ILMathnorm Method (InArrayDouble, Double)

public static RetArray<double> norm(
	InArray<double> A,
	double degree = 2
)

Public Shared Function norm ( 
	A As InArray(Of Double),
	Optional degree As Double = 2
) As RetArray(Of Double)

Dim A As InArray(Of Double)
Dim degree As Double
Dim returnValue As RetArray(Of Double)

returnValue = ILMath.norm(A, degree)

Parameters

A

Type: ILNumericsInArrayDouble
Input matrix or vector.

degree (Optional)

Type: SystemDouble
[Optional] Degree of the norm. Default: 2.

Return Value

• 0 : returns sqrt(sum(A * A))
• System.double.PositiveInfinity: returns max(abs(A))
• System.double.NegativeInfinity: returns min(abs(A))
• other double values: returns sum(pow(abs(A),degree))^(1/degree)

• 0: returns Frobenius norm: sqrt(sum(diag(multiply(A, A.T))))
• 1: returns 1-norm, max(sum(abs(A)))
• 2: returns the largest singular value of A, max(svd(A))
• PositiveInfinity: returns maxall(sum(abs(A), 1)), the largest value of the sums along the rows

norm(A,0) with A being a vector extends naturally to the frobenius norm for matrices.

For empty arrays A, scalar 0 is returned.

[ILNumerics Computing Engine]

Reference