CAPD DynSys Library  5.2.0
Public Types | Public Member Functions | List of all members
capd::vectalg::EuclNorm< VectorType, MatrixType > Class Template Reference

Euclidean norm. More...

#include <capd/vectalg/Norm.h>

Public Types

typedef VectorType::ScalarType ScalarType
 
typedef MatrixType::size_type size_type
 

Public Member Functions

virtual ScalarType operator() (const VectorType &iv) const
 Computes norm of the vector. More...
 
virtual ScalarType operator() (const MatrixType &iv) const
 Computes norm of the matrix. More...
 
virtual std::string show (void) const
 Returns the name of the norm. More...
 
Norm< VectorType, MatrixType > * clone (void) const
 Makes virtual copy of the object. More...
 

Detailed Description

template<typename VectorType, typename MatrixType>
class capd::vectalg::EuclNorm< VectorType, MatrixType >

Euclidean norm.

Member Typedef Documentation

◆ ScalarType

template<typename VectorType , typename MatrixType >
typedef VectorType::ScalarType capd::vectalg::EuclNorm< VectorType, MatrixType >::ScalarType

◆ size_type

template<typename VectorType , typename MatrixType >
typedef MatrixType::size_type capd::vectalg::EuclNorm< VectorType, MatrixType >::size_type

Member Function Documentation

◆ clone()

template<typename VectorType , typename MatrixType >
Norm< VectorType, MatrixType > * capd::vectalg::EuclNorm< VectorType, MatrixType >::clone ( void  ) const
virtual

Makes virtual copy of the object.

Implements capd::vectalg::Norm< VectorType, MatrixType >.

◆ operator()() [1/2]

template<typename VectorType , typename MatrixType >
EuclNorm< VectorType, MatrixType >::ScalarType capd::vectalg::EuclNorm< VectorType, MatrixType >::operator() ( const MatrixType &  A) const
virtual

Computes norm of the matrix.

$ |A| = \sqrt{ \rho(A^T A) } $ where $\rho$ is spectral radius of a matrix (the biggest modulus of an eigenvalue)

Implements capd::vectalg::Norm< VectorType, MatrixType >.

◆ operator()() [2/2]

template<typename VectorType , typename MatrixType >
EuclNorm< VectorType, MatrixType >::ScalarType capd::vectalg::EuclNorm< VectorType, MatrixType >::operator() ( const VectorType &  x) const
virtual

Computes norm of the vector.

$ |x| = \sqrt{ x_1^2 + x_2^2 + \dots + x_n^2} $

Implements capd::vectalg::Norm< VectorType, MatrixType >.

◆ show()

template<typename VectorType , typename MatrixType >
std::string capd::vectalg::EuclNorm< VectorType, MatrixType >::show ( void  ) const
virtual

Returns the name of the norm.

Implements capd::vectalg::Norm< VectorType, MatrixType >.