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: PA = LU, L is lower triangular, and U is upper triangular and P is a permutation matrix. All matrices are m×m.

Since field elements do not provide an ordering operator, the permutation matrix is computed here only in order to avoid a zero pivot element, no attempt is done to get the largest pivot element.

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the solve and isNonSingular methods have been replaced by a getSolver method and the equivalent methods provided by the returned DecompositionSolver.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	FieldLUDecomposition.Solver< the type of the field elements T extends FieldElement<T>> Specialized solver.

Field Summary

Modifier and Type	Field and Description
private FieldMatrix<T>	cachedL Cached value of L.
private FieldMatrix<T>	cachedP Cached value of P.
private FieldMatrix<T>	cachedU Cached value of U.
private boolean	even Parity of the permutation associated with the LU decomposition.
private final Field<T>	field Field to which the elements belong.
private T[][]	lu Entries of LU decomposition.
private int[]	pivot Pivot permutation associated with LU decomposition.
private boolean	singular Singularity indicator.

Access	Constructor and Description
public	FieldLUDecomposition(FieldMatrix<T> The matrix to decompose. matrix) Calculates the LU-decomposition of the given matrix.

Method Summary

Modifier and Type	Method and Description
public T	Returns: determinant of the matrix getDeterminant() Return the determinant of the matrix.
public FieldMatrix<T>	Returns: the L matrix (or null if decomposed matrix is singular) getL() Returns the matrix L of the decomposition.
public FieldMatrix<T>	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 FieldDecompositionSolver<T>	Returns: a solver getSolver() Get a solver for finding the A × X = B solution in exact linear sense.
public FieldMatrix<T>	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 FieldMatrix<T> cachedL Cached value of L.

cachedP	back to summary
private FieldMatrix<T> cachedP Cached value of P.

cachedU	back to summary
private FieldMatrix<T> cachedU Cached value of U.

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

field	back to summary
private final Field<T> field Field to which the elements belong.

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

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

singular	back to summary
private boolean singular Singularity indicator.

FieldLUDecomposition	back to summary
public FieldLUDecomposition(FieldMatrix<T> matrix) Calculates the LU-decomposition of the given matrix. Parameters matrix:FieldMatrix<T> The matrix to decompose. Exceptions NonSquareMatrixException: if matrix is not square

Method Detail

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

getDeterminant

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public T getDeterminant()

Return the determinant of the matrix.

Returns:T: determinant of the matrix

getL	back to summary
public FieldMatrix<T> getL() Returns the matrix L of the decomposition. L is a lower-triangular matrix Returns:FieldMatrix<T> the L matrix (or null if decomposed matrix is singular)

getL

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public FieldMatrix<T> getL()

Returns the matrix L of the decomposition.

L is a lower-triangular matrix

Returns:FieldMatrix<T>: the L matrix (or null if decomposed matrix is singular)

getP back to summary

getP	back to summary
public FieldMatrix<T> 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:FieldMatrix<T> the P rows permutation matrix (or null if decomposed matrix is singular) See Also `getPivot()`

public FieldMatrix<T> 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:FieldMatrix<T>: 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 FieldDecompositionSolver<T> getSolver() Get a solver for finding the A × X = B solution in exact linear sense. Returns:FieldDecompositionSolver<T> a solver

getSolver

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public FieldDecompositionSolver<T> getSolver()

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

Returns:FieldDecompositionSolver<T>: a solver

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

getU

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public FieldMatrix<T> getU()

Returns the matrix U of the decomposition.

U is an upper-triangular matrix

Returns:FieldMatrix<T>: the U matrix (or null if decomposed matrix is singular)

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

private Class FieldLUDecomposition.Solver<T extends FieldElement<T>>

Class Inheritance

extends Object
implements FieldDecompositionSolver<T extends FieldElement<T>>

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

All Implemented Interfaces

org.apache.commons.math3.linear.FieldDecompositionSolver

Type Parameters

<T>: the type of the field elements

Specialized solver.

Field Summary

Modifier and Type	Field and Description
private final Field<T>	field Field to which the elements belong.
private final T[][]	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 Field<T> field to which the matrix elements belong field, final T[][] 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 FieldMatrix<T>	getInverse() Implements org.apache.commons.math3.linear.FieldDecompositionSolver.getInverse. Get the inverse (or pseudo-inverse) of the decomposed matrix.
public boolean	isNonSingular() Implements org.apache.commons.math3.linear.FieldDecompositionSolver.isNonSingular. Check if the decomposed matrix is non-singular.
public FieldVector<T>	solve(FieldVector<T> right-hand side of the equation A × X = B b) Implements org.apache.commons.math3.linear.FieldDecompositionSolver.solve. Solve the linear equation A × X = B for matrices A.
public ArrayFieldVector<T>	Returns: a vector X such that A × X = B solve(ArrayFieldVector<T> right-hand side of the equation A × X = B b) Solve the linear equation A × X = B.
public FieldMatrix<T>	solve(FieldMatrix<T> right-hand side of the equation A × X = B b) Implements org.apache.commons.math3.linear.FieldDecompositionSolver.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

field	back to summary
private final Field<T> field Field to which the elements belong.

lu	back to summary
private final T[][] 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 Field<T> field, final T[][] lu, final int[] pivot, final boolean singular) Build a solver from decomposed matrix. Parameters field:Field<T> field to which the matrix elements belong lu:T[][] entries of LU decomposition pivot:int[] pivot permutation associated with LU decomposition singular:boolean singularity indicator

Solver

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private Solver(final Field<T> field, final T[][] lu, final int[] pivot, final boolean singular)

Build a solver from decomposed matrix.

Parameters

field:Field<T>: field to which the matrix elements belong
lu:T[][]: entries of LU decomposition
pivot:int[]: pivot permutation associated with LU decomposition
singular:boolean: singularity indicator

Method Detail

getInverse	back to summary
public FieldMatrix<T> getInverse() Implements org.apache.commons.math3.linear.FieldDecompositionSolver.getInverse. Doc from org.apache.commons.math3.linear.FieldDecompositionSolver.getInverse. Get the inverse (or pseudo-inverse) of the decomposed matrix. Returns:FieldMatrix<T> inverse matrix

getInverse

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public FieldMatrix<T> getInverse()

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

Doc from org.apache.commons.math3.linear.FieldDecompositionSolver.getInverse.

Get the inverse (or pseudo-inverse) of the decomposed matrix.

Returns:FieldMatrix<T>: inverse matrix

isNonSingular	back to summary
public boolean isNonSingular() Implements org.apache.commons.math3.linear.FieldDecompositionSolver.isNonSingular. Doc from org.apache.commons.math3.linear.FieldDecompositionSolver.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.FieldDecompositionSolver.isNonSingular.

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

Check if the decomposed matrix is non-singular.

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

solve	back to summary
public FieldVector<T> solve(FieldVector<T> b) Implements org.apache.commons.math3.linear.FieldDecompositionSolver.solve. Doc from org.apache.commons.math3.linear.FieldDecompositionSolver.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:FieldVector<T> right-hand side of the equation A × X = B Returns:FieldVector<T> a vector X that minimizes the two norm of A × X - B

solve

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public FieldVector<T> solve(FieldVector<T> b)

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

Doc from org.apache.commons.math3.linear.FieldDecompositionSolver.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:FieldVector<T>: right-hand side of the equation A × X = B

Returns:FieldVector<T>

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

solve	back to summary
public ArrayFieldVector<T> solve(ArrayFieldVector<T> b) Solve the linear equation A × X = B. The A matrix is implicit here. It is Parameters b:ArrayFieldVector<T> right-hand side of the equation A × X = B Returns:ArrayFieldVector<T> a vector X such that A × X = B Exceptions DimensionMismatchException: if the matrices dimensions do not match. SingularMatrixException: if the decomposed matrix is singular.

solve

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public ArrayFieldVector<T> solve(ArrayFieldVector<T> b)

Solve the linear equation A × X = B.

The A matrix is implicit here. It is

Parameters

b:ArrayFieldVector<T>: right-hand side of the equation A × X = B

Returns:ArrayFieldVector<T>

a vector X such that A × X = B

Exceptions

DimensionMismatchException:: if the matrices dimensions do not match.
SingularMatrixException:: if the decomposed matrix is singular.

solve	back to summary
public FieldMatrix<T> solve(FieldMatrix<T> b) Implements org.apache.commons.math3.linear.FieldDecompositionSolver.solve. Doc from org.apache.commons.math3.linear.FieldDecompositionSolver.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:FieldMatrix<T> right-hand side of the equation A × X = B Returns:FieldMatrix<T> a matrix X that minimizes the two norm of A × X - B

solve

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public FieldMatrix<T> solve(FieldMatrix<T> b)

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

Doc from org.apache.commons.math3.linear.FieldDecompositionSolver.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:FieldMatrix<T>: right-hand side of the equation A × X = B

Returns:FieldMatrix<T>

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

public Class FieldLUDecomposition<T extends FieldElement<T>>

Nested and Inner Type Summary

Field Summary

Constructor Summary

Method Summary

Field Detail

Constructor Detail

Method Detail

private Class FieldLUDecomposition.Solver<T extends FieldElement<T>>

Field Summary

Constructor Summary

Method Summary

Field Detail

Constructor Detail

Method Detail