﻿ILMath.norm Method (InArray(complex), Double)

ILNumerics Ultimate VS Documentation
ILNumerics - Technical Application Development
Vector or matrix norm.

[ILNumerics Computing Engine]

Namespace:  ILNumerics
Assembly:  ILNumerics.Computing (in ILNumerics.Computing.dll) Version: 5.5.0.0 (5.5.7503.3146)
Syntax

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

#### Parameters

A
Type: ILNumericsInArraycomplex
Input matrix or vector.
degree (Optional)
Type: SystemDouble
[Optional] Degree of the norm. Default: 2.

#### Return Value

Type: RetArrayDouble
Array of same type as input array A.
Remarks

For vectors, degree must be one of:
• 0 : returns sqrt(sum(A * A))
• System.complex.PositiveInfinity: returns max(abs(A))
• System.complex.NegativeInfinity: returns min(abs(A))
• other complex values: returns sum(pow(abs(A),degree))^(1/degree)
For matrices degree must be one of:
• 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]