Module ojalgo

Package org.ojalgo.matrix.decomposition

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

All Superinterfaces:

DeterminantTask<N>, InverterTask<N>, InvertibleFactor<N>, LDU<N>, MatrixDecomposition<N>, MatrixDecomposition.Determinant<N>, MatrixDecomposition.Ordered<N>, MatrixDecomposition.Pivoting<N>, MatrixDecomposition.RankRevealing<N>, MatrixDecomposition.Solver<N>, MatrixDecomposition.Updatable<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 Implementing Classes:

DenseLU, DenseLU.C128, DenseLU.H256, DenseLU.Q128, DenseLU.R064, DenseLU.R128, RawLU, SparseLU

public interface LU<N extends java.lang.Comparable<N>>
extends LDU<N>, MatrixDecomposition.Updatable<N>, MatrixDecomposition.Pivoting<N>

LU: [A] = [L][U]

Decomposes [this] into [L] and [U] (with pivot order information in an int[]) where:

• [L] is a unit lower (left) triangular matrix. It has the same number of rows as [this], and ones on the diagonal.
• [U] is an upper (right) triangular matrix. It has the same number of columns as [this].
• [this] = [L][U] (with reordered rows according to the pivot order)

Note: The number of columns in [L] and the number of rows in [U] is not specified by this interface.

The LU decomposition always exists - the compute method should always succeed - even for non-square and/or singular matrices. The primary use of the LU decomposition is in the solution of systems of simultaneous linear equations. That will, however, only work for square non-singular matrices.

Nested Class Summary

Nested Classes

Modifier and Type	Interface	Description
static interface	LU.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.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.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

Modifier and Type	Field	Description
static LU.Factory<ComplexNumber>	C128
static LU.Factory<Quaternion>	H256
static LU.Factory<RationalNumber>	Q128
static LU.Factory<java.lang.Double>	R064
static LU.Factory<Quadruple>	R128

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

TYPICAL

Method Summary

Modifier and Type	Method	Description
static <N extends java.lang.Comparable<N>> boolean	equals(MatrixStore<N> matrix, LU<N> decomposition, NumberContext context)
MatrixStore<N>	getL()
default MatrixStore<N>	getSolution(Access2D.Collectable<N,? super PhysicalStore<N>> rhs)	[A][X]=[B] or [this][return]=[rhs]
MatrixStore<N>	getU()	http://en.wikipedia.org/wiki/Row_echelon_form This is the same as [D][U].
static LU<java.lang.Double>	newSparseR064()
default MatrixStore<N>	reconstruct()

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.LDU

isOrdered

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

decompose, isComputed, reset

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

getDeterminant, toDeterminantProvider

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

decomposeWithoutPivoting, getPivotOrder, getReversePivotOrder, isPivoted

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, invert, isSolvable, preallocate, solve, toInverseProvider, toSolutionProvider

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

updateColumn

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

Field Detail

C128

static final LU.Factory<ComplexNumber> C128

H256

static final LU.Factory<Quaternion> H256

Q128

static final LU.Factory<RationalNumber> Q128

R064

static final LU.Factory<java.lang.Double> R064

R128

static final LU.Factory<Quadruple> R128

Method Detail

newSparseR064

static LU<java.lang.Double> newSparseR064()

equals

static <N extends java.lang.Comparable<N>> boolean equals(MatrixStore<N> matrix,
                                                          LU<N> decomposition,
                                                          NumberContext context)

getL

MatrixStore<N> getL()

getSolution

default MatrixStore<N> getSolution(Access2D.Collectable<N,? super PhysicalStore<N>> rhs)

Description copied from interface: MatrixDecomposition.Solver

[A][X]=[B] or [this][return]=[rhs]

Specified by:

getSolution in interface MatrixDecomposition.Solver<N extends java.lang.Comparable<N>>

getU

MatrixStore<N> getU()

http://en.wikipedia.org/wiki/Row_echelon_form

This is the same as [D][U]. Together with the pivotOrder and [L] this constitutes an alternative, more compact, way to express the decomposition.

See Also:

MatrixDecomposition.Pivoting.getPivotOrder(), getL()

reconstruct

default MatrixStore<N> reconstruct()

Specified by:

reconstruct in interface MatrixDecomposition<N extends java.lang.Comparable<N>>