math::SemiNorm< N, Vector, Scalar > Struct Template Reference
[Concepts]

Concept SemiNorm. More...

#include <vector_concepts.hpp>

Inheritance diagram for math::SemiNorm< N, Vector, Scalar >:
math::Norm< N, Vector, Scalar >

List of all members.

Public Member Functions

axiom PositiveDefiniteness (N norm, Vector v, magnitude_type ref)
 The norm of a vector is zero if and only if the vector is the zero vector.

Detailed Description

template<typename N, typename Vector, typename Scalar = typename Vector::value_type>
struct math::SemiNorm< N, Vector, Scalar >

Concept SemiNorm.

Semantic requirements of a semi-norm

Parameters:
N Norm functor
Vector The the type of a vector or a collection
Scalar The scalar over which the vector field is defined
Refinement of:
  • Norm <N, Vector, Scalar>

Member Function Documentation

template<typename N , typename Vector , typename Scalar = typename Vector::value_type>
axiom math::SemiNorm< N, Vector, Scalar >::PositiveDefiniteness ( norm,
Vector  v,
magnitude_type  ref 
) [inline]

The norm of a vector is zero if and only if the vector is the zero vector.

if (norm(v) == zero(ref)) v == zero(v);

if (v == zero(v)) norm(v) == zero(ref);


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