ParaMonte Fortran 2.0.0
Parallel Monte Carlo and Machine Learning Library
See the latest version documentation.
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.
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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


If you believe this algorithm or its documentation can be improved, we appreciate your contribution and help to edit this page's documentation and source file on GitHub.
For details on the naming abbreviations, see this page.
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.
  2. If you regenerate any parts/ideas from this library in a programming environment other than those currently supported by this ParaMonte library (i.e., other than C, C++, Fortran, MATLAB, Python, R), please also ask the end users to cite this original ParaMonte library.

This software is available to the public under a highly permissive license.
Help us justify its continued development and maintenance by acknowledging its benefit to society, distributing it, and contributing to it.

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.