norm_matrixnorm_matrixNormMatrixNormMatrix (Operator)

Name

norm_matrixnorm_matrixNormMatrixNormMatrix — Norm of a matrix.

Signature

Description

The operator norm_matrixnorm_matrixNormMatrixNormMatrixNormMatrix computes the norm of the elements of the MatrixMatrixMatrixMatrixmatrix defined by the matrix handle MatrixIDMatrixIDMatrixIDMatrixIDmatrixID. The return value is a floating point number.

The type of norming of the matrix can be selected via the parameter NormTypeNormTypeNormTypeNormTypenormType:

'frobenius-norm'"frobenius-norm""frobenius-norm""frobenius-norm""frobenius-norm":

The Frobenius norm is computed. The formula for the calculation of the result is:

with m = number of rows and n = number of columns of the MatrixMatrixMatrixMatrixmatrix.

Example:

'infinity-norm'"infinity-norm""infinity-norm""infinity-norm""infinity-norm":

The infinity norm is computed. The result is the largest value of the sum of the absolute values of the elements of the rows. The formula for the calculation is:

with m = number of rows and n = number of columns of the MatrixMatrixMatrixMatrixmatrix.

Example:

'1-norm'"1-norm""1-norm""1-norm""1-norm":

The 1-norm is computed. The result is the largest value of the sum of the absolute values of the elements of the columns. The formula for the calculation is:

with m = number of rows and n = number of columns of the MatrixMatrixMatrixMatrixmatrix.

Example:

'2-norm'"2-norm""2-norm""2-norm""2-norm":

The 2-norm is computed. The result is the largest singular value of the MatrixMatrixMatrixMatrixmatrix. The formula for the calculation of the result is:

   Value = max (singular values (Matrix))

  

Example:

Execution Information

• Multithreading type: reentrant (runs in parallel with non-exclusive operators).
• Multithreading scope: global (may be called from any thread).
• Processed without parallelization.

Parameters

Result

If the parameters are valid, the operator norm_matrixnorm_matrixNormMatrixNormMatrixNormMatrix returns the value 2 (H_MSG_TRUE). If necessary, an exception is raised.

Possible Predecessors

create_matrixcreate_matrixCreateMatrixCreateMatrixCreateMatrix

See also

sum_matrixsum_matrixSumMatrixSumMatrixSumMatrix, mean_matrixmean_matrixMeanMatrixMeanMatrixMeanMatrix

References

David Poole: “Linear Algebra: A Modern Introduction”; Thomson; Belmont; 2006.
Gene H. Golub, Charles F. van Loan: “Matrix Computations”; The Johns Hopkins University Press; Baltimore and London; 1996.

Module

Foundation