Name
norm_matrixnorm_matrixNormMatrixnorm_matrixNormMatrixNormMatrix — Norm of a matrix.
The operator norm_matrixnorm_matrixNormMatrixnorm_matrixNormMatrixNormMatrix computes the norm of the elements
of the MatrixMatrixMatrixMatrixMatrixmatrix defined by the matrix handle
MatrixIDMatrixIDMatrixIDMatrixIDMatrixIDmatrixID. The return value is a floating point number.
The type of norming of the matrix can be selected via the parameter
NormTypeNormTypeNormTypeNormTypeNormTypenormType:
- 'frobenius-norm'"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
MatrixMatrixMatrixMatrixMatrixmatrix.
Example:
- 'infinity-norm'"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
MatrixMatrixMatrixMatrixMatrixmatrix.
Example:
- '1-norm'"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
MatrixMatrixMatrixMatrixMatrixmatrix.
Example:
- '2-norm'"2-norm""2-norm""2-norm""2-norm""2-norm":
-
The 2-norm is computed. The
result is the largest singular value of the MatrixMatrixMatrixMatrixMatrixmatrix. The
formula for the calculation of the result is:
Value = max (singular values (Matrix))
Example:
- Multithreading type: reentrant (runs in parallel with non-exclusive operators).
- Multithreading scope: global (may be called from any thread).
- Processed without parallelization.
Matrix handle of the input matrix.
Type of norm.
Default value:
'2-norm'
"2-norm"
"2-norm"
"2-norm"
"2-norm"
"2-norm"
List of values: '1-norm'"1-norm""1-norm""1-norm""1-norm""1-norm", '2-norm'"2-norm""2-norm""2-norm""2-norm""2-norm", 'frobenius-norm'"frobenius-norm""frobenius-norm""frobenius-norm""frobenius-norm""frobenius-norm", 'infinity-norm'"infinity-norm""infinity-norm""infinity-norm""infinity-norm""infinity-norm"
Norm of the input matrix.
If the parameters are valid, the operator norm_matrixnorm_matrixNormMatrixnorm_matrixNormMatrixNormMatrix
returns the value 2 (H_MSG_TRUE). If necessary, an exception is raised.
create_matrixcreate_matrixCreateMatrixcreate_matrixCreateMatrixCreateMatrix
sum_matrixsum_matrixSumMatrixsum_matrixSumMatrixSumMatrix,
mean_matrixmean_matrixMeanMatrixmean_matrixMeanMatrixMeanMatrix
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