org.ojalgo.matrix.decomposition

Interface MatrixDecomposition.RankRevealing<N extends Number>

All Superinterfaces:

MatrixDecomposition<N>, MatrixDecomposition.Ordered<N>, Structure1D, Structure2D

All Known Subinterfaces:

Cholesky<N>, LDL<N>, LDU<N>, LU<N>, QR<N>, SingularValue<N>

Enclosing interface:

MatrixDecomposition<N extends Number>

public static interface MatrixDecomposition.RankRevealing<N extends Number>
extends MatrixDecomposition.Ordered<N>

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.

Nested Class Summary

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

Field Summary

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

TYPICAL

Method Summary

Modifier and Type	Method and Description
int	countSignificant(double threshold)
default int	getRank() The best (and most expensive) way to get the effective numerical rank is by calculating a SingularValue decomposition and then find the number of nonnegligible singular values.
double	getRankThreshold()
default boolean	isFullRank()

Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition.Ordered

isOrdered

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

countSignificant

int countSignificant(double threshold)

Parameters:

threshold - Significance limit

Returns:

The number of elements in the diagonal matrix that are greater than the threshold

getRank

default int getRank()

The best (and most expensive) way to get the effective numerical rank is by calculating a SingularValue decomposition and then find the number of nonnegligible singular values.

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