Package org.ojalgo.matrix.decomposition
Interface MatrixDecomposition.RankRevealing<N extends Comparable<N>>
- All Superinterfaces:
MatrixDecomposition<N>
,MatrixDecomposition.Ordered<N>
,Provider2D
,Provider2D.Rank
,Structure1D
,Structure2D
- All Known Implementing Classes:
CholeskyDecomposition
,CholeskyDecomposition.C128
,CholeskyDecomposition.H256
,CholeskyDecomposition.Q128
,CholeskyDecomposition.R064
,CholeskyDecomposition.R128
,LDLDecomposition
,LDLDecomposition.C128
,LDLDecomposition.H256
,LDLDecomposition.Q128
,LDLDecomposition.R064
,LDLDecomposition.R128
,LUDecomposition
,LUDecomposition.C128
,LUDecomposition.H256
,LUDecomposition.Q128
,LUDecomposition.R064
,LUDecomposition.R128
,QRDecomposition
,QRDecomposition.C128
,QRDecomposition.H256
,QRDecomposition.Q128
,QRDecomposition.R064
,QRDecomposition.R128
,RawCholesky
,RawLU
,RawQR
,RawSingularValue
,SingularValueDecomposition
,SingularValueDecomposition.C128
,SingularValueDecomposition.H256
,SingularValueDecomposition.Q128
,SingularValueDecomposition.R064
,SingularValueDecomposition.R128
- Enclosing interface:
MatrixDecomposition<N extends Comparable<N>>
public static interface MatrixDecomposition.RankRevealing<N extends Comparable<N>>
extends MatrixDecomposition.Ordered<N>, Provider2D.Rank
A rank-revealing matrix decomposition of a matrix [A] is a decomposition that is, or can be transformed
to be, on the form [A]=[X][D][Y]T where:
- [X] and [Y] are square and well conditioned.
- [D] is diagonal with nonnegative and non-increasing values on the diagonal.
The defintion that [X] and [Y] should be well conditioned is subject to interpretation. A specific
decomposition algorithm can be more or less good at revealing the rank. Typically the
SingularValue
decomposition is the best.
The requirement to have the diagonal elements of [D] ordered can be very practical, but is not always
strictly necessary in order to just reveal the rank. The method MatrixDecomposition.Ordered.isOrdered()
indicates if the
elements (rows and columns) of the returned matrix factors actually are ordered or not for this
particular implementation.
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Nested Class Summary
Nested classes/interfaces inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition
MatrixDecomposition.Determinant<N extends Comparable<N>>, MatrixDecomposition.EconomySize<N extends Comparable<N>>, MatrixDecomposition.Factory<D extends MatrixDecomposition<?>>, 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.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>>
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 inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition
TYPICAL
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Method Summary
Modifier and TypeMethodDescriptionint
countSignificant
(double threshold) default int
getRank()
The best (and most expensive) way to get the effective numerical rank is by calculating aSingularValue
decomposition and then find the number of nonnegligible singular values.double
default boolean
Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition
decompose, isComputed, reconstruct, reset
Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition.Ordered
isOrdered
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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Method Details
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countSignificant
int countSignificant(double threshold) - Parameters:
threshold
- Significance limit- Returns:
- The number of elements in the diagonal matrix that are greater than the threshold
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getRank
default int getRank()The best (and most expensive) way to get the effective numerical rank is by calculating aSingularValue
decomposition and then find the number of nonnegligible singular values.- Specified by:
getRank
in interfaceProvider2D.Rank
- Returns:
- The effective numerical rank (best estimate)
-
getRankThreshold
double getRankThreshold() -
isFullRank
default boolean isFullRank()- Returns:
- true if the rank is equal to the minimum of the row and column dimensions; false if not
-