Package org.ojalgo.matrix.decomposition
package org.ojalgo.matrix.decomposition
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ClassDescriptionBidiagonal<N extends 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 Comparable<N>>Cholesky<N extends Comparable<N>>Cholesky: [A] = [L][L]H (or [R]H[R])Cholesky.Factory<N extends Comparable<N>>DecompositionStore<N extends Comparable<N>>Only classes that will act as a delegate to a MatrixDecomposition implementation from this package should implement this interface.DeferredTridiagonal<N extends Comparable<N>>DenseBidiagonal<N extends Comparable<N>>DenseCholesky<N extends Comparable<N>>DenseEigenvalue<N extends Comparable<N>>DenseHessenberg<N extends Comparable<N>>DenseLDL<N extends Comparable<N>>DenseLU<N extends Comparable<N>>DenseQR<N extends Comparable<N>>DenseSingularValue<N extends Comparable<N>>DenseTridiagonal<N extends Comparable<N>>DynamicEvD<N extends Comparable<N>>Eigenvalue<N extends 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 Comparable<N>>Eigenvalue.Generalised<N extends Comparable<N>>Eigenvalue.Spectral<N extends Comparable<N>>“Spectral decomposition” refers specifically to the orthogonal/unitary eigen-decomposition of a normal matrix (most commonly Hermitian / symmetric).Implements the Fletcher-Matthews form preserving method for LU factorization updates.GeneralEvD<N extends Comparable<N>>Eigenvalues and eigenvectors of a real matrix.GeneralisedEvD<N extends Comparable<N>>HermitianEvD<N extends Comparable<N>>Eigenvalues and eigenvectors of a real matrix.Hessenberg<N extends 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 Comparable<N>>InPlaceDecomposition<N extends Comparable<N>>LDL<N extends Comparable<N>>LDL: [A] = [L][D][L]H (or [R]H[D][R])LDL.Factory<N extends Comparable<N>>LDL.ModifiedFactory<N extends Comparable<N>>LDU<N extends Comparable<N>>LDU: [A] = [L][D][U] ( [PL][L][D][U][PU] )LU<N extends Comparable<N>>LU: [A] = [L][U]LU.Factory<N extends Comparable<N>>MatrixDecomposition<N extends Comparable<N>>Notation used to describe the various matrix decompositions: [A] could be any matrix.MatrixDecomposition.Determinant<N extends Comparable<N>>MatrixDecomposition.EconomySize<N extends 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 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 Comparable<N>>MatrixDecomposition.Pivoting<N extends 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 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 Comparable<N>>MatrixDecomposition.Updatable<N extends Comparable<N>>MatrixDecomposition.Values<N extends Comparable<N>>Eigenvalue and Singular Value decompositions can calculate the "values" only.Approximate Minimum Degree (AMD) style ordering for pre-ordering a symmetric sparse matrix prior to numerical factorisation (Cholesky or LDL).QR<N extends Comparable<N>>QR: [A] = [Q][R] Decomposes [this] into [Q] and [R] where: [Q] is an orthogonal matrix (orthonormal columns).QR.Factory<N extends Comparable<N>>In many ways similar to InPlaceDecomposition but this class is hardwired to work with double[][] data.Eigenvalues and eigenvectors of a real matrix.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.Singular Value Decomposition.Computes Q while decomposing.SingularValue<N extends 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 Comparable<N>>A sparse, primitive double based, LU decomposition with support for incremental Forrest-Tomlin updates.Quasi-Definite LDL (QDLDL) sparse decomposition.Symbolic elimination treeTridiagonal<N extends 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 Comparable<N>>