Interface MatrixDecomposition.Pivoting<N extends Comparable<N>>

All Superinterfaces:
MatrixDecomposition<N>, Structure1D, Structure2D
All Known Subinterfaces:
LDL<N>, LU<N>
All Known Implementing Classes:
DenseLDL, DenseLDL.C128, DenseLDL.H256, DenseLDL.Q128, DenseLDL.R064, DenseLDL.R128, DenseLU, DenseLU.C128, DenseLU.H256, DenseLU.Q128, DenseLU.R064, DenseLU.R128, RawLU, SparseLU, SparseQDLDL
Enclosing interface:
MatrixDecomposition<N extends Comparable<N>>
public static interface MatrixDecomposition.Pivoting<N extends Comparable<N>> 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.

  • Method Details

    • decomposeWithoutPivoting

      default boolean decomposeWithoutPivoting(Access2D.Collectable<N, ? super TransformableRegion<N>> matrix)
      The normal MatrixDecomposition.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 calls MatrixDecomposition.decompose(Access2D.Collectable).

    • getPivotOrder

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

    • getReversePivotOrder

      int[] getReversePivotOrder()

    • isPivoted

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