Uses of Package
org.ojalgo.matrix.decomposition

Packages that use org.ojalgo.matrix.decomposition

Package	Description
org.ojalgo.matrix.decomposition
org.ojalgo.matrix.store

Classes in org.ojalgo.matrix.decomposition used by org.ojalgo.matrix.decomposition

Class and Description
Bidiagonal 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
Cholesky Cholesky: [A] = [L][L]H (or [R]H[R])
Cholesky.Factory
DecompositionStore Only classes that will act as a delegate to a MatrixDecomposition implementation from this package should implement this interface.
Eigenvalue [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.Eigenpair
Eigenvalue.Factory
Hessenberg 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
LDL LDL: [A] = [L][D][L]H (or [R]H[D][R])
LDL.Factory
LDU LDU: [A] = [L][D][U] ( [P1][L][D][U][P2] )
LU LU: [A] = [L][U]
LU.Factory
MatrixDecomposition Notation used to describe the various matrix decompositions: [A] could be any matrix.
MatrixDecomposition.Determinant
MatrixDecomposition.EconomySize 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
MatrixDecomposition.Hermitian 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
MatrixDecomposition.RankRevealing 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
MatrixDecomposition.Values Eigenvalue and Singular Value decompositions can calculate the "values" only, and the resulting matrices and arrays can have their elements sorted (descending) or not.
QR QR: [A] = [Q][R] Decomposes [this] into [Q] and [R] where: [Q] is an orthogonal matrix (orthonormal columns).
QR.Factory
Schur Deprecated. v43 Use Eigenvalue instead
SingularValue Singular Value: [A] = [Q1][D][Q2]T Decomposes [this] into [Q1], [D] and [Q2] where: [Q1] is an orthogonal matrix.
SingularValue.Factory
Tridiagonal 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

Classes in org.ojalgo.matrix.decomposition used by org.ojalgo.matrix.store

Class and Description
DecompositionStore Only classes that will act as a delegate to a MatrixDecomposition implementation from this package should implement this interface.