pm_matrixClass::gauss_type Type Reference

This is a concrete derived type whose instances are exclusively used to signify the Gauss-Transformation class of a given matrix within an interface of a procedure of the ParaMonte library.
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Inheritance diagram for pm_matrixClass::gauss_type:

Collaboration diagram for pm_matrixClass::gauss_type:

Detailed Description

This is a concrete derived type whose instances are exclusively used to signify the Gauss-Transformation 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 Gauss matrix is a special form of the atomic triangular matrix that differs from an Identity matrix only in the elements of a single row preceding the diagonal entry of that row (as opposed to the Frobenius matrix definition which has the matrix differing from the identity matrix in a single column below the diagonal).
The following example shows a 4-by-4 Gauss matrix with its 3rd row differing from the identity matrix.

\begin{equation} A = \begin{pmatrix} 1&0&0&0\\ 0&1&0&0\\ a_{31}&a_{32}&1&0\\ 0&0&0&1 \end{pmatrix} \end{equation}

An alternative name for the Gauss matrix is Gauss transformation matrix, after Carl Friedrich Gauss.
The Gauss matrix is used in the process of Gaussian elimination to represent the Gaussian transformations.

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., gauss) as directed by the documentation of the specific procedure they intend to use.

See also

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 ⛓

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For details on the naming conventions, see this page.
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Copyright

Computational Data Science Lab

Author:

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

Definition at line 1991 of file pm_matrixClass.F90.

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

• src/fortran/main/pm_matrixClass.F90