Package org.ojalgo.matrix.decomposition

Interface Summary

Interface	Description
Bidiagonal<N extends Number>	A general matrix [A] can be factorized by similarity transformations into the form [A]=[Q1][D][Q2] -1 where: [A] (m-by-n) is any, real or complex, matrix [D] (r-by-r) or (m-by-n) is, upper or lower, bidiagonal [Q1] (m-by-r) or (m-by-m) is orthogonal [Q2] (n-by-r) or (n-by-n) is orthogonal r = min(m,n)
Bidiagonal.Factory<N extends Number>
Cholesky<N extends Number>	Cholesky: [A] = [L][L]H (or [R]H[R])
Cholesky.Factory<N extends Number>
DecompositionStore<N extends Number>	Only classes that will act as a delegate to a MatrixDecomposition implementation from this package should implement this interface.
Eigenvalue<N extends Number>	[A] = [V][D][V]-1 ([A][V] = [V][D]) [A] = any square matrix. [V] = contains the eigenvectors as columns. [D] = a diagonal matrix with the eigenvalues on the diagonal (possibly in blocks).
Eigenvalue.Factory<N extends Number>
Hessenberg<N extends Number>	Hessenberg: [A] = [Q][H][Q]T A general square matrix [A] can be decomposed by orthogonal similarity transformations into the form [A]=[Q][H][Q]T where [H] is upper (or lower) hessenberg matrix [Q] is orthogonal/unitary
Hessenberg.Factory<N extends Number>
LDL<N extends Number>	LDL: [A] = [L][D][L]H (or [R]H[D][R])
LDL.Factory<N extends Number>
LDU<N extends Number>	LDU: [A] = [L][D][U] ( [PL][L][D][U][PU] )
LU<N extends Number>	LU: [A] = [L][U]
LU.Factory<N extends Number>
MatrixDecomposition<N extends Number>	Notation used to describe the various matrix decompositions: [A] could be any matrix.
MatrixDecomposition.Determinant<N extends Number>
MatrixDecomposition.EconomySize<N extends Number>	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.
MatrixDecomposition.Factory<D extends MatrixDecomposition<?>>
MatrixDecomposition.Hermitian<N extends Number>	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.
MatrixDecomposition.Ordered<N extends Number>
MatrixDecomposition.Pivoting<N extends Number>	The pivot or pivot element is the element of a matrix, or an array, which is selected first by an algorithm (e.g.
MatrixDecomposition.RankRevealing<N extends Number>	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.
MatrixDecomposition.Solver<N extends Number>
MatrixDecomposition.Values<N extends Number>	Eigenvalue and Singular Value decompositions can calculate the "values" only.
QR<N extends Number>	QR: [A] = [Q][R] Decomposes [this] into [Q] and [R] where: [Q] is an orthogonal matrix (orthonormal columns).
QR.Factory<N extends Number>
SingularValue<N extends Number>	Singular Value: [A] = [Q1][D][Q2]T Decomposes [this] into [Q1], [D] and [Q2] where: [Q1] is an orthogonal matrix.
SingularValue.Factory<N extends Number>
Tridiagonal<N extends Number>	Tridiagonal: [A] = [Q][D][Q]H Any square symmetric (hermitian) matrix [A] can be factorized by similarity transformations into the form, [A]=[Q][D][Q]-1 where [Q] is an orthogonal (unitary) matrix and [D] is a real symmetric tridiagonal matrix.
Tridiagonal.Factory<N extends Number>

Class Summary

Class	Description
Eigenvalue.Eigenpair
EvD1D
EvD2D
HermitianEvD<N extends Number>	Eigenvalues and eigenvectors of a real matrix.