Uses of Package
org.ojalgo.matrix.decomposition
Packages that use org.ojalgo.matrix.decomposition
Package
Description
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Classes in org.ojalgo.matrix.decomposition used by org.ojalgo.dataClassDescriptionSingular Value: [A] = [U][D][V]T Decomposes [this] into [U], [D] and [V] where: [U] is an orthogonal matrix.
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Classes in org.ojalgo.matrix.decomposition used by org.ojalgo.function.polynomial
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Classes in org.ojalgo.matrix.decomposition used by org.ojalgo.matrixClassDescriptionCholesky: [A] = [L][L]H (or [R]H[R])[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).LDL: [A] = [L][D][L]H (or [R]H[D][R])LDU: [A] = [L][D][U] ( [PL][L][D][U][PU] )LU: [A] = [L][U]Notation used to describe the various matrix decompositions: [A] could be any matrix.QR: [A] = [Q][R] Decomposes [this] into [Q] and [R] where: [Q] is an orthogonal matrix (orthonormal columns).Singular Value: [A] = [U][D][V]T Decomposes [this] into [U], [D] and [V] where: [U] is an orthogonal matrix.
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Classes in org.ojalgo.matrix.decomposition used by org.ojalgo.matrix.decompositionClassDescriptionA 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)Cholesky: [A] = [L][L]H (or [R]H[R])Only classes that will act as a delegate to a MatrixDecomposition implementation from this package should implement this interface.[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).AbstractDecompositionEigenvalues and eigenvectors of a real matrix.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/unitaryLDL: [A] = [L][D][L]H (or [R]H[D][R])LDU: [A] = [L][D][U] ( [PL][L][D][U][PU] )LU: [A] = [L][U]Notation used to describe the various matrix decompositions: [A] could be any matrix.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.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.The pivot or pivot element is the element of a matrix, or an array, which is selected first by an algorithm (e.g.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.Eigenvalue and Singular Value decompositions can calculate the "values" only.QR: [A] = [Q][R] Decomposes [this] into [Q] and [R] where: [Q] is an orthogonal matrix (orthonormal columns).In many ways similar to InPlaceDecomposition but this class is hardwired to work with double[][] data.Eigenvalues and eigenvectors of a real matrix.Singular Value: [A] = [U][D][V]T Decomposes [this] into [U], [D] and [V] where: [U] is an orthogonal matrix.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.
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Classes in org.ojalgo.matrix.decomposition used by org.ojalgo.matrix.storeClassDescriptionOnly classes that will act as a delegate to a MatrixDecomposition implementation from this package should implement this interface.
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Classes in org.ojalgo.matrix.decomposition used by org.ojalgo.optimisation.convex
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Classes in org.ojalgo.matrix.decomposition used by org.ojalgo.optimisation.linear
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Classes in org.ojalgo.matrix.decomposition used by org.ojalgo.random.process