public class RectangularCholeskyDecomposition extends Object
The rectangular Cholesky decomposition of a real symmetric positive semidefinite matrix A consists of a rectangular matrix B with the same number of rows such that: A is almost equal to BBT, depending on a user-defined tolerance. In a sense, this is the square root of A.
The difference with respect to the regular CholeskyDecomposition
is that rows/columns may be permuted (hence the rectangular shape instead
of the traditional triangular shape) and there is a threshold to ignore
small diagonal elements. This is used for example to generate correlated
random n-dimensions vectors in a p-dimension subspace (p < n).
In other words, it allows generating random vectors from a covariance
matrix that is only positive semidefinite, and not positive definite.
Rectangular Cholesky decomposition is not suited for solving
linear systems, so it does not provide any decomposition solver.
| Constructor and Description |
|---|
RectangularCholeskyDecomposition(RealMatrix matrix)
Decompose a symmetric positive semidefinite matrix.
|
RectangularCholeskyDecomposition(RealMatrix matrix,
double small)
Decompose a symmetric positive semidefinite matrix.
|
| Modifier and Type | Method and Description |
|---|---|
int |
getRank()
Get the rank of the symmetric positive semidefinite matrix.
|
RealMatrix |
getRootMatrix()
Get the root of the covariance matrix.
|
public RectangularCholeskyDecomposition(RealMatrix matrix) throws NonPositiveDefiniteMatrixException
Note: this constructor follows the linpack method to detect dependent columns by proceeding with the Cholesky algorithm until a nonpositive diagonal element is encountered.
matrix - Symmetric positive semidefinite matrix.NonPositiveDefiniteMatrixException - if the matrix is not
positive semidefinite.public RectangularCholeskyDecomposition(RealMatrix matrix, double small) throws NonPositiveDefiniteMatrixException
matrix - Symmetric positive semidefinite matrix.small - Diagonal elements threshold under which columns are
considered to be dependent on previous ones and are discarded.NonPositiveDefiniteMatrixException - if the matrix is not
positive semidefinite.public RealMatrix getRootMatrix()
B such that
the covariance matrix is equal to B.BTgetRank()public int getRank()
getRootMatrix()Copyright © 2003–2016 The Apache Software Foundation. All rights reserved.