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From "Luc Maisonobe (JIRA)" <j...@apache.org>
Subject [jira] [Resolved] (MATH-541) add a "rectangular" Cholesky-like decomposition
Date Mon, 25 Apr 2011 16:29:03 GMT

     [ https://issues.apache.org/jira/browse/MATH-541?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel
]

Luc Maisonobe resolved MATH-541.
--------------------------------

    Resolution: Fixed

fixed in subversion repository as of r1096496

> add a "rectangular" Cholesky-like decomposition
> -----------------------------------------------
>
>                 Key: MATH-541
>                 URL: https://issues.apache.org/jira/browse/MATH-541
>             Project: Commons Math
>          Issue Type: Improvement
>    Affects Versions: 2.2
>            Reporter: Luc Maisonobe
>            Assignee: Luc Maisonobe
>            Priority: Minor
>             Fix For: 3.0
>
>
> The CorrelatedRandomVectorGenerator class uses a kind of rectangular Cholesky-like transform
M = B.Bt where B is a rectangular matrix. The difference with respect to a regular Cholesky
decomposition 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.
> It would be nice to have this decomposition available as a stand-alone class outside
of the CorrelatedRandomVectorGenerator.

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