Calculates the LUP-decomposition of a square matrix.

The LUP-decomposition of a matrix A consists of three matrices L, U and P that satisfy: P×A = L×U. L is lower triangular (with unit diagonal terms), U is upper triangular and P is a permutation matrix. All matrices are m×m.

As shown by the presence of the P matrix, this decomposition is implemented using partial pivoting.

This class is based on the class with similar name from the JAMA library.

a getP method has been added,
the det method has been renamed as getDeterminant,
the getDoublePivot method has been removed (but the int based getPivot method has been kept),
the solve and isNonSingular methods have been replaced by a getSolver method and the equivalent methods provided by the returned DecompositionSolver.

Nested and Inner Type Summary

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

Field Summary

Modifier and Type	Field and Description
private RealMatrix	cachedL Cached value of L.
private RealMatrix	cachedP Cached value of P.
private RealMatrix	cachedU Cached value of U.
private static final double	DEFAULT_TOO_SMALL Default bound to determine effective singularity in LU decomposition.
private boolean	even Parity of the permutation associated with the LU decomposition.
private final double[][]	lu Entries of LU decomposition.
private final int[]	pivot Pivot permutation associated with LU decomposition.
private boolean	singular Singularity indicator.

Access	Constructor and Description
public	LUDecomposition(RealMatrix Matrix to decompose. matrix) Calculates the LU-decomposition of the given matrix.
public	LUDecomposition(RealMatrix The matrix to decompose. matrix, double threshold (based on partial row norm) under which a matrix is considered singular singularityThreshold) Calculates the LU-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 (or null if decomposed matrix is singular) getL() Returns the matrix L of the decomposition.
public RealMatrix	Returns: the P rows permutation matrix (or null if decomposed matrix is singular) getP() Returns the P rows permutation matrix.
public int[]	Returns: the pivot permutation vector getPivot() Returns the pivot permutation vector.
public DecompositionSolver	Returns: a solver getSolver() Get a solver for finding the A × X = B solution in exact linear sense.
public RealMatrix	Returns: the U matrix (or null if decomposed matrix is singular) getU() Returns the matrix U of the decomposition.

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.

cachedP	back to summary
private RealMatrix cachedP Cached value of P.

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

DEFAULT_TOO_SMALL	back to summary
private static final double DEFAULT_TOO_SMALL Default bound to determine effective singularity in LU decomposition.

even	back to summary
private boolean even Parity of the permutation associated with the LU decomposition.

lu	back to summary
private final double[][] lu Entries of LU decomposition.

pivot	back to summary
private final int[] pivot Pivot permutation associated with LU decomposition.

singular	back to summary
private boolean singular Singularity indicator.

LUDecomposition	back to summary
public LUDecomposition(RealMatrix matrix) Calculates the LU-decomposition of the given matrix. This constructor uses 1e-11 as default value for the singularity threshold. Parameters matrix:RealMatrix Matrix to decompose. Exceptions NonSquareMatrixException: if matrix is not square.

LUDecomposition	back to summary
public LUDecomposition(RealMatrix matrix, double singularityThreshold) Calculates the LU-decomposition of the given matrix. Parameters matrix:RealMatrix The matrix to decompose. singularityThreshold:double threshold (based on partial row norm) under which a matrix is considered singular Exceptions NonSquareMatrixException: if matrix is not square

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 a lower-triangular matrix Returns:RealMatrix the L matrix (or null if decomposed matrix is singular)

getL

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public RealMatrix getL()

Returns the matrix L of the decomposition.

L is a lower-triangular matrix

Returns:RealMatrix: the L matrix (or null if decomposed matrix is singular)

getP back to summary

getP	back to summary
public RealMatrix getP() Returns the P rows permutation matrix. P is a sparse matrix with exactly one element set to 1.0 in each row and each column, all other elements being set to 0.0. The positions of the 1 elements are given by the `pivot permutation vector`. Returns:RealMatrix the P rows permutation matrix (or null if decomposed matrix is singular) See Also `getPivot()`

public RealMatrix getP()

Returns the P rows permutation matrix.

P is a sparse matrix with exactly one element set to 1.0 in each row and each column, all other elements being set to 0.0.

The positions of the 1 elements are given by the pivot permutation vector.

Returns:RealMatrix: the P rows permutation matrix (or null if decomposed matrix is singular)
See Also: getPivot()

getPivot back to summary

getPivot	back to summary
public int[] getPivot() Returns the pivot permutation vector. Returns:int[] the pivot permutation vector See Also `getP()`

public int[] getPivot()

Returns the pivot permutation vector.

Returns:int[]: the pivot permutation vector
See Also: getP()

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

getSolver

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public DecompositionSolver getSolver()

Get a solver for finding the A × X = B solution in exact linear sense.

Returns:DecompositionSolver: a solver

getU	back to summary
public RealMatrix getU() Returns the matrix U of the decomposition. U is an upper-triangular matrix Returns:RealMatrix the U matrix (or null if decomposed matrix is singular)

getU

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public RealMatrix getU()

Returns the matrix U of the decomposition.

U is an upper-triangular matrix

Returns:RealMatrix: the U matrix (or null if decomposed matrix is singular)

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

private Class LUDecomposition.Solver

Class Inheritance

extends Object
implements DecompositionSolver

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

All Implemented Interfaces

org.apache.commons.math3.linear.DecompositionSolver

Specialized solver.

Field Summary

Modifier and Type	Field and Description
private final double[][]	lu Entries of LU decomposition.
private final int[]	pivot Pivot permutation associated with LU decomposition.
private final boolean	singular Singularity indicator.

Constructor Summary

Access	Constructor and Description
private	Solver(final double[][] entries of LU decomposition lu, final int[] pivot permutation associated with LU decomposition pivot, final boolean singularity indicator singular) 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(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

lu	back to summary
private final double[][] lu Entries of LU decomposition.

pivot	back to summary
private final int[] pivot Pivot permutation associated with LU decomposition.

singular	back to summary
private final boolean singular Singularity indicator.

Constructor Detail

Solver	back to summary
private Solver(final double[][] lu, final int[] pivot, final boolean singular) Build a solver from decomposed matrix. Parameters lu:double[][] entries of LU decomposition pivot:int[] pivot permutation associated with LU decomposition singular:boolean singularity indicator

Solver

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private Solver(final double[][] lu, final int[] pivot, final boolean singular)

Build a solver from decomposed matrix.

Parameters

lu:double[][]: entries of LU decomposition
pivot:int[]: pivot permutation associated with LU decomposition
singular:boolean: singularity indicator

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. Exceptions SingularMatrixException: if the decomposed matrix is singular.

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.

Exceptions

SingularMatrixException:: if the decomposed matrix is singular.

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(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(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

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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 LUDecomposition

Nested and Inner Type Summary

Field Summary

Constructor Summary

Method Summary

Field Detail

Constructor Detail

Method Detail

private Class LUDecomposition.Solver

Field Summary

Constructor Summary

Method Summary

Field Detail

Constructor Detail

Method Detail