norm_matrix — 矩阵的范数。
算子 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. 结果的计算公式为:
with m = number of rows and n = number of columns of the
Matrix.
示例:
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.
示例:
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.
示例:
The 2-norm is computed. The
result is the largest singular value of the Matrix. 结果的计算公式为:
示例:
MatrixID (输入控制) matrix → (handle)
输入矩阵的矩阵句柄。
NormType (输入控制) string → (string)
Type of norm.
默认值: '2-norm'
值列表: '1-norm', '2-norm', 'frobenius-norm', 'infinity-norm'
Value (输出控制) real → (real)
Norm of the input matrix.
如果参数有效,算子 norm_matrix 返回值 2 ( H_MSG_TRUE )。如有必要,则抛出异常。
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.
基础