LieAlgebraBase< T_DERIVED, T_GROUP, T_DOF, T_SCALAR_TYPE > Class Template Reference

#include <LieAlgebraBase.hpp>

Inheritance diagram for LieAlgebraBase< T_DERIVED, T_GROUP, T_DOF, T_SCALAR_TYPE >:

Collaboration diagram for LieAlgebraBase< T_DERIVED, T_GROUP, T_DOF, T_SCALAR_TYPE >:

Public Member Functions
T_DERIVED	inverse () const
void	inverted ()
void	operator+= (const T_DERIVED &g)
T_DERIVED	operator+ (const T_DERIVED &g) const
T_DERIVED	operator- (const T_DERIVED &g) const
void	operator*= (T_SCALAR_TYPE s)
T_DERIVED	operator* (const T_SCALAR_TYPE &s) const
T_DERIVED	bracket (const T_DERIVED &g) const
T_DERIVED	Ad (const T_GROUP &g) const
T_DERIVED	Ad_star (const T_GROUP &g) const
T_SCALAR_TYPE	norm () const
T_GROUP	exp () const
NOXVector< T_DOF >	toNOXVector () const
Public Member Functions inherited from CRTP< T_DERIVED >
T_DERIVED &	underlying ()
T_DERIVED const &	underlying () const

Static Public Member Functions
static T_DERIVED	Zero ()
static T_DERIVED	static_bracket (const T_DERIVED &g1, const T_DERIVED &g2)
static T_DERIVED	static_Ad (const T_DERIVED &a, const T_GROUP &g)
static T_DERIVED	static_Ad_star (const T_GROUP &g, const T_DERIVED &a)
static T_GROUP	exp (const T_DERIVED &g)
static const unsigned int	dof ()

Static Public Attributes
static const unsigned int	DOF = T_DOF

Detailed Description

template<typename T_DERIVED, typename T_GROUP, unsigned int T_DOF, typename T_SCALAR_TYPE>
class LieAlgebraBase< T_DERIVED, T_GROUP, T_DOF, T_SCALAR_TYPE >

This class defines a Lie algebra \((\mathfrak g,[\cdot,\cdot])\) where \((\mathfrak g,\mathbb F,+,\cdot)\) is a vector space over the field \(\mathbb F\), with the vector space addition \( +:\mathfrak g\times\mathfrak g\rightarrow\mathfrak g\). and the scalar multiplication \(\cdot:\mathbb F\times\mathfrak g\rightarrow\mathfrak g\). Here the field \(\mathbb F\) is represented by the templated type T_SCALAR_TYPE.

The design of the class is based on the Curious Recurring Template Pattern. The class is intended to be inherited. The function members to be implemented by the user are the following:

• operator+= (const T_DERIVED&)
• inverse ()
• Zero ()
• operator*= (T_SCALAR_TYPE)
• bracket (const T_DERIVED&g)
• Ad (const T_GROUP&)
• Ad_star (const T_GROUP&)
• norm ()
• toNOXVector ()

Member Function Documentation

bracket()

template<typename T_DERIVED, typename T_GROUP, unsigned int T_DOF, typename T_SCALAR_TYPE>

T_DERIVED LieAlgebraBase< T_DERIVED, T_GROUP, T_DOF, T_SCALAR_TYPE >::bracket

(

const T_DERIVED &

g

)

const

This function has to be implemented by the user. It should perform the Lie bracket operation \([a,b]\) where \(a\) is *this and \(b\) is g.

exp()

template<typename T_DERIVED, typename T_GROUP, unsigned int T_DOF, typename T_SCALAR_TYPE>

T_GROUP LieAlgebraBase< T_DERIVED, T_GROUP, T_DOF, T_SCALAR_TYPE >::exp

(

)

const

Implements the exponential map \(\exp:\mathfrak{so}(3)\rightarrow SO(3)\) evalutated at *this.

inverse()

template<typename T_DERIVED, typename T_GROUP, unsigned int T_DOF, typename T_SCALAR_TYPE>

T_DERIVED LieAlgebraBase< T_DERIVED, T_GROUP, T_DOF, T_SCALAR_TYPE >::inverse

(

)

const

This function has to be implemented by the user. It should return the mathematical inverse of *this with respect to the vector space addition.

inverted()

template<typename T_DERIVED, typename T_GROUP, unsigned int T_DOF, typename T_SCALAR_TYPE>

void LieAlgebraBase< T_DERIVED, T_GROUP, T_DOF, T_SCALAR_TYPE >::inverted ( )

inline

Inverts *this in place.

See also

inverse()

operator*()

template<typename T_DERIVED, typename T_GROUP, unsigned int T_DOF, typename T_SCALAR_TYPE>

T_DERIVED LieAlgebraBase< T_DERIVED, T_GROUP, T_DOF, T_SCALAR_TYPE >::operator* ( const T_SCALAR_TYPE &  s ) const

inline

Performs the scalar multiplication of g and *this.

See also

operator*=(T_SCALAR_TYPE s)

operator*=()

template<typename T_DERIVED, typename T_GROUP, unsigned int T_DOF, typename T_SCALAR_TYPE>

void LieAlgebraBase< T_DERIVED, T_GROUP, T_DOF, T_SCALAR_TYPE >::operator*=

(

T_SCALAR_TYPE

s

)

This function has to be implemented by the user. It should perform the scalar multiplication of the argument s and *this. The operation must be done in place.

operator+()

template<typename T_DERIVED, typename T_GROUP, unsigned int T_DOF, typename T_SCALAR_TYPE>

T_DERIVED LieAlgebraBase< T_DERIVED, T_GROUP, T_DOF, T_SCALAR_TYPE >::operator+ ( const T_DERIVED &  g ) const

inline

Performs the vector space addition of *this and g.

See also

operator+=(const T_DRIVED& g)

operator+=()

template<typename T_DERIVED, typename T_GROUP, unsigned int T_DOF, typename T_SCALAR_TYPE>

void LieAlgebraBase< T_DERIVED, T_GROUP, T_DOF, T_SCALAR_TYPE >::operator+=

(

const T_DERIVED &

g

)

This function has to be implemented by the user. It should perform the vector space addition of the argument g and *this. The operation must be done in place.

operator-()

template<typename T_DERIVED, typename T_GROUP, unsigned int T_DOF, typename T_SCALAR_TYPE>

T_DERIVED LieAlgebraBase< T_DERIVED, T_GROUP, T_DOF, T_SCALAR_TYPE >::operator- ( const T_DERIVED &  g ) const

inline

Adds *this to the vector space addition inverse of g.

static_bracket()

template<typename T_DERIVED, typename T_GROUP, unsigned int T_DOF, typename T_SCALAR_TYPE>

static T_DERIVED LieAlgebraBase< T_DERIVED, T_GROUP, T_DOF, T_SCALAR_TYPE >::static_bracket ( const T_DERIVED &  g1, const T_DERIVED &  g2  )

inlinestatic

Static version of bracket(const T_DERIVED&).

See also

bracket(const T_DERIVED&)

Zero()

template<typename T_DERIVED, typename T_GROUP, unsigned int T_DOF, typename T_SCALAR_TYPE>

static T_DERIVED LieAlgebraBase< T_DERIVED, T_GROUP, T_DOF, T_SCALAR_TYPE >::Zero ( )

static

This function has to be implemented by the user. It should return the Lie algebra representing the identity element for the vector space addition.

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The documentation for this class was generated from the following file:

• Geomi/src/Common/LieAlgebraBase.hpp