apache.commons.math3.linear.DecompositionSolver.isNonSingular. Check if the decomposed matrix is non-singular.
public RealVector	solve(final RealVector right-hand side of the equation A × X = B b) Implements org.apache.commons.math3.linear.DecompositionSolver.solve. Solve the linear equation A × X = B for matrices A.
public RealMatrix	solve(RealMatrix right-hand side of the equation A × X = B b) Implements org.apache.commons.math3.linear.DecompositionSolver.solve. Solve the linear equation A × X = B for matrices A.

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

Field Detail

lTData	back to summary
private final double[][] lTData Row-oriented storage for L^T matrix data.

Constructor Detail

Solver	back to summary
private Solver(final double[][] lTData) Build a solver from decomposed matrix. Parameters lTData:double[][] row-oriented storage for L^T matrix data

Solver

back to summary

private Solver(final double[][] lTData)

Build a solver from decomposed matrix.

Parameters

lTData:double[][]: row-oriented storage for L^T matrix data

Method Detail

getInverse	back to summary
public RealMatrix getInverse() Implements org.apache.commons.math3.linear.DecompositionSolver.getInverse. Get the inverse of the decomposed matrix. Returns:RealMatrix the inverse matrix.

getInverse

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public RealMatrix getInverse()

Implements org.apache.commons.math3.linear.DecompositionSolver.getInverse.

Get the inverse of the decomposed matrix.

Returns:RealMatrix: the inverse matrix.

isNonSingular	back to summary
public boolean isNonSingular() Implements org.apache.commons.math3.linear.DecompositionSolver.isNonSingular. Doc from org.apache.commons.math3.linear.DecompositionSolver.isNonSingular. Check if the decomposed matrix is non-singular. Returns:boolean true if the decomposed matrix is non-singular.

isNonSingular

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public boolean isNonSingular()

Implements org.apache.commons.math3.linear.DecompositionSolver.isNonSingular.

Doc from org.apache.commons.math3.linear.DecompositionSolver.isNonSingular.

Check if the decomposed matrix is non-singular.

Returns:boolean: true if the decomposed matrix is non-singular.

solve	back to summary
public RealVector solve(final RealVector b) Implements org.apache.commons.math3.linear.DecompositionSolver.solve. Doc from org.apache.commons.math3.linear.DecompositionSolver.solve. Solve the linear equation A × X = B for matrices A. The A matrix is implicit, it is provided by the underlying decomposition algorithm. Parameters b:RealVector right-hand side of the equation A × X = B Returns:RealVector a vector X that minimizes the two norm of A × X - B

solve

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public RealVector solve(final RealVector b)

Implements org.apache.commons.math3.linear.DecompositionSolver.solve.

Doc from org.apache.commons.math3.linear.DecompositionSolver.solve.

Solve the linear equation A × X = B for matrices A.

The A matrix is implicit, it is provided by the underlying decomposition algorithm.

Parameters

b:RealVector: right-hand side of the equation A × X = B

Returns:RealVector

a vector X that minimizes the two norm of A × X - B

solve	back to summary
public RealMatrix solve(RealMatrix b) Implements org.apache.commons.math3.linear.DecompositionSolver.solve. Doc from org.apache.commons.math3.linear.DecompositionSolver.solve. Solve the linear equation A × X = B for matrices A. The A matrix is implicit, it is provided by the underlying decomposition algorithm. Parameters b:RealMatrix right-hand side of the equation A × X = B Returns:RealMatrix a matrix X that minimizes the two norm of A × X - B

solve

back to summary

public RealMatrix solve(RealMatrix b)

Implements org.apache.commons.math3.linear.DecompositionSolver.solve.

Doc from org.apache.commons.math3.linear.DecompositionSolver.solve.

Solve the linear equation A × X = B for matrices A.

The A matrix is implicit, it is provided by the underlying decomposition algorithm.

Parameters

b:RealMatrix: right-hand side of the equation A × X = B

Returns:RealMatrix

a matrix X that minimizes the two norm of A × X - B

public Class CholeskyDecomposition

Nested and Inner Type Summary

Field Summary

Constructor Summary

Method Summary

Field Detail

Constructor Detail

Method Detail

private Class CholeskyDecomposition.Solver

Field Summary

Constructor Summary

Method Summary

Field Detail

Constructor Detail

Method Detail