Package org.ojalgo.matrix.decomposition
Interface LU<N extends java.lang.Comparable<N>>
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- 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>
,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:
LUDecomposition
,LUDecomposition.C128
,LUDecomposition.H256
,LUDecomposition.Q128
,LUDecomposition.R064
,LUDecomposition.R128
,RawLU
public interface LU<N extends java.lang.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.
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Nested Class Summary
Nested Classes Modifier and Type Interface Description static interface
LU.Factory<N extends java.lang.Comparable<N>>
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Nested classes/interfaces inherited from interface org.ojalgo.matrix.transformation.InvertibleFactor
InvertibleFactor.IdentityFactor<N extends java.lang.Comparable<N>>
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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.Values<N extends java.lang.Comparable<N>>
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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>>
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Nested classes/interfaces inherited from interface org.ojalgo.structure.Structure1D
Structure1D.BasicMapper<T>, Structure1D.IndexMapper<T>, Structure1D.IntIndex, Structure1D.LongIndex, Structure1D.LoopCallback
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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>
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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
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Fields inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition
TYPICAL
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Method Summary
All Methods Static Methods Instance Methods Abstract Methods Default Methods Modifier and Type Method Description static <N extends java.lang.Comparable<N>>
booleanequals(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()
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Methods inherited from interface org.ojalgo.matrix.task.DeterminantTask
calculateDeterminant
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Methods inherited from interface org.ojalgo.matrix.task.InverterTask
invert, invert, preallocate, preallocate
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Methods inherited from interface org.ojalgo.matrix.transformation.InvertibleFactor
btran, btran
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Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition
decompose, isComputed, reset
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Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition.Determinant
getDeterminant, toDeterminantProvider
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Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition.Pivoting
decomposeWithoutPivoting, getPivotOrder, getReversePivotOrder, isPivoted
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Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition.RankRevealing
countSignificant, getRank, getRankThreshold, isFullRank
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Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition.Solver
compute, ftran, ftran, getInverse, getInverse, getSolution, getSolution, invert, isSolvable, solve, toInverseProvider, toSolutionProvider
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Methods inherited from interface org.ojalgo.matrix.task.SolverTask
preallocate, preallocate, solve, solve
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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
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Field Detail
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C128
static final LU.Factory<ComplexNumber> C128
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H256
static final LU.Factory<Quaternion> H256
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Q128
static final LU.Factory<RationalNumber> Q128
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R064
static final LU.Factory<java.lang.Double> R064
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R128
static final LU.Factory<Quadruple> R128
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Method Detail
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equals
static <N extends java.lang.Comparable<N>> boolean equals(MatrixStore<N> matrix, LU<N> decomposition, NumberContext context)
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getL
MatrixStore<N> getL()
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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.
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reconstruct
default MatrixStore<N> reconstruct()
- Specified by:
reconstruct
in interfaceMatrixDecomposition<N extends java.lang.Comparable<N>>
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