ParaMonte Fortran 2.0.0 Parallel Monte Carlo and Machine Learning LibrarySee the latest version documentation.
pm_matrixClass::triang_type Type Reference

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.
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Inheritance diagram for pm_matrixClass::triang_type:
Collaboration diagram for pm_matrixClass::triang_type:

## Detailed Description

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,

$$L = \begin{bmatrix} \ell_{1,1}&&&&0 \\ \ell_{2,1}&\ell_{2,2}&&&\\ \ell_{3,1}&\ell_{3,2}&\ddots &&\\ \vdots &\vdots &\ddots &\ddots &\\ \ell_{n,1}&\ell_{n,2}&\ldots &\ell_{n,n-1}&\ell_{n,n} \end{bmatrix}$$

is called a lower triangular matrix or left triangular matrix, and analogously a matrix of the form,

$$U = \begin{bmatrix} u_{1,1}&u_{1,2}&u_{1,3}&\ldots &u_{1,n}\\ &u_{2,2}&u_{2,3}&\ldots &u_{2,n}\\ &&\ddots &\ddots &\vdots\\ &&&\ddots &u_{n-1,n}\\ 0&&&&u_{n,n} \end{bmatrix}$$

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.

Note
This concrete derived type is not meant to be directly accessed by the end users.
Instead, the end users should use the specific object parameter instance of this derived type (e.g., triang) as directed by the documentation of the specific procedure they intend to use.
genrecmat
posdefmat
symmetric
hermitian
triang_type
posdefmat_type
symmetric_type
hermitian_type
upperDiag_type
lowerDiag_type
upperZero_type
lowerZero_type
upperUnit_type
lowerUnit_type
unitTriang_type
atomicTriang_type
frobenius_type
genrecmat_type
matrix_type
gauss_type

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.

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, September 1, 2017, 12:00 AM, Institute for Computational Engineering and Sciences (ICES), The University of Texas at Austin

Definition at line 1104 of file pm_matrixClass.F90.

The documentation for this type was generated from the following file: