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Posted to issues@commons.apache.org by "Luc Maisonobe (JIRA)" <ji...@apache.org> on 2011/03/06 14:54:25 UTC
[jira] Created: (MATH-541) add a "rectangular" Cholesky-like
decomposition
add a "rectangular" Cholesky-like decomposition
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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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[jira] [Resolved] (MATH-541) add a "rectangular" Cholesky-like
decomposition
Posted by "Luc Maisonobe (JIRA)" <ji...@apache.org>.
[ https://issues.apache.org/jira/browse/MATH-541?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel ]
Luc Maisonobe resolved MATH-541.
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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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