nrm

MatrixOperations.nrm(name='', normtype='', parr='', normalize='', **kwargs)

Computes the norm of the specified matrix or vector.

Mechanical APDL Command: *NRM

Parameters:

namestr

Matrix or vector for which the norm will be computed. This can be a dense matrix (created by the dmat command), a sparse matrix (created by the smat command) or a vector (created by the vec command)

normtypestr

Mathematical norm to use:

• NRM2 - L2 (Euclidian or SRSS) norm (default).

• NRM1 - L1 (absolute sum) norm (vectors and dense matrices only).

• NRMINF - Maximum norm.

parrstr

Parameter name that contains the result.

normalizestr

Normalization key; to be used only for vectors created by vec :

• YES - Normalize the vector such that the norm is 1.0.

• NO - Do not normalize the vector (default).

Notes

Warning

This function contains specificities regarding the argument definitions. Please refer to the command documentation for further explanations.

Argument Descriptions

• name : str - Matrix or vector for which the norm will be computed. This can be a dense matrix (created by the dmat command), a sparse matrix (created by the smat command) or a vector (created by the vec command)

• normtype : str - Mathematical norm to use:

  • NRM2 - L2 (Euclidian or SRSS) norm (default).

  • NRM1 - L1 (absolute sum) norm (vectors and dense matrices only).

  • NRMINF - Maximum norm.

• parr : str - Parameter name that contains the result.

• normalize : str - Normalization key; to be used only for vectors created by vec :

  • YES - Normalize the vector such that the norm is 1.0.

  • NO - Do not normalize the vector (default).

The NRM2 option corresponds to the Euclidian or L2 norm and is applicable to either vectors or matrices:

\(equation not available\), \(equation not available\)

\(equation not available\), \(equation not available\) where \(equation not available\) is the complex conjugate of \(equation not available\)

\(equation not available\), \(equation not available\) = largest eigenvalue of \(equation not available\)

The NRM1 option corresponds to the L1 norm and is applicable to vectors and dense matrices:

\(equation not available\) or \(equation not available\), \(equation not available\)

\(equation not available\) or \(equation not available\), \(equation not available\)

The NRMINF option is the maximum norm and is applicable to either vectors or matrices:

\(equation not available\) or \(equation not available\), \(equation not available\)

\(equation not available\) or \(equation not available\), \(equation not available\)