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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