ParaMonte Fortran 2.0.0
Parallel Monte Carlo and Machine Learning Library
See the latest version documentation. |
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" |
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.
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.
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.
character(*, SK), parameter pm_distChol::MODULE_NAME = "@pm_distChol" |
Definition at line 51 of file pm_distChol.F90.