ParaMonte Fortran 2.0.0
Parallel Monte Carlo and Machine Learning Library
See the latest version documentation. |
This is a concrete derived type whose instances are exclusively used to signify the triangular class of a given matrix within an interface of a procedure of the ParaMonte library.
More...
This is a concrete derived type whose instances are exclusively used to signify the triangular class of a given matrix within an interface of a procedure of the ParaMonte library.
Objects instantiated from this derived type are exclusively used to differentiate the procedures within the various generic interfaces of the ParaMonte library.
As such, this concrete derived type does not contain any attributes.
A matrix of the form,
\begin{equation} L = \begin{bmatrix} \ell_{1,1}&&&&0 \\ \ell_{2,1}&\ell_{2,2}&&&\\ \ell_{3,1}&\ell_{3,2}&\ddots &&\\ \vdots &\vdots &\ddots &\ddots &\\ \ell_{n,1}&\ell_{n,2}&\ldots &\ell_{n,n-1}&\ell_{n,n} \end{bmatrix} \end{equation}
is called a lower triangular matrix or left triangular matrix, and analogously a matrix of the form,
\begin{equation} U = \begin{bmatrix} u_{1,1}&u_{1,2}&u_{1,3}&\ldots &u_{1,n}\\ &u_{2,2}&u_{2,3}&\ldots &u_{2,n}\\ &&\ddots &\ddots &\vdots\\ &&&\ddots &u_{n-1,n}\\ 0&&&&u_{n,n} \end{bmatrix} \end{equation}
is called an upper triangular matrix or right triangular matrix.
A lower or left triangular matrix is commonly denoted with the variable L, and an upper or right triangular matrix is commonly denoted with the variable U.
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.
Definition at line 1104 of file pm_matrixClass.F90.