Module ojalgo

Package org.ojalgo.matrix.decomposition

Interface MatrixDecomposition<N extends java.lang.Comparable<N>>

All Superinterfaces:

Structure1D, Structure2D

All Known Subinterfaces:

Bidiagonal<N>, Cholesky<N>, Eigenvalue<N>, Eigenvalue.Generalised<N>, Eigenvalue.Spectral<N>, Hessenberg<N>, LDL<N>, LDU<N>, LU<N>, MatrixDecomposition.Determinant<N>, MatrixDecomposition.EconomySize<N>, MatrixDecomposition.Hermitian<N>, MatrixDecomposition.Ordered<N>, MatrixDecomposition.Pivoting<N>, MatrixDecomposition.RankRevealing<N>, MatrixDecomposition.Solver<N>, MatrixDecomposition.Updatable<N>, MatrixDecomposition.Values<N>, QR<N>, SingularValue<N>, Tridiagonal<N>

All Known Implementing Classes:

AbstractDecomposition, DeferredTridiagonal, DeferredTridiagonal.C128, DeferredTridiagonal.H256, DeferredTridiagonal.Q128, DeferredTridiagonal.R064, DeferredTridiagonal.R128, DenseBidiagonal, DenseBidiagonal.C128, DenseBidiagonal.H256, DenseBidiagonal.Q128, DenseBidiagonal.R064, DenseBidiagonal.R128, DenseCholesky, DenseCholesky.C128, DenseCholesky.H256, DenseCholesky.Q128, DenseCholesky.R064, DenseCholesky.R128, DenseEigenvalue, DenseHessenberg, DenseHessenberg.C128, DenseHessenberg.H256, DenseHessenberg.Q128, DenseHessenberg.R064, DenseHessenberg.R128, DenseLDL, DenseLDL.C128, DenseLDL.H256, DenseLDL.Q128, DenseLDL.R064, DenseLDL.R128, DenseLU, DenseLU.C128, DenseLU.H256, DenseLU.Q128, DenseLU.R064, DenseLU.R128, DenseQR, DenseQR.C128, DenseQR.H256, DenseQR.Q128, DenseQR.R064, DenseQR.R128, DenseSingularValue, DenseSingularValue.C128, DenseSingularValue.H256, DenseSingularValue.Q128, DenseSingularValue.R064, DenseSingularValue.R128, DenseTridiagonal, DynamicEvD, DynamicEvD.R064, GeneralEvD, GeneralEvD.R064, GeneralisedEvD, HermitianEvD, HermitianEvD.C128, HermitianEvD.H256, HermitianEvD.Q128, HermitianEvD.R064, HermitianEvD.R128, InPlaceDecomposition, RawCholesky, RawDecomposition, RawEigenvalue, RawEigenvalue.Dynamic, RawEigenvalue.General, RawEigenvalue.Symmetric, RawLU, RawQR, RawSingularValue, SimultaneousTridiagonal, SparseLU

public interface MatrixDecomposition<N extends java.lang.Comparable<N>>
extends Structure2D

Notation used to describe the various matrix decompositions:

• [A] could be any matrix. (The original matrix to decompose.)
• [A]^-1 is the inverse of [A].
• [A]^T is the transpose of [A].
• [A]^H is the conjugate transpose of [A]. [A]^H is equivalent to [A]^T if the elements are all real.
• [D] is a diagonal matrix. Possibly bi-, tri- or block-diagonal.
• [H] is an, upper or lower, Hessenberg matrix.
• [I] is an identity matrix - obviously orthogonal/unitary.
• [L] is a lower (left) triangular matrix.
• [P] is a permutation matrix - an identity matrix with interchanged rows or columns - and orthogonal/unitary.
• [Q] is an orthogonal/unitary matrix. [Q]^-1 = [Q]^H, and with real matrices = [Q] ^T.
• [R] is a right (upper) tringular matrix. It is equivalent to [U].
• [U] is an upper (right) triangular matrix. It is equivalent to [R]. Alternatively [U] is also used to denominate the left, orthonormal, singular vectors.
• [V] is an eigenvector matrix and/or an orthogonal matrix – the columns are the eigenvectors or the right, orthonormal, singular vectors.

Nested Class Summary

Nested Classes

Modifier and Type	Interface	Description
static interface	MatrixDecomposition.Determinant<N extends java.lang.Comparable<N>>
static interface	MatrixDecomposition.EconomySize<N extends java.lang.Comparable<N>>	Several matrix decompositions can be expressed "economy sized" - some rows or columns of the decomposed matrix parts are not needed for the most releveant use cases, and can therefore be left out.
static interface	MatrixDecomposition.Factory<D extends MatrixDecomposition<?>>
static interface	MatrixDecomposition.Hermitian<N extends java.lang.Comparable<N>>	Some matrix decompositions are only available with hermitian (symmetric) matrices or different decomposition algorithms could be used depending on if the matrix is hemitian or not.
static interface	MatrixDecomposition.Ordered<N extends java.lang.Comparable<N>>
static interface	MatrixDecomposition.Pivoting<N extends java.lang.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.
static interface	MatrixDecomposition.RankRevealing<N extends java.lang.Comparable<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.
static interface	MatrixDecomposition.Solver<N extends java.lang.Comparable<N>>
static interface	MatrixDecomposition.Updatable<N extends java.lang.Comparable<N>>
static interface	MatrixDecomposition.Values<N extends java.lang.Comparable<N>>	Eigenvalue and Singular Value decompositions can calculate the "values" only.

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

Modifier and Type	Field	Description
static Structure2D	TYPICAL

Method Summary

Modifier and Type	Method	Description
boolean	decompose(Access2D.Collectable<N,? super TransformableRegion<N>> matrix)
boolean	isComputed()
MatrixStore<N>	reconstruct()
void	reset()	Delete computed results, and resets attributes to default values

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

Field Detail

TYPICAL

static final Structure2D TYPICAL

Method Detail

decompose

boolean decompose(Access2D.Collectable<N,? super TransformableRegion<N>> matrix)

Parameters:

matrix - A matrix to decompose

Returns:

true if decomposition suceeded; false if not

isComputed

boolean isComputed()

Returns:

true if decomposition has been attemped and was successful; false if not.

See Also:

decompose(Access2D.Collectable)

reconstruct

MatrixStore<N> reconstruct()

reset

void reset()

Delete computed results, and resets attributes to default values