Vector.NormL1 Method

Overload List

#	Signature	Description
1	Double NormL1	Calculate the L1-norm of the calling vector.
	└ indexed: Double NormL1(Int32 Index, Int32 Len)
2	Double NormL1(TDenseMtxVec Vec, Boolean RelativeError)	The L1-norm.
	└ indexed: Double NormL1(TDenseMtxVec Vec, Int32 VecIndex, Int32 Index, Int32 Len, Boolean RelativeError)

Overload 1: Double NormL1

Calculate the L1-norm of the calling vector.

Returns: Double

Remarks:

NormL1 = sum | a[i] |, 0 < i < Length-1

Indexed: Double NormL1(Int32 Index, Int32 Len)

Calculates the L1 norm from calling vector elements [Index]..[Index+Len-1].

#	Name	Type	Description
1	Index	Int32	start index
2	Len	Int32	element count

Returns: Double

Overload 2: Double NormL1(TDenseMtxVec Vec, Boolean RelativeError)

The L1-norm.

#	Name	Type	Description
1	Vec	TDenseMtxVec	source TVec or TMtx
2	RelativeError	Boolean

Returns: Double

Remarks:

Calculates the L1 norm : ||V-Vec||, where V is calling vector. If the NormL1 is called without any parameters, the NormL1 calculates the norm of calling vector. The L1 norm of ||V-Vec|| is defined by the formula:

\|\text{V} - \text{Vec}\| _{L1} = \sum _{k=0} ^{\text{Length}-1}|\text{V}[k]-\text{Vec}[k]|

If RelativeError is true then the computed norm is divided by the norm of V, and the function returns the "relative error":

\frac{\| \text{V} - \text{Vec}\|}{\|\text{V}\|}

Examples

Vector a;
Vector b;
double c;
a.SetIt(false,new double[] {1,2,3,4});
b.SetIt(false,new double[] {4,3,2,1});
c = a.NormL1(b,true);

See Also: Vector.NormC, Vector.NormL2

Indexed: Double NormL1(TDenseMtxVec Vec, Int32 VecIndex, Int32 Index, Int32 Len, Boolean RelativeError)

Calculates the L1 norm ||V-Vec|| between Vec elements [VecIndex]..[VecIndex+Len-1] and calling vector elements [Index]..[Index+Len-1].

#	Name	Type	Description
1	Vec	TDenseMtxVec	source TVec or TMtx
2	VecIndex	Int32
3	Index	Int32	start index
4	Len	Int32	element count
5	RelativeError	Boolean

Returns: Double