pm_distChol Module Reference

This module contains classes and procedures for generating random upper or lower Cholesky factor triangular matrices. More...

Data Types
interface	getCholRand
	Generate and return a random upper and lower Cholesky factorization. More...
interface	setCholRand
	Return a random upper or lower Cholesky factorization. More...

Variables
character(*, SK), parameter	MODULE_NAME = "@pm_distChol"

Detailed Description

This module contains classes and procedures for generating random upper or lower Cholesky factor triangular matrices.

The output random Cholesky factors can be subsequently used to generate random positive-definite matrices.
Note that every real positive definite matrix \(M\) has a Cholesky factorization

\begin{equation} M = LL* \end{equation}

where \(L\) is a uniquely defined lower triangular matrix with positive diagonal entries.
Therefore, \(M\) can be constructed from a given random \(L\).
This approach, called Gram method is fast, however, the resulting matrix \(M\) does not possess any particular structure.

See also

pm_distCov

Test:

test_pm_distChol

Final Remarks ⛓

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For details on the naming conventions, see this page.
This software is distributed under the MIT license with additional terms outlined below.

1. If you use any parts or concepts from this library to any extent, please acknowledge the usage by citing the relevant publications of the ParaMonte library.
   
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Copyright

Computational Data Science Lab

Author:

Amir Shahmoradi, Monday March 6, 2017, 3:22 pm, Institute for Computational Engineering and Sciences (ICES), The University of Texas at Austin.

Variable Documentation

MODULE_NAME

character(*, SK), parameter pm_distChol::MODULE_NAME = "@pm_distChol"

Definition at line 51 of file pm_distChol.F90.