Matrix.NormC Method

Overload List

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

Overload 1: Double NormC

The C-norm of calling Matrix.

Returns: Double

Remarks:

Computes:

NormC = max|a[i]|, 0 < i < Length-1

Indexed: Double NormC(Int32 Index, Int32 Len)

Calculates the C 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 NormC(TDenseMtxVec Vec, Boolean RelativeError)

The C-norm.

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

Returns: Double

Remarks:

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

\|\text{V} - \text{Vec}\| _C = \max _k |\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

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.NormC(b,false);

See Also: Matrix.NormL1, Matrix.NormL2

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

Calculates the C 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