Package  Description 

org.ojalgo.matrix.decomposition 
Modifier and Type  Interface and Description 

static interface 
MatrixDecomposition.Factory<D extends MatrixDecomposition<?>> 
Modifier and Type  Interface and Description 

interface 
Bidiagonal<N extends Number>
A general matrix [A] can be factorized by similarity transformations into the form [A]=[Q1][D][Q2]
^{1} where:
[A] (mbyn) is any, real or complex, matrix
[D] (rbyr) or (mbyn) is, upper or lower, bidiagonal
[Q1] (mbyr) or (mbym) is orthogonal
[Q2] (nbyr) or (nbyn) is orthogonal
r = min(m,n)

interface 
Cholesky<N extends Number>
Cholesky: [A] = [L][L]^{H} (or [R]^{H}[R])

interface 
Eigenvalue<N extends Number>
[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).

interface 
Hessenberg<N extends Number>
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

interface 
LDL<N extends Number>
LDL: [A] = [L][D][L]^{H} (or [R]^{H}[D][R])

interface 
LDU<N extends Number>
LDU: [A] = [L][D][U] ( [P1][L][D][U][P2] )

interface 
LU<N extends Number>
LU: [A] = [L][U]

static interface 
MatrixDecomposition.Determinant<N extends Number> 
static interface 
MatrixDecomposition.EconomySize<N extends Number>
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.

static interface 
MatrixDecomposition.Hermitian<N extends Number>
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.

static interface 
MatrixDecomposition.Ordered<N extends Number> 
static interface 
MatrixDecomposition.RankRevealing<N extends Number>
A rankrevealing 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 nonincreasing values on the diagonal.

static interface 
MatrixDecomposition.Solver<N extends Number> 
static interface 
MatrixDecomposition.Values<N extends Number>
Eigenvalue and Singular Value decompositions can calculate the "values" only, and the resulting
matrices and arrays can have their elements sorted (descending) or not.

interface 
QR<N extends Number>
QR: [A] = [Q][R] Decomposes [this] into [Q] and [R] where:
[Q] is an orthogonal matrix (orthonormal columns).

interface 
Schur<N extends Number>
Deprecated.
v43 Use Eigenvalue instead

interface 
SingularValue<N extends Number>
Singular Value: [A] = [Q1][D][Q2]^{T} Decomposes [this] into [Q1], [D] and [Q2] where:
[Q1] is an orthogonal matrix.

interface 
Tridiagonal<N extends Number>
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.

Modifier and Type  Class and Description 

class 
HermitianEvD<N extends Number>
Eigenvalues and eigenvectors of a real matrix.

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