math::LinearOperator< Operator, VectorDomain, VectorImage > Struct Template Reference
Concept LinearOperator. More...
#include <linear_operator.hpp>
Public Types | |
typedef associated_type | result_type |
Associated type: result of multiplication; automatically deducted. | |
typedef associated_type | assign_type |
Associated type: return type of assigning product to vector. | |
typedef associated_type | plus_assign_type |
Associated type: return type of incrementally assigning product to vector. | |
typedef associated_type | minus_assign_type |
Associated type: return type of decrementally assigning product to vector. | |
Public Member Functions | |
result_type | operator* (Operator, VectorDomain) |
Multiplication of linear operator with vector. | |
assign_type | operator= (VectorImage, result_type) |
Product must be assignable. | |
plus_assign_type | operator+= (VectorImage, result_type) |
Product must be assignable with increment. | |
minus_assign_type | operator+= (VectorImage, result_type) |
Product must be assignable with decrement. | |
axiom | Addability (Operator a, VectorDomain x, VectorDomain y) |
Invariant: the linear projection of a sum is the sum of the linear projections. | |
axiom | Scalability (Operator a, VectorSpace< VectorDomain >::scalar_type alpha, VectorDomain x) |
Invariant: the linear projection of a scaled vector is the scaling of the vector's linear projections. |
Concept LinearOperator.
Linear operator from one vector space into another one.
Operator | The type of the operator, e.g., some matrix type |
VectorDomain | The the type of a vector in the domain vector space |
VectorImage | The the type of a vector in the image vector space |
a | Object of type Operation |
x, y | Objects of type VectorDomain |
u | Object of type VectorImage |
Assign product: | u= a * x |
Add product: | u+= a * x |
Subtract product: | u-= a * x |
Addability | a * (x + y) == a*x + a*y |
Scalability | alpha * (a * x) == a * (alpha * x) |
typedef associated_type math::LinearOperator< Operator, VectorDomain, VectorImage >::assign_type |
Associated type: return type of assigning product to vector.
Automatically deducted. Using expression templates it can be different from VectorImage&
typedef associated_type math::LinearOperator< Operator, VectorDomain, VectorImage >::minus_assign_type |
Associated type: return type of decrementally assigning product to vector.
Automatically deducted. Using expression templates it can be different from VectorImage&
typedef associated_type math::LinearOperator< Operator, VectorDomain, VectorImage >::plus_assign_type |
Associated type: return type of incrementally assigning product to vector.
Automatically deducted. Using expression templates it can be different from VectorImage&
math::LinearOperator< Operator, VectorDomain, VectorImage > Struct Template Reference -- MTL 4 -- Peter Gottschling and Andrew Lumsdaine
-- Gen. with
rev. 7542
on Sat Aug 11 2012 by doxygen 1.7.6.1 -- © 2010 by SimuNova UG.