Matrix.NormL2 Method

Overload List

#	Signature	Description
1	Double NormL2	The L2-norm of the calling Matrix.
	└ indexed: Double NormL2(Int32 Index, Int32 Len)
2	Double NormL2(TDenseMtxVec Vec, Boolean RelativeError)	The L2-norm.
	└ indexed: Double NormL2(TDenseMtxVec Vec, Int32 VecIndex, Int32 Index, Int32 Len, Boolean RelativeError)

Overload 1: Double NormL2

The L2-norm of the calling Matrix.

Returns: Double

Remarks:

Calculates:

NormL2 = ( sum | a[i] |^2 )^(0.5), 0 < i < Length-1

Indexed: Double NormL2(Int32 Index, Int32 Len)

Calculates the L2 norm from calling Matrix elements [Index]..[Index+Len-1].

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

Returns: Double

Overload 2: Double NormL2(TDenseMtxVec Vec, Boolean RelativeError)

The L2-norm.

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

Returns: Double

Remarks:

Calculates the L2 norm : ||V-Vec||, where V is calling Matrix. If the NormL2 is called without any parameters, the NormL2 calculates the norm of calling Matrix. The L2 norm of ||V-Vec|| is defined by the formula:

\|\text{V} - \text{Vec}\| _{L2} = \sqrt{\sum _{k=0} ^{\text{Length}-1}\left(|\text{V}[k]-\text{Vec}[k]| \right)^2}

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

Matrix a;
Matrix b;
double c;
a.SetIt(1,4,false,new double[] {1,2,3,4});
b.SetIt(1,4,false,new double[] {4,3,2,1});
c = a.NormL2(b,true);  // or
c = NormL2(a,b,true);

See Also: Matrix.NormC, Matrix.NormL1

Indexed: Double NormL2(TDenseMtxVec Vec, Int32 VecIndex, Int32 Index, Int32 Len, Boolean RelativeError)

Calculates the L2 norm ||V-Vec|| between Vec elements [VecIndex]..[VecIndex+Len-1] and calling Matrix 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