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:
with m = number of rows and n = number of columns of the
Matrix.
Example:
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
Matrix.
Example:
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
Matrix.
Example:
The 2-norm is computed. The
result is the largest singular value of the Matrix. The
formula for the calculation of the result is:
Example:
MatrixID (input_control) matrix → (handle)
Matrix handle of the input matrix.
NormType (input_control) string → (string)
Type of norm.
Default: '2-norm'
List of values: '1-norm', '2-norm', 'frobenius-norm', 'infinity-norm'
Value (output_control) real → (real)
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