Module ojalgo

Package org.ojalgo.matrix.decomposition

Interface LDU<N extends java.lang.Comparable<N>>

All Superinterfaces:

DeterminantTask<N>, InverterTask<N>, InvertibleFactor<N>, MatrixDecomposition<N>, MatrixDecomposition.Determinant<N>, MatrixDecomposition.Ordered<N>, MatrixDecomposition.RankRevealing<N>, MatrixDecomposition.Solver<N>, MatrixTask<N>, Provider2D, Provider2D.Determinant<N>, Provider2D.Inverse<java.util.Optional<MatrixStore<N>>>, Provider2D.Rank, Provider2D.Solution<java.util.Optional<MatrixStore<N>>>, SolverTask<N>, Structure1D, Structure2D

All Known Subinterfaces:

Cholesky<N>, LDL<N>, LU<N>

All Known Implementing Classes:

DenseCholesky, DenseCholesky.C128, DenseCholesky.H256, DenseCholesky.Q128, DenseCholesky.R064, DenseCholesky.R128, DenseLDL, DenseLDL.C128, DenseLDL.H256, DenseLDL.Q128, DenseLDL.R064, DenseLDL.R128, DenseLU, DenseLU.C128, DenseLU.H256, DenseLU.Q128, DenseLU.R064, DenseLU.R128, RawCholesky, RawLU, SparseLU, SparseQDLDL

public interface LDU<N extends java.lang.Comparable<N>>
extends MatrixDecomposition.Solver<N>, MatrixDecomposition.Determinant<N>, MatrixDecomposition.RankRevealing<N>

LDU: [A] = [L][D][U] ( [P_L][L][D][U][P_U] )

• [A] can be any matrix.
• [L] is a unit lower (left) triangular matrix. It has the same number of rows as [A], and ones on the diagonal.
• [D] is a square diagonal matrix.
• [U] is a unit upper (right) triangular matrix. It has the same number of columns as [A], and ones on the diagonal.
• [P_L] is a permutation matrix (row pivot order).
• [P_U] is a permutation matrix (column pivot order).

Row and/or column permutations may not be necessary and are therefore optional. Numerical stability usually does require ordering of either the rows or columns (most algorithms reorder rows).

Solving the equation system [A][X]=[B] turns into this [L][D][U][X] = [B] and is solved in these steps:

1. [L][Z]=[B] ( [Z] = [D][U][X] )
2. [D][Y]=[Z] ( [Y] = [U][X] )
3. [U][X]=[Y]

[A]^H = [U]^H[D]^H[L]^H

ojAlgo does not have a full/general LDU decompositions but contains 3 variations of it:

• LU: [A] = [L][U] where [U_LU] = [D_LDU][U_LDU]
• Cholesky: [A] = [L][L]^H where [A] is hermitian positive definite and [L_Cholesky] = [L_LDU][D_LDU]^½
• LDL: [A] = [L][D][L]^H where [A] is hermitian and [L_LDL]^H = [U _LDU]

Nested Class Summary

Nested classes/interfaces inherited from interface org.ojalgo.matrix.task.DeterminantTask

DeterminantTask.Factory<N extends java.lang.Comparable<N>>

Nested classes/interfaces inherited from interface org.ojalgo.matrix.task.InverterTask

InverterTask.Factory<N extends java.lang.Comparable<N>>

Nested classes/interfaces inherited from interface org.ojalgo.matrix.transformation.InvertibleFactor

InvertibleFactor.IdentityFactor<N extends java.lang.Comparable<N>>

Nested classes/interfaces inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition

MatrixDecomposition.Determinant<N extends java.lang.Comparable<N>>, MatrixDecomposition.EconomySize<N extends java.lang.Comparable<N>>, MatrixDecomposition.Factory<D extends MatrixDecomposition<?>>, MatrixDecomposition.Hermitian<N extends java.lang.Comparable<N>>, MatrixDecomposition.Ordered<N extends java.lang.Comparable<N>>, MatrixDecomposition.Pivoting<N extends java.lang.Comparable<N>>, MatrixDecomposition.RankRevealing<N extends java.lang.Comparable<N>>, MatrixDecomposition.Solver<N extends java.lang.Comparable<N>>, MatrixDecomposition.Updatable<N extends java.lang.Comparable<N>>, MatrixDecomposition.Values<N extends java.lang.Comparable<N>>

Nested classes/interfaces inherited from interface org.ojalgo.matrix.Provider2D

Provider2D.Condition, Provider2D.Determinant<N extends java.lang.Comparable<N>>, Provider2D.Eigenpairs, Provider2D.Hermitian, Provider2D.Inverse<M>, Provider2D.Rank, Provider2D.Solution<M>, Provider2D.Symmetric, Provider2D.Trace<N extends java.lang.Comparable<N>>

Nested classes/interfaces inherited from interface org.ojalgo.matrix.task.SolverTask

SolverTask.Factory<N extends java.lang.Comparable<N>>

Nested classes/interfaces inherited from interface org.ojalgo.structure.Structure1D

Structure1D.BasicMapper<T>, Structure1D.IndexMapper<T>, Structure1D.IntIndex, Structure1D.LongIndex, Structure1D.LoopCallback

Nested classes/interfaces inherited from interface org.ojalgo.structure.Structure2D

Structure2D.IntRowColumn, Structure2D.Logical<S extends Structure2D,B extends Structure2D.Logical<S,B>>, Structure2D.LongRowColumn, Structure2D.ReducibleTo1D<R extends Structure1D>, Structure2D.Reshapable, Structure2D.RowColumnKey<R,C>, Structure2D.RowColumnMapper<R,C>

Field Summary

Fields inherited from interface org.ojalgo.matrix.task.DeterminantTask

C128, H256, Q128, R064, R128

Fields inherited from interface org.ojalgo.matrix.task.InverterTask

C128, H256, Q128, R064, R128

Fields inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition

TYPICAL

Fields inherited from interface org.ojalgo.matrix.task.SolverTask

C128, H256, Q128, R064, R128

Method Summary

Modifier and Type	Method	Description
default boolean	isOrdered()	This is a property of the algorithm/implementation, not the data.

Methods inherited from interface org.ojalgo.matrix.task.DeterminantTask

calculateDeterminant

Methods inherited from interface org.ojalgo.matrix.task.InverterTask

invert, invert, preallocate

Methods inherited from interface org.ojalgo.matrix.transformation.InvertibleFactor

btran, btran, ftran, ftran

Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition

decompose, isComputed, reconstruct, reset

Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition.Determinant

getDeterminant, toDeterminantProvider

Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition.RankRevealing

countSignificant, getRank, getRankThreshold, isFullRank

Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition.Solver

compute, getInverse, getInverse, getSolution, getSolution, invert, isSolvable, preallocate, solve, toInverseProvider, toSolutionProvider

Methods inherited from interface org.ojalgo.matrix.task.SolverTask

preallocate, preallocate, solve, solve

Methods inherited from interface org.ojalgo.structure.Structure2D

count, countColumns, countRows, firstInColumn, firstInRow, getColDim, getMaxDim, getMinDim, getRowDim, isEmpty, isFat, isScalar, isSquare, isTall, isVector, limitOfColumn, limitOfRow, size

Method Detail

isOrdered

default boolean isOrdered()

Description copied from interface: MatrixDecomposition.Ordered

This is a property of the algorithm/implementation, not the data. Typically relevant for SingularValue, Eigenvalue or any MatrixDecomposition.RankRevealing decomposition.

Specified by:

isOrdered in interface MatrixDecomposition.Ordered<N extends java.lang.Comparable<N>>

Returns:

true if the rows/columns of the returned matrix factors are guaranteed some specific order; false if there is no such guarantee.