| Package | Description |
|---|---|
| org.ojalgo.data | |
| org.ojalgo.matrix.decomposition | |
| org.ojalgo.matrix.store |
| Class and Description |
|---|
| SingularValue
Singular Value: [A] = [Q1][D][Q2]T Decomposes [this] into [Q1], [D] and [Q2] where:
[Q1] is an orthogonal matrix.
|
| 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] ( [PL][L][D][U][PU] )
|
| 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.Pivoting
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
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.
|
| QR
QR: [A] = [Q][R] Decomposes [this] into [Q] and [R] where:
[Q] is an orthogonal matrix (orthonormal columns).
|
| QR.Factory |
| 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 |
| Class and Description |
|---|
| DecompositionStore
Only classes that will act as a delegate to a MatrixDecomposition implementation from this
package should implement this interface.
|
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