Class QRDecomposition<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.QRDecomposition<N>
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- All Implemented Interfaces:
MatrixDecomposition<N>
,MatrixDecomposition.Determinant<N>
,MatrixDecomposition.EconomySize<N>
,MatrixDecomposition.Ordered<N>
,MatrixDecomposition.RankRevealing<N>
,MatrixDecomposition.Solver<N>
,QR<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:
QRDecomposition.C128
,QRDecomposition.H256
,QRDecomposition.Q128
,QRDecomposition.R064
,QRDecomposition.R128
abstract class QRDecomposition<N extends java.lang.Comparable<N>> extends InPlaceDecomposition<N> implements QR<N>
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Nested Class Summary
Nested Classes Modifier and Type Class Description (package private) static class
QRDecomposition.C128
(package private) static class
QRDecomposition.H256
(package private) static class
QRDecomposition.Q128
(package private) static class
QRDecomposition.R064
(package private) static class
QRDecomposition.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.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.matrix.decomposition.QR
QR.Factory<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 private boolean
myFullSize
private int
myNumberOfHouseholderTransformations
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Fields inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition
TYPICAL
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Constructor Summary
Constructors Modifier Constructor Description protected
QRDecomposition(PhysicalStore.Factory<N,? extends DecompositionStore<N>> factory, boolean fullSize)
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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)
N
getDeterminant()
A matrix' determinant is the product of its eigenvalues.MatrixStore<N>
getInverse(PhysicalStore<N> preallocated)
Implementing this method is optional.protected DecompositionStore<N>
getL()
MatrixStore<N>
getQ()
MatrixStore<N>
getR()
double
getRankThreshold()
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)
Solve [A]*[X]=[B] by first solving [Q]*[Y]=[B] and then [R]*[X]=[Y].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
isFullSize()
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)
.void
reset()
Delete computed results, and resets attributes to default valuesMatrixStore<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
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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.MatrixDecomposition
isComputed
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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.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.decomposition.QR
isOrdered, reconstruct
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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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Constructor Detail
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QRDecomposition
protected QRDecomposition(PhysicalStore.Factory<N,? extends DecompositionStore<N>> factory, boolean fullSize)
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Method Detail
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btran
public 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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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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getQ
public MatrixStore<N> getQ()
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getR
public MatrixStore<N> getR()
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getRankThreshold
public double getRankThreshold()
- Specified by:
getRankThreshold
in interfaceMatrixDecomposition.RankRevealing<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)
Solve [A]*[X]=[B] by first solving [Q]*[Y]=[B] and then [R]*[X]=[Y]. [X] minimises the 2-norm of [Q]*[R]*[X]-[B].- Specified by:
getSolution
in interfaceMatrixDecomposition.Solver<N extends java.lang.Comparable<N>>
- Parameters:
rhs
- The right hand side [B]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. UseSolverTask.preallocate(int, int, int)
orSolverTask.preallocate(Structure2D, Structure2D)
to get a suitable instance.- Returns:
- [X] "preallocated" is used to form the results, but the solution is in the returned MatrixStore.
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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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isFullSize
public boolean isFullSize()
- Specified by:
isFullSize
in interfaceMatrixDecomposition.EconomySize<N extends java.lang.Comparable<N>>
- Returns:
- True if it will generate a full sized decomposition.
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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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reset
public void reset()
Description copied from interface:MatrixDecomposition
Delete computed results, and resets attributes to default values- Specified by:
reset
in interfaceMatrixDecomposition<N extends java.lang.Comparable<N>>
- Overrides:
reset
in classAbstractDecomposition<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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checkSolvability
protected boolean checkSolvability()
- Overrides:
checkSolvability
in classAbstractDecomposition<N extends java.lang.Comparable<N>>
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getL
protected DecompositionStore<N> getL()
- Returns:
- L as in RT.
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