Norm Method

Returns the specified matrix norm.

Syntax

MatrixObject.Norm(NormType)

Return Value

A Double value equal to the specified matrix norm.

Parameters

NormType: Optional. A NormTypeEnum value specifying the type of matrix norm to be returned.

The following table describes the possible values for the NormType parameter.

	Description	Value
bmNormOne	Calculates the one norm, the maximum column sum of absolute values.	1
bmNormFrobenius	(Default) Calculates the Frobenius norm of the matrix, the square root of the sum of the absolute squares of matrix elements.	2
bmNormEuclidean	Calculates the Euclidean norm of the matrix, the largest singular value of the matrix.	3
bmNormInfinity	Calculates the infinity norm of the matrix, the largest row sum of absolute values.	4

Example

This example demonstrates the use of Norm method. A matrix is defined and the 4 types of norms are calculated.

Private Sub MatrixNorm()

Dim A As Matrix, Norm As Double
    Set A = New Matrix
    A.Size 4, 4
    A.FillRandom
    Debug.Print "A ="
    Debug.Print A.GetString
    
    Debug.Print "One Norm   ="; A.Norm(bmNormOne)
    Debug.Print "Frobenious ="; A.Norm(bmNormFrobenius)
    Debug.Print "Euclidean  ="; A.Norm(bmNormEuclidean)
    Debug.Print "Infinity   ="; A.Norm(bmNormInfinity)

End Sub

Output

A =
| 6.000 2.000 8.000 6.000 |
| 5.000 4.000 9.000 8.000 |
| 7.000 2.000 9.000 7.000 |
| 5.000 3.000 0.000 1.000 |

One Norm   = 26 
Frobenious = 23.3238075793812 
Euclidean  = 22.7204825366697 
Infinity   = 26

Syntax

Return Value

Parameters

Example

Output

See Also