Interface MatrixDecomposition.Pivoting<N extends Comparable<N>>
- All Superinterfaces:
MatrixDecomposition<N>
,Structure1D
,Structure2D
- All Known Implementing Classes:
LDLDecomposition
,LDLDecomposition.C128
,LDLDecomposition.H256
,LDLDecomposition.Q128
,LDLDecomposition.R064
,LDLDecomposition.R128
,LUDecomposition
,LUDecomposition.C128
,LUDecomposition.H256
,LUDecomposition.Q128
,LUDecomposition.R064
,LUDecomposition.R128
,RawLU
- Enclosing interface:
MatrixDecomposition<N extends Comparable<N>>
The pivot or pivot element is the element of a matrix, or an array, which is selected first by an algorithm (e.g. Gaussian elimination, simplex algorithm, etc.), to do certain calculations. In the case of matrix algorithms, a pivot entry is usually required to be at least distinct from zero, and often distant from it; in this case finding this element is called pivoting. Pivoting may be followed by an interchange of rows or columns to bring the pivot to a fixed position and allow the algorithm to proceed successfully, and possibly to reduce round-off error. It is often used for verifying row echelon form.
Pivoting might be thought of as swapping or sorting rows or columns in a matrix, and thus it can be represented as multiplication by permutation matrices. However, algorithms rarely move the matrix elements because this would cost too much time; instead, they just keep track of the permutations.
Overall, pivoting adds more operations to the computational cost of an algorithm. These additional operations are sometimes necessary for the algorithm to work at all. Other times these additional operations are worthwhile because they add numerical stability to the final result.
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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.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 TypeMethodDescriptiondefault boolean
decomposeWithoutPivoting
(Access2D.Collectable<N, ? super PhysicalStore<N>> matrix) The normalMatrixDecomposition.decompose(Access2D.Collectable)
method must handle cases where pivoting is necessary.int[]
int[]
boolean
Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition
decompose, isComputed, reconstruct, reset
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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decomposeWithoutPivoting
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)
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getPivotOrder
int[] getPivotOrder()- Returns:
- The pivot (row and/or columnn) order
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getReversePivotOrder
int[] getReversePivotOrder() -
isPivoted
boolean isPivoted()- Returns:
- true if any pivoting was actually done
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