org.ojalgo.matrix.decomposition

## Interface MatrixDecomposition.Pivoting<N extends Number>

• All Superinterfaces:
MatrixDecomposition<N>, Structure1D, Structure2D
All Known Subinterfaces:
LDL<N>, LU<N>
Enclosing interface:
MatrixDecomposition<N extends Number>

```public static interface MatrixDecomposition.Pivoting<N extends Number>
extends MatrixDecomposition<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.

Author:
apete

• ### Nested classes/interfaces inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition

`MatrixDecomposition.Determinant<N extends Number>, MatrixDecomposition.EconomySize<N extends Number>, MatrixDecomposition.Factory<D extends MatrixDecomposition<?>>, MatrixDecomposition.Hermitian<N extends Number>, MatrixDecomposition.Ordered<N extends Number>, MatrixDecomposition.Pivoting<N extends Number>, MatrixDecomposition.RankRevealing<N extends Number>, MatrixDecomposition.Solver<N extends Number>, MatrixDecomposition.Values<N extends Number>`
• ### Nested classes/interfaces inherited from interface org.ojalgo.structure.Structure2D

`Structure2D.IntRowColumn, Structure2D.Logical<S extends Structure2D,B extends Structure2D.Logical<S,?>>, Structure2D.LongRowColumn, Structure2D.ReducibleTo1D<R extends Structure1D>, Structure2D.RowColumnCallback, Structure2D.RowColumnKey<R,C>, Structure2D.RowColumnMapper<R,C>`
• ### Nested classes/interfaces inherited from interface org.ojalgo.structure.Structure1D

`Structure1D.BasicMapper<T>, Structure1D.IndexCallback, Structure1D.IndexMapper<T>, Structure1D.IntIndex, Structure1D.LongIndex, Structure1D.LoopCallback`

• ### Fields inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition

`TYPICAL`
• ### Method Summary

All Methods
Modifier and Type Method and Description
`default boolean` `decomposeWithoutPivoting(Access2D.Collectable<N,? super PhysicalStore<N>> matrix)`
The normal `MatrixDecomposition.decompose(Access2D.Collectable)` method must handle cases where pivoting is necessary.
`int[]` `getPivotOrder()`
`boolean` `isPivoted()`
• ### Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition

`decompose, isComputed, reconstruct, reset`
• ### Methods inherited from interface org.ojalgo.structure.Structure2D

`column, column, column, column, column, count, count, countColumns, countRows, index, index, isEmpty, isFat, isScalar, isSquare, isTall, isVector, loopAll, loopColumn, loopColumn, loopDiagonal, loopMatching, loopRow, loopRow, mapperOf, row, row, row, row, row`
• ### Methods inherited from interface org.ojalgo.structure.Structure1D

`index, loopAll, loopMatching, loopRange, mapper, size`
• ### Method Detail

• #### getPivotOrder

`int[] getPivotOrder()`
Returns:
The pivot (row and/or columnn) order
• #### isPivoted

`boolean isPivoted()`
Returns:
true if any pivoting was actually done

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