math::BanachSpace< N, Vector, Scalar > Struct Template Reference
[Concepts]
Concept
BanachSpace.
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#include <vector_concepts.hpp>
List of all members.
Detailed Description
template<typename N, typename Vector, typename Scalar = typename Vector::value_type>
struct math::BanachSpace< N, Vector, Scalar >
Concept
BanachSpace.
A Banach space is a vector space with a 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:
-
- Note:
- The (expressible) requirements of Banach Space are already given in Norm.
- The difference between the requirements is the completeness of the Banach space, i.e. that every Cauchy sequence w.r.t. norm(v-w) has a limit in the space. Unfortunately, completeness is never satisfied for finite precision arithmetic types.
- Another subtle difference is that Norm is not a refinement of Vectorspace
The documentation for this struct was generated from the following file:
- /usr/src/RPM/BUILD/mtl4-2.r6668.alpha/boost/numeric/linear_algebra/vector_concepts.hpp