org.ojalgo.matrix.decomposition

Interface LU<N extends Comparable<N>>

All Superinterfaces:

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

public interface LU<N extends Comparable<N>>
extends LDU<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.

Author:

apete

Nested Class Summary

Nested Classes

Modifier and Type	Interface and Description
static interface	LU.Factory<N extends Comparable<N>>

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

MatrixDecomposition.Determinant<N extends Comparable<N>>, MatrixDecomposition.EconomySize<N extends Comparable<N>>, MatrixDecomposition.Hermitian<N extends Comparable<N>>, MatrixDecomposition.Ordered<N extends Comparable<N>>, MatrixDecomposition.Pivoting<N extends Comparable<N>>, MatrixDecomposition.RankRevealing<N extends Comparable<N>>, MatrixDecomposition.Solver<N extends Comparable<N>>, MatrixDecomposition.Values<N extends Comparable<N>>

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.RowColumnCallback, Structure2D.RowColumnKey<R,C>, Structure2D.RowColumnMapper<R,C>

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

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

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

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

Field Summary

Fields

Modifier and Type	Field and Description
static LU.Factory<ComplexNumber>	COMPLEX
static LU.Factory<Double>	PRIMITIVE
static LU.Factory<Quaternion>	QUATERNION
static LU.Factory<RationalNumber>	RATIONAL

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

TYPICAL

Method Summary

Modifier and Type	Method and Description
static <N extends Comparable<N>> boolean	equals(MatrixStore<N> matrix, LU<N> decomposition, NumberContext context)
MatrixStore<N>	getL()
MatrixStore<N>	getU() http://en.wikipedia.org/wiki/Row_echelon_form This is the same as [D][U].
default MatrixStore<N>	reconstruct()

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

isOrdered

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

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

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

preallocate, preallocate, solve, solve

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

invert, invert, preallocate, preallocate

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

getDeterminant, toDeterminantProvider

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

calculateDeterminant

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

countSignificant, getRank, getRankThreshold, isFullRank

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

decompose, isComputed, reset

Methods inherited from interface org.ojalgo.structure.Structure2D

column, column, column, column, column, count, count, countColumns, countRows, firstInColumn, firstInColumn, firstInColumn, firstInRow, firstInRow, firstInRow, getColDim, getMaxDim, getMinDim, getRowDim, index, isEmpty, isFat, isScalar, isSquare, isTall, isVector, limitOfColumn, limitOfColumn, limitOfColumn, limitOfRow, limitOfRow, limitOfRow, loopAll, loopColumn, loopColumn, loopDiagonal, loopMatching, loopRow, loopRow, mapperOf, row, row, row, row, row

Methods inherited from interface org.ojalgo.structure.Structure1D

index, loopAll, loopMatching, loopRange, mapper, size, toIntIndexes

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

decomposeWithoutPivoting, getPivotOrder, isPivoted

Field Detail

COMPLEX

static final LU.Factory<ComplexNumber> COMPLEX

PRIMITIVE

static final LU.Factory<Double> PRIMITIVE

QUATERNION

static final LU.Factory<Quaternion> QUATERNION

RATIONAL

static final LU.Factory<RationalNumber> RATIONAL

Method Detail

equals

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

getL

MatrixStore<N> getL()

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 Comparable<N>>