ILMathnorm Method (InArrayfcomplex, Single)

public static RetArray<float> norm(
	InArray<fcomplex> A,
	float degree = 2f
)

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

Dim A As InArray(Of fcomplex)
Dim degree As Single
Dim returnValue As RetArray(Of Single)

returnValue = ILMath.norm(A, degree)

Parameters

A

Type: ILNumericsInArrayfcomplex
Input matrix or vector.

degree (Optional)

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

Return Value

• 0 : returns sqrt(sum(A * A))
• System.fcomplex.PositiveInfinity: returns max(abs(A))
• System.fcomplex.NegativeInfinity: returns min(abs(A))
• other fcomplex 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