Operators |
norm_matrix — Norm of a matrix.
The operator norm_matrix computes the norm of the elements of the Matrix defined by the matrix handle MatrixID. The return value is a floating point number.
The type of norming of the matrix can be selected via the parameter NormType:
The Frobenius norm is computed. The formula for the calculation of the result is:
_________________________ | m-1 n-1 | --- --- | \ \ Value = \ | / / (Matrix )^2 \ | --- --- ij \| i=0 j=0
with m = number of rows and n = number of columns of the Matrix .
Example:
/ 3.0 1.0 \ Matrix = | 4.0 -3.0 | -> MValue = 10.0 \ -7.0 4.0 /
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:
n-1 --- \ Value = max / | Matrix | i=0,m-1 --- ij j=0
with m = number of rows and n = number of columns of the Matrix .
Example:
/ 3.0 1.0 \ Matrix = | 4.0 -3.0 | -> MValue = 11.0 \ -7.0 4.0 /
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:
m-1 --- \ Value = max / | Matrix | j=0,n-1 --- ij i=0
with m = number of rows and n = number of columns of the Matrix .
Example:
/ 3.0 1.0 \ Matrix = | 4.0 -3.0 | -> MValue = 14.0 \ -7.0 4.0 /
The 2-norm is computed. The result is the largest singular value of the Matrix . The formula for the calculation of the result is:
Value = max (singular values (Matrix))
Example:
/ 3.0 1.0 \ Matrix = | 4.0 -3.0 | -> MValue = 9.7006 \ -7.0 4.0 /
Matrix handle of the input matrix.
Type of norm.
Default value: '2-norm'
List of values: '1-norm' , '2-norm' , 'frobenius-norm' , 'infinity-norm'
Norm of the input matrix.
If the parameters are valid, the operator norm_matrix returns the value 2 (H_MSG_TRUE). If necessary, an exception is raised.
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.
Foundation
Operators |