Module ojalgo
Package org.ojalgo.matrix.decomposition
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Interface Summary Interface Description Bidiagonal<N extends java.lang.Comparable<N>> A general matrix [A] can be factorized by similarity transformations into the form [A]=[LQ][D][RQ] -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 [LQ] (m-by-r) or (m-by-m) is orthogonal [RQ] (n-by-r) or (n-by-n) is orthogonal r = min(m,n)Bidiagonal.Factory<N extends java.lang.Comparable<N>> Cholesky<N extends java.lang.Comparable<N>> Cholesky: [A] = [L][L]H (or [R]H[R])Cholesky.Factory<N extends java.lang.Comparable<N>> DecompositionStore<N extends java.lang.Comparable<N>> Only classes that will act as a delegate to a MatrixDecomposition implementation from this package should implement this interface.Eigenvalue<N extends java.lang.Comparable<N>> [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 java.lang.Comparable<N>> Eigenvalue.Generalised<N extends java.lang.Comparable<N>> Eigenvalue.Spectral<N extends java.lang.Comparable<N>> “Spectral decomposition” refers specifically to the orthogonal/unitary eigen-decomposition of a normal matrix (most commonly Hermitian / symmetric).Hessenberg<N extends java.lang.Comparable<N>> 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/unitaryHessenberg.Factory<N extends java.lang.Comparable<N>> LDL<N extends java.lang.Comparable<N>> LDL: [A] = [L][D][L]H (or [R]H[D][R])LDL.Factory<N extends java.lang.Comparable<N>> LDU<N extends java.lang.Comparable<N>> LDU: [A] = [L][D][U] ( [PL][L][D][U][PU] )LU<N extends java.lang.Comparable<N>> LU: [A] = [L][U]LU.Factory<N extends java.lang.Comparable<N>> MatrixDecomposition<N extends java.lang.Comparable<N>> Notation used to describe the various matrix decompositions: [A] could be any matrix.MatrixDecomposition.Determinant<N extends java.lang.Comparable<N>> 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.MatrixDecomposition.Factory<D extends MatrixDecomposition<?>> 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.MatrixDecomposition.Ordered<N extends java.lang.Comparable<N>> 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.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.MatrixDecomposition.Solver<N extends java.lang.Comparable<N>> MatrixDecomposition.Updatable<N extends java.lang.Comparable<N>> MatrixDecomposition.Values<N extends java.lang.Comparable<N>> Eigenvalue and Singular Value decompositions can calculate the "values" only.QR<N extends java.lang.Comparable<N>> QR: [A] = [Q][R] Decomposes [this] into [Q] and [R] where: [Q] is an orthogonal matrix (orthonormal columns).QR.Factory<N extends java.lang.Comparable<N>> SingularValue<N extends java.lang.Comparable<N>> Singular Value: [A] = [U][S][V]T Decomposes [this] into [U], [S] and [V] where: [U] is an orthogonal matrix.SingularValue.Factory<N extends java.lang.Comparable<N>> Tridiagonal<N extends java.lang.Comparable<N>> 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 java.lang.Comparable<N>> -
Class Summary Class Description AbstractDecomposition<N extends java.lang.Comparable<N>,M extends PhysicalStore<N>> DeferredTridiagonal<N extends java.lang.Comparable<N>> DeferredTridiagonal.C128 DeferredTridiagonal.H256 DeferredTridiagonal.Q128 DeferredTridiagonal.R064 DeferredTridiagonal.R128 DenseBidiagonal<N extends java.lang.Comparable<N>> DenseBidiagonal.C128 DenseBidiagonal.H256 DenseBidiagonal.Q128 DenseBidiagonal.R064 DenseBidiagonal.R128 DenseCholesky<N extends java.lang.Comparable<N>> DenseCholesky.C128 DenseCholesky.H256 DenseCholesky.Q128 DenseCholesky.R064 DenseCholesky.R128 DenseEigenvalue<N extends java.lang.Comparable<N>> DenseHessenberg<N extends java.lang.Comparable<N>> DenseHessenberg.C128 DenseHessenberg.H256 DenseHessenberg.Q128 DenseHessenberg.R064 DenseHessenberg.R128 DenseLDL<N extends java.lang.Comparable<N>> DenseLDL.C128 DenseLDL.H256 DenseLDL.Q128 DenseLDL.R064 DenseLDL.R128 DenseLU<N extends java.lang.Comparable<N>> DenseLU.C128 DenseLU.H256 DenseLU.Q128 DenseLU.R064 DenseLU.R128 DenseQR<N extends java.lang.Comparable<N>> DenseQR.C128 DenseQR.H256 DenseQR.Q128 DenseQR.R064 DenseQR.R128 DenseSingularValue<N extends java.lang.Comparable<N>> DenseSingularValue.C128 DenseSingularValue.H256 DenseSingularValue.Q128 DenseSingularValue.R064 DenseSingularValue.R128 DenseTridiagonal<N extends java.lang.Comparable<N>> DynamicEvD<N extends java.lang.Comparable<N>> DynamicEvD.R064 Eigenvalue.Eigenpair EvD1D EvD2D FletcherMatthews Implements the Fletcher-Matthews form preserving method for LU factorization updates.GeneralEvD<N extends java.lang.Comparable<N>> GeneralEvD.R064 Eigenvalues and eigenvectors of a real matrix.GeneralisedEvD<N extends java.lang.Comparable<N>> HermitianEvD<N extends java.lang.Comparable<N>> Eigenvalues and eigenvectors of a real matrix.HermitianEvD.C128 HermitianEvD.H256 HermitianEvD.Q128 HermitianEvD.R064 HermitianEvD.R128 InPlaceDecomposition<N extends java.lang.Comparable<N>> LDL.ModifiedFactory<N extends java.lang.Comparable<N>> MinimumDegree Approximate Minimum Degree (AMD) style ordering for pre-ordering a symmetric sparse matrix prior to numerical factorisation (Cholesky or LDL).Pivot RawCholesky RawDecomposition In many ways similar to InPlaceDecomposition but this class is hardwired to work with double[][] data.RawEigenvalue Eigenvalues and eigenvectors of a real matrix.RawEigenvalue.Dynamic RawEigenvalue.General RawEigenvalue.Symmetric RawLU RawQR For an m-by-n matrix A with m >= n, the QR decomposition is an m-by-n orthogonal matrix Q and an n-by-n upper triangular matrix R so that A = Q*R.RawSingularValue Singular Value Decomposition.SimultaneousTridiagonal Computes Q while decomposing.SparseLU A sparse, primitive double based, LU decomposition with support for incremental Forrest-Tomlin updates.SparseLU.PermutationEta SparseQDLDL Quasi-Definite LDL (QDLDL) sparse decomposition.SparseQDLDL.EliminationTree Symbolic elimination treeSparseQDLDL.WorkerCache -
Enum Summary Enum Description Eigenvalue.Generalisation