Class LDLDecomposition<N extends java.lang.Comparable<N>>
- java.lang.Object
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- org.ojalgo.matrix.decomposition.AbstractDecomposition<N>
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- org.ojalgo.matrix.decomposition.GenericDecomposition<N>
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- org.ojalgo.matrix.decomposition.InPlaceDecomposition<N>
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- org.ojalgo.matrix.decomposition.LDLDecomposition<N>
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- All Implemented Interfaces:
LDL<N>
,LDU<N>
,MatrixDecomposition<N>
,MatrixDecomposition.Determinant<N>
,MatrixDecomposition.Hermitian<N>
,MatrixDecomposition.Ordered<N>
,MatrixDecomposition.Pivoting<N>
,MatrixDecomposition.RankRevealing<N>
,MatrixDecomposition.Solver<N>
,Provider2D
,Provider2D.Determinant<N>
,Provider2D.Inverse<java.util.Optional<MatrixStore<N>>>
,Provider2D.Rank
,Provider2D.Solution<java.util.Optional<MatrixStore<N>>>
,DeterminantTask<N>
,InverterTask<N>
,MatrixTask<N>
,SolverTask<N>
,InvertibleFactor<N>
,Structure1D
,Structure2D
- Direct Known Subclasses:
LDLDecomposition.C128
,LDLDecomposition.H256
,LDLDecomposition.Q128
,LDLDecomposition.R064
,LDLDecomposition.R128
abstract class LDLDecomposition<N extends java.lang.Comparable<N>> extends InPlaceDecomposition<N> implements LDL<N>
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Nested Class Summary
Nested Classes Modifier and Type Class Description (package private) static class
LDLDecomposition.C128
(package private) static class
LDLDecomposition.H256
(package private) static class
LDLDecomposition.Q128
(package private) static class
LDLDecomposition.R064
(package private) static class
LDLDecomposition.R128
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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.LDL
LDL.Factory<N extends java.lang.Comparable<N>>, LDL.ModifiedFactory<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.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.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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Constructor Summary
Constructors Modifier Constructor Description protected
LDLDecomposition(PhysicalStore.Factory<N,? extends DecompositionStore<N>> factory)
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description void
btran(PhysicalStore<N> arg)
Backwards-transformationN
calculateDeterminant(Access2D<?> matrix)
protected boolean
checkSolvability()
int
countSignificant(double threshold)
boolean
decompose(Access2D.Collectable<N,? super PhysicalStore<N>> matrix)
boolean
decomposeWithoutPivoting(Access2D.Collectable<N,? super PhysicalStore<N>> matrix)
The normalMatrixDecomposition.decompose(Access2D.Collectable)
method must handle cases where pivoting is necessary.private boolean
doDecompose(Access2D.Collectable<N,? super PhysicalStore<N>> matrix, boolean pivoting)
MatrixStore<N>
getD()
N
getDeterminant()
A matrix' determinant is the product of its eigenvalues.MatrixStore<N>
getInverse(PhysicalStore<N> preallocated)
Implementing this method is optional.MatrixStore<N>
getL()
Must implement eitherLDL.getL()
orLDL.getR()
.int[]
getPivotOrder()
double
getRankThreshold()
int[]
getReversePivotOrder()
MatrixStore<N>
getSolution(Access2D.Collectable<N,? super PhysicalStore<N>> rhs)
[A][X]=[B] or [this][return]=[rhs]MatrixStore<N>
getSolution(Access2D.Collectable<N,? super PhysicalStore<N>> rhs, PhysicalStore<N> preallocated)
Implementing this method is optional.MatrixStore<N>
invert(Access2D<?> original)
The output must be a "right inverse" and a "generalised inverse".MatrixStore<N>
invert(Access2D<?> original, PhysicalStore<N> preallocated)
Exactly how (if at all) a specific implementation makes use ofpreallocated
is not specified by this interface.boolean
isPivoted()
boolean
isSolvable()
Please note that producing a pseudoinverse and/or a least squares solution is ok! The return value, of this method, is not an indication of if the decomposed matrix is square, has full rank, is postive definite or whatever.PhysicalStore<N>
preallocate(Structure2D template)
Will create a PhysicalStore instance suitable for use withInverterTask.invert(Access2D, PhysicalStore)
.PhysicalStore<N>
preallocate(Structure2D templateBody, Structure2D templateRHS)
Will create a PhysicalStore instance suitable for use withSolverTask.solve(Access2D, Access2D, PhysicalStore)
.(package private) void
setThreshold(N threshold)
MatrixStore<N>
solve(Access2D<?> body, Access2D<?> rhs)
[A][X]=[B] or [body][return]=[rhs]MatrixStore<N>
solve(Access2D<?> body, Access2D<?> rhs, PhysicalStore<N> preallocated)
Exactly how (if at all) a specific implementation makes use ofpreallocated
is not specified by this interface.-
Methods inherited from class org.ojalgo.matrix.decomposition.InPlaceDecomposition
getColDim, getInPlace, getInverse, getRowDim, setInPlace
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Methods inherited from class org.ojalgo.matrix.decomposition.GenericDecomposition
aggregator, allocate, collect, copy, function, makeArray, makeDiagonal, makeEye, makeHouseholder, makeIdentity, makeRotation, makeRotation, makeZero, makeZero, scalar, wrap
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Methods inherited from class org.ojalgo.matrix.decomposition.AbstractDecomposition
computed, countColumns, countRows, getDimensionalEpsilon, isAspectRatioNormal, isComputed, reset
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Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
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Methods inherited from interface org.ojalgo.matrix.task.InverterTask
preallocate
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Methods inherited from interface org.ojalgo.matrix.transformation.InvertibleFactor
btran
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Methods inherited from interface org.ojalgo.matrix.decomposition.LDL
getR, reconstruct
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Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition
isComputed, reset
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Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition.Determinant
toDeterminantProvider
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Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition.Hermitian
checkAndDecompose
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Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition.RankRevealing
getRank, isFullRank
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Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition.Solver
compute, ftran, ftran, getInverse, invert, solve, toInverseProvider, toSolutionProvider
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Methods inherited from interface org.ojalgo.matrix.task.SolverTask
preallocate
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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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myPivot
private final Pivot myPivot
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myThreshold
private double myThreshold
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Constructor Detail
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LDLDecomposition
protected LDLDecomposition(PhysicalStore.Factory<N,? extends DecompositionStore<N>> factory)
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Method Detail
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btran
public final void btran(PhysicalStore<N> arg)
Description copied from interface:InvertibleFactor
Backwards-transformationSolve [x]T[A] = [b]T (equivalent to [A]T[x] = [b]) by transforming [b] into [x] in-place.
- Specified by:
btran
in interfaceInvertibleFactor<N extends java.lang.Comparable<N>>
- Parameters:
arg
- [b] transformed into [x]
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calculateDeterminant
public N calculateDeterminant(Access2D<?> matrix)
- Specified by:
calculateDeterminant
in interfaceDeterminantTask<N extends java.lang.Comparable<N>>
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countSignificant
public int countSignificant(double threshold)
- Specified by:
countSignificant
in interfaceMatrixDecomposition.RankRevealing<N extends java.lang.Comparable<N>>
- Parameters:
threshold
- Significance limit- Returns:
- The number of elements in the diagonal matrix that are greater than the threshold
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decompose
public boolean decompose(Access2D.Collectable<N,? super PhysicalStore<N>> matrix)
- Specified by:
decompose
in interfaceMatrixDecomposition<N extends java.lang.Comparable<N>>
- Parameters:
matrix
- A matrix to decompose- Returns:
- true if decomposition suceeded; false if not
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decomposeWithoutPivoting
public boolean decomposeWithoutPivoting(Access2D.Collectable<N,? super PhysicalStore<N>> matrix)
Description copied from interface:MatrixDecomposition.Pivoting
The normalMatrixDecomposition.decompose(Access2D.Collectable)
method must handle cases where pivoting is necessary. If you know that pivoting is not needed you may call this method instead - it may be faster. Implementing this method, to actually decompose without pivoting, is optional. The default implementation simply callsMatrixDecomposition.decompose(Access2D.Collectable)
.- Specified by:
decomposeWithoutPivoting
in interfaceMatrixDecomposition.Pivoting<N extends java.lang.Comparable<N>>
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getD
public MatrixStore<N> getD()
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getDeterminant
public N getDeterminant()
Description copied from interface:MatrixDecomposition.Determinant
A matrix' determinant is the product of its eigenvalues.
- Specified by:
getDeterminant
in interfaceMatrixDecomposition.Determinant<N extends java.lang.Comparable<N>>
- Specified by:
getDeterminant
in interfaceProvider2D.Determinant<N extends java.lang.Comparable<N>>
- Returns:
- The matrix' determinant
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getInverse
public MatrixStore<N> getInverse(PhysicalStore<N> preallocated)
Description copied from interface:MatrixDecomposition.Solver
Implementing this method is optional.
Exactly how a specific implementation makes use of
preallocated
is not specified by this interface. It must be documented for each implementation.Should produce the same results as calling
MatrixDecomposition.Solver.getInverse()
.- Specified by:
getInverse
in interfaceMatrixDecomposition.Solver<N extends java.lang.Comparable<N>>
- Overrides:
getInverse
in classInPlaceDecomposition<N extends java.lang.Comparable<N>>
- Parameters:
preallocated
- Preallocated memory for the results, possibly some intermediate results. You must assume this is modified, but you cannot assume it will contain the full/final/correct solution. UseInverterTask.preallocate(int, int)
orInverterTask.preallocate(Structure2D)
to get a suitable instance.- Returns:
- The inverse, this is where you get the solution
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getL
public MatrixStore<N> getL()
Description copied from interface:LDL
Must implement eitherLDL.getL()
orLDL.getR()
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getPivotOrder
public int[] getPivotOrder()
- Specified by:
getPivotOrder
in interfaceMatrixDecomposition.Pivoting<N extends java.lang.Comparable<N>>
- Returns:
- The pivot (row and/or columnn) order
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getRankThreshold
public double getRankThreshold()
- Specified by:
getRankThreshold
in interfaceMatrixDecomposition.RankRevealing<N extends java.lang.Comparable<N>>
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getReversePivotOrder
public int[] getReversePivotOrder()
- Specified by:
getReversePivotOrder
in interfaceMatrixDecomposition.Pivoting<N extends java.lang.Comparable<N>>
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getSolution
public 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 interfaceMatrixDecomposition.Solver<N extends java.lang.Comparable<N>>
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getSolution
public MatrixStore<N> getSolution(Access2D.Collectable<N,? super PhysicalStore<N>> rhs, PhysicalStore<N> preallocated)
Description copied from interface:MatrixDecomposition.Solver
Implementing this method is optional.
Exactly how a specific implementation makes use of
preallocated
is not specified by this interface. It must be documented for each implementation.Should produce the same results as calling
MatrixDecomposition.Solver.getSolution(Collectable)
.- Specified by:
getSolution
in interfaceMatrixDecomposition.Solver<N extends java.lang.Comparable<N>>
- Parameters:
rhs
- The Right Hand Side, wont be modfiedpreallocated
- Preallocated memory for the results, possibly some intermediate results. You must assume this is modified, but you cannot assume it will contain the full/final/correct solution. UseSolverTask.preallocate(int, int, int)
orSolverTask.preallocate(Structure2D, Structure2D)
to get a suitable instance.- Returns:
- The solution
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invert
public MatrixStore<N> invert(Access2D<?> original) throws RecoverableCondition
Description copied from interface:InverterTask
The output must be a "right inverse" and a "generalised inverse".- Specified by:
invert
in interfaceInverterTask<N extends java.lang.Comparable<N>>
- Throws:
RecoverableCondition
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invert
public MatrixStore<N> invert(Access2D<?> original, PhysicalStore<N> preallocated) throws RecoverableCondition
Description copied from interface:InverterTask
Exactly how (if at all) a specific implementation makes use of
preallocated
is not specified by this interface. It must be documented for each implementation.Should produce the same results as calling
InverterTask.invert(Access2D)
.Use
InverterTask.preallocate(Structure2D)
to obtain a suitbalepreallocated
.- Specified by:
invert
in interfaceInverterTask<N extends java.lang.Comparable<N>>
preallocated
- Preallocated memory for the results, possibly some intermediate results. You must assume this is modified, but you cannot assume it will contain the full/ /correct solution.- Returns:
- The inverse
- Throws:
RecoverableCondition
- TODO
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isPivoted
public boolean isPivoted()
- Specified by:
isPivoted
in interfaceMatrixDecomposition.Pivoting<N extends java.lang.Comparable<N>>
- Returns:
- true if any pivoting was actually done
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isSolvable
public boolean isSolvable()
Description copied from interface:MatrixDecomposition.Solver
Please note that producing a pseudoinverse and/or a least squares solution is ok! The return value, of this method, is not an indication of if the decomposed matrix is square, has full rank, is postive definite or whatever. It's that in combination with the specific decomposition algorithm's capabilities.- Specified by:
isSolvable
in interfaceMatrixDecomposition.Solver<N extends java.lang.Comparable<N>>
- Overrides:
isSolvable
in classAbstractDecomposition<N extends java.lang.Comparable<N>>
- Returns:
- true if this matrix decomposition is in a state to be able to deliver an inverse or an equation system solution (with some degree of numerical stability).
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preallocate
public PhysicalStore<N> preallocate(Structure2D template)
Description copied from interface:InverterTask
Will create a PhysicalStore instance suitable for use with
InverterTask.invert(Access2D, PhysicalStore)
.When inverting a matrix (mxn) the preallocated memory/matrix will typically be nxm (and of course most of the time A is square).
- Specified by:
preallocate
in interfaceInverterTask<N extends java.lang.Comparable<N>>
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preallocate
public PhysicalStore<N> preallocate(Structure2D templateBody, Structure2D templateRHS)
Description copied from interface:SolverTask
Will create a PhysicalStore instance suitable for use with
SolverTask.solve(Access2D, Access2D, PhysicalStore)
. The dimensions of the returned instance is not specified by this interface - it is specified by the behaviour/requirements of each implementation.When solving an equation system [A][X]=[B] ([mxn][nxb]=[mxb]) the preallocated memory/matrix will typically be either mxb or nxb.
- Specified by:
preallocate
in interfaceSolverTask<N extends java.lang.Comparable<N>>
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solve
public MatrixStore<N> solve(Access2D<?> body, Access2D<?> rhs) throws RecoverableCondition
Description copied from interface:SolverTask
[A][X]=[B] or [body][return]=[rhs]- Specified by:
solve
in interfaceSolverTask<N extends java.lang.Comparable<N>>
- Throws:
RecoverableCondition
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solve
public MatrixStore<N> solve(Access2D<?> body, Access2D<?> rhs, PhysicalStore<N> preallocated) throws RecoverableCondition
Description copied from interface:SolverTask
Exactly how (if at all) a specific implementation makes use of
preallocated
is not specified by this interface. It must be documented for each implementation.Should produce the same results as calling
SolverTask.solve(Access2D, Access2D)
.Use
SolverTask.preallocate(Structure2D, Structure2D)
to obtain a suitbalepreallocated
.- Specified by:
solve
in interfaceSolverTask<N extends java.lang.Comparable<N>>
rhs
- The Right Hand Side, wont be modfiedpreallocated
- Preallocated memory for the results, possibly some intermediate results. You must assume this is modified, but you cannot assume it will contain the full/ /correct solution.- Returns:
- The solution
- Throws:
RecoverableCondition
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doDecompose
private boolean doDecompose(Access2D.Collectable<N,? super PhysicalStore<N>> matrix, boolean pivoting)
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checkSolvability
protected boolean checkSolvability()
- Overrides:
checkSolvability
in classAbstractDecomposition<N extends java.lang.Comparable<N>>
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setThreshold
void setThreshold(N threshold)
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