Vector::NormL1 Method

Overload List

#	Signature	Description
1	double NormL1(TDenseMtxVec Vec, bool* RelativeError = false) const;	The L1-norm.
2	double NormL1(TDenseMtxVec Vec, int* VecIndex, int Index, int Len, bool RelativeError = false) const;	Calculates the L1 norm \|\|V-Vec\|\| between Vec elements [VecIndex]..[VecIndex+Len-1] and calling vector elements [Index]..[Index+Len-1].
3	double NormL1() const;	Calculate the L1-norm of the calling vector.
4	double NormL1(int Index, int Len) const;	Calculates the L1 norm from calling vector elements [Index]..[Index+Len-1].

Overload 1: double NormL1(TDenseMtxVec *Vec, bool RelativeError = false) const;

The L1-norm.

#	Name	Type	Description
1	Vec	TDenseMtxVec *
2	RelativeError = false	bool

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

#include "MtxExpr.h"

using namespace Dew;
using namespace Dew::Math;

void Example()
{
    Vector a, b;
    double c;

    a.SetIt(false, DewArray<double>{1, 2, 3, 4});
    b.SetIt(false, DewArray<double>{4, 3, 2, 1});
    c = a.NormL1(b, true);
}

See Also: Vector::NormC, Vector::NormL2

Declared in Dew::Math::Vector · Dew.Math/MtxExpr.h · Cross-compiler

Overload 2: double NormL1(TDenseMtxVec *Vec, int VecIndex, int Index, int Len, bool RelativeError = false) const;

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

#	Name	Type
1	Vec	TDenseMtxVec *
2	VecIndex	int
3	Index	int
4	Len	int
5	RelativeError = false	bool

Examples

#include "MtxExpr.h"

using namespace Dew;
using namespace Dew::Math;

void Example()
{
    Vector a, b;
    double c;

    a = {1, 2, 3, 4};
    b = {4, 3, 2, 1};
    c = a.NormL1(b, true);
}

Declared in Dew::Math::Vector · Dew.Math/MtxExpr.h · Cross-compiler

Overload 3: double NormL1() const;

Calculate the L1-norm of the calling vector.

Remarks:

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

Declared in Dew::Math::Vector · Dew.Math/MtxExpr.h · Cross-compiler

Overload 4: double NormL1(int Index, int Len) const;

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

#	Name	Type	Description
1	Index	int
2	Len	int

Declared in Dew::Math::Vector · Dew.Math/MtxExpr.h · Cross-compiler