AbstractDecomposition |
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Bidiagonal |
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)
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Bidiagonal.Factory |
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BidiagonalDecomposition |
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Cholesky |
Cholesky: [A] = [L][L]H (or [R]H[R])
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Cholesky.Factory |
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CholeskyDecomposition |
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DecompositionStore |
Only classes that will act as a delegate to a MatrixDecomposition implementation from this
package should implement this interface.
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DeferredTridiagonal |
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DynamicEvD |
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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).
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Eigenvalue.Eigenpair |
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Eigenvalue.Factory |
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Eigenvalue.Generalisation |
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Eigenvalue.Generalised |
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EigenvalueDecomposition |
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GeneralEvD |
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GenericDecomposition |
AbstractDecomposition
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HermitianEvD |
Eigenvalues and eigenvectors of a real matrix.
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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
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Hessenberg.Factory |
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HessenbergDecomposition |
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InPlaceDecomposition |
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LDL |
LDL: [A] = [L][D][L]H (or [R]H[D][R])
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LDL.Factory |
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LDLDecomposition |
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LDU |
LDU: [A] = [L][D][U] ( [PL][L][D][U][PU] )
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LU |
LU: [A] = [L][U]
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LU.Factory |
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LUDecomposition |
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MatrixDecomposition |
Notation used to describe the various matrix decompositions:
[A] could be any matrix.
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MatrixDecomposition.Determinant |
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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.
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MatrixDecomposition.Factory |
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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.
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MatrixDecomposition.Ordered |
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MatrixDecomposition.Pivoting |
The pivot or pivot element is the element of a matrix, or an array, which is selected first by an
algorithm (e.g.
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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.
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MatrixDecomposition.Solver |
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MatrixDecomposition.Values |
Eigenvalue and Singular Value decompositions can calculate the "values" only.
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Pivot |
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QR |
QR: [A] = [Q][R] Decomposes [this] into [Q] and [R] where:
[Q] is an orthogonal matrix (orthonormal columns).
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QR.Factory |
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QRDecomposition |
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RawDecomposition |
In many ways similar to InPlaceDecomposition but this class is hardwired to work with double[][] data.
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RawEigenvalue |
Eigenvalues and eigenvectors of a real matrix.
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SingularValue |
Singular Value: [A] = [U][D][V]T Decomposes [this] into [U], [D] and [V] where:
[U] is an orthogonal matrix.
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SingularValue.Factory |
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SingularValueDecomposition |
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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.
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Tridiagonal.Factory |
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TridiagonalDecomposition |
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