simple template expression library for linear algebra More...

Namespaces
	cross_matrix

	euler

Classes
class	_CrossMatrix
	cross-product matrix of a vector More...

class	_Difference
	expression template for difference of two matrix expressions More...

class	_LValue
	expression template for rvalues More...

class	_Normalize
	Expression template presents a view of a matrix where each element is normalized, such that the sum of the elements is 1.0. More...

class	_RValue
	expression template for rvalues More...

class	_RView
	expression template for subset of a matrix expression More...

class	_Scale

class	_Sum
	expression template for sum of two matrix expressions More...

class	_Transpose
	expression template for difference of two matrix expressions More...

class	AxisAngle
	Encodes a rotation in 3-dimensions by an return RView<Scalar, Exp, rows, Exp::COLS>(static_cast<Exp const&>(A), i, 0);axis of rotation and an angle magnitude of rotation about that axis. More...

class	CoordinateAxis
	A 3x1 normal vector with one unity element. More...

class	CoordinateAxisAngle
	An axis angle rotation about a coordinate axis. More...

class	Eye
	A `N x N` matrix expression for the identity matrix. More...

class	LView
	expression template for subset of a matrix expression More...

class	Matrix

class	Quaternion

class	StreamAssignment
	assignment More...

Typedefs
typedef AxisAngle< double >	AxisAngled

typedef AxisAngle< float >	AxisAnglef

typedef CoordinateAxis< double, 0 >	AxisXd

typedef CoordinateAxis< float, 0 >	AxisXf

typedef CoordinateAxis< double, 1 >	AxisYd

typedef CoordinateAxis< float, 1 >	AxisYf

typedef CoordinateAxis< double, 2 >	AxisZd

typedef CoordinateAxis< float, 2 >	AxisZf

typedef CoordinateAxisAngle < double, 0 >	CoordinateAxisAngleXd

typedef CoordinateAxisAngle < float, 0 >	CoordinateAxisAngleXf

typedef CoordinateAxisAngle < double, 1 >	CoordinateAxisAngleYd

typedef CoordinateAxisAngle < float, 1 >	CoordinateAxisAngleYf

typedef CoordinateAxisAngle < double, 2 >	CoordinateAxisAngleZd

typedef CoordinateAxisAngle < float, 2 >	CoordinateAxisAngleZf

typedef Eye< double, 2 >	Eye2d

typedef Eye< float, 2 >	Eye2f

typedef Eye< double, 3 >	Eye3d

typedef Eye< float, 3 >	Eye3f

typedef Eye< double, 4 >	Eye4d

typedef Eye< float, 4 >	Eye4f

typedef int	Index

typedef Matrix< double, 2, 2 >	Matrix2d

typedef Matrix< float, 2, 2 >	Matrix2f

typedef Matrix< double, 3, 3 >	Matrix3d

typedef Matrix< float, 3, 3 >	Matrix3f

typedef Matrix< double, 4, 4 >	Matrix4d

typedef Matrix< float, 4, 4 >	Matrix4f

typedef Quaternion< double >	Quaterniond

typedef Quaternion< float >	Quaternionf

typedef unsigned int	Size

typedef Matrix< double, 2, 1 >	Vector2d

typedef Matrix< float, 2, 1 >	Vector2f

typedef Matrix< double, 3, 1 >	Vector3d

typedef Matrix< float, 3, 1 >	Vector3f

typedef Matrix< double, 4, 1 >	Vector4d

typedef Matrix< float, 4, 1 >	Vector4f

Functions
template<typename Scalar , class Exp >
void	AxisAngleToQuaternion (const fiber::_RValue< Scalar, Exp > &axis, const Scalar angle, Quaternion< Scalar > *q)

template<typename Scalar >
void	AxisAngleToQuaternion (const AxisAngle< Scalar > &axis_angle, Quaternion< Scalar > *q)

template<typename Scalar , class Exp >
void	AxisAngleToRotationMatrix (const AxisAngle< Scalar > &axis_angle, _LValue< Scalar, Exp > *R)

template<int rows, int cols, typename Scalar , class Exp >
LView< Scalar, Exp, rows, cols >	Block (_LValue< Scalar, Exp > &A, int i, int j)

template<typename Scalar , class Exp >
LView< Scalar, Exp, Exp::ROWS_, 1 >	Column (_LValue< Scalar, Exp > &A, int j)

template<int cols, typename Scalar , class Exp >
LView< Scalar, Exp, Exp::ROWS_, cols >	Columns (_LValue< Scalar, Exp > &A, int j)

template<typename Scalar >
Quaternion< Scalar >	Conjugate (Quaternion< Scalar > const &q)

template<typename Scalar , int Axis>
void	CoordinateAxisAngleToQuaternion (const CoordinateAxisAngle< Scalar, Axis > &axis_angle, Quaternion< Scalar > *q)

template<typename Scalar , int Axis, class Exp >
void	CoordinateAxisAngleToRotationMatrix (const CoordinateAxisAngle< Scalar, Axis > &axis_angle, _LValue< Scalar, Exp > *R)

template<typename Scalar , class Exp >
_CrossMatrix< Scalar, Exp >	CrossMatrix (_RValue< Scalar, Exp > const &A)
	cross-product matrix of a vector More...

template<typename Scalar , class Exp1 , class Exp2 >
Scalar	Dot (_RValue< Scalar, Exp1 > const &A, _RValue< Scalar, Exp2 > const &B)
	Dot product of two vectors. More...

template<typename Scalar , int Axis1, int Axis2, int Axis3>
void	EulerAnglesToQuaternion (const euler::Angles< Scalar, Axis1, Axis2, Axis3 > &euler, Quaternion< Scalar > *q)

template<typename Scalar , class Exp >
_RView< Scalar, Exp, Exp::ROWS_, 1 >	GetColumn (_RValue< Scalar, Exp > const &A, int j)

template<int cols, typename Scalar , class Exp >
_RView< Scalar, Exp, Exp::ROWS_, cols >	GetColumns (_RValue< Scalar, Exp > const &A, int j)

template<typename Scalar , class Exp >
_RView< Scalar, Exp, 1, Exp::COLS_ >	GetRow (_RValue< Scalar, Exp > const &A, int i)

template<int rows, typename Scalar , class Exp >
_RView< Scalar, Exp, rows, Exp::COLS_ >	GetRows (_RValue< Scalar, Exp > const &A, int i)

template<typename Scalar , class Exp >
_LValue< Scalar, Exp > &	LValue (_LValue< Scalar, Exp > &exp)
	Explicitly expose _LValue of an expressions, can be used to help the compiler disambiguate overloads. More...

template<typename Scalar , class Exp >
Scalar	Norm (_RValue< Scalar, Exp > const &A)
	Return the 2-norm of a vector. More...

template<typename Scalar , class Exp >
Scalar	Norm (_RValue< Scalar, Exp > const &A, int n)
	Return the n-norm of a vector. More...

template<typename Scalar , class Exp >
_Normalize< Scalar, Exp >	Normalize (_RValue< Scalar, Exp > const &A)
	Prresents a view of a matrix or vector where each element is normalized, such that the sum of the elements is 1.0. More...

template<typename Scalar , class Exp1 , class Exp2 >
Matrix< Scalar, Exp1::ROWS_, Exp2::COLS_ >	operator* (_RValue< Scalar, Exp1 > const &A, _RValue< Scalar, Exp2 > const &B)
	Matrix multiplication. More...

template<typename Scalar , class Exp >
_Scale< Scalar, Exp >	operator* (Scalar s, _RValue< Scalar, Exp > const &A)

template<typename Scalar , class Exp >
_Scale< Scalar, Exp >	operator* (_RValue< Scalar, Exp > const &A, Scalar s)

template<typename Scalar >
Quaternion< Scalar >	operator* (Quaternion< Scalar > const &q_A, Quaternion< Scalar > const &q_B)
	We define quaternion multiplication as in Diebel. More...

template<typename Scalar , class Exp1 , class Exp2 >
_Sum< Scalar, Exp1, Exp2 >	operator+ (_RValue< Scalar, Exp1 > const &A, _RValue< Scalar, Exp2 > const &B)

template<typename Scalar , class Exp1 , class Exp2 >
_Difference< Scalar, Exp1, Exp2 >	operator- (_RValue< Scalar, Exp1 > const &A, _RValue< Scalar, Exp2 > const &B)

template<typename Scalar , class Mat >
std::ostream &	operator<< (std::ostream &out, _RValue< Scalar, Mat > const &M)

template<typename Scalar , class Exp >
void	QuaternionToAxisAngle (const Quaternion< Scalar > &q, fiber::_LValue< Scalar, Exp > axis, Scalar angle)

template<typename Scalar , class Exp >
void	QuaternionToRotationMatrix (const Quaternion< Scalar > &q, fiber::_LValue< Scalar, Exp > *R)

template<typename Scalar , class Exp >
void	RotationMatrixToQuaternion (const fiber::_RValue< Scalar, Exp > &R, Quaternion< Scalar > *q)

template<typename Scalar , class Exp >
LView< Scalar, Exp, 1, Exp::COLS_ >	Row (_LValue< Scalar, Exp > &A, int i)

template<int rows, typename Scalar , class Exp >
LView< Scalar, Exp, rows, Exp::COLS_ >	Rows (_LValue< Scalar, Exp > &A, int i)

template<typename Scalar , class Exp >
const _RValue< Scalar, Exp > &	RValue (const _RValue< Scalar, Exp > &exp)
	Explicitly expose _RValue of an expressions, can be used to help the compiler disambiguate overloads. More...

template<typename Scalar , class Exp >
Scalar	SquaredNorm (_RValue< Scalar, Exp > const &A)
	Return the squared 2-norm of a vector. More...

template<typename Scalar , class Exp >
_Transpose< Scalar, Exp >	Transpose (_RValue< Scalar, Exp > const &A)

template<int rows, int cols, typename Scalar , class Exp >
_RView< Scalar, Exp, rows, cols >	View (_RValue< Scalar, Exp > const &A, Index i, Index j)

Detailed Description

simple template expression library for linear algebra

Typedef Documentation

typedef AxisAngle<double> fiber::AxisAngled

Definition at line 135 of file axis_angle.h.

typedef AxisAngle<float> fiber::AxisAnglef

Definition at line 136 of file axis_angle.h.

typedef CoordinateAxis<double,0> fiber::AxisXd

Definition at line 138 of file axis_angle.h.

typedef CoordinateAxis<float,0> fiber::AxisXf

Definition at line 142 of file axis_angle.h.

typedef CoordinateAxis<double,1> fiber::AxisYd

Definition at line 139 of file axis_angle.h.

typedef CoordinateAxis<float,1> fiber::AxisYf

Definition at line 143 of file axis_angle.h.

typedef CoordinateAxis<double,2> fiber::AxisZd

Definition at line 140 of file axis_angle.h.

typedef CoordinateAxis<float,2> fiber::AxisZf

Definition at line 144 of file axis_angle.h.

typedef CoordinateAxisAngle<double,0> fiber::CoordinateAxisAngleXd

Definition at line 146 of file axis_angle.h.

typedef CoordinateAxisAngle<float,0> fiber::CoordinateAxisAngleXf

Definition at line 150 of file axis_angle.h.

typedef CoordinateAxisAngle<double,1> fiber::CoordinateAxisAngleYd

Definition at line 147 of file axis_angle.h.

typedef CoordinateAxisAngle<float,1> fiber::CoordinateAxisAngleYf

Definition at line 151 of file axis_angle.h.

typedef CoordinateAxisAngle<double,2> fiber::CoordinateAxisAngleZd

Definition at line 148 of file axis_angle.h.

typedef CoordinateAxisAngle<float,2> fiber::CoordinateAxisAngleZf

Definition at line 152 of file axis_angle.h.

typedef Eye<double,2> fiber::Eye2d

Definition at line 60 of file identity.h.

typedef Eye<float,2> fiber::Eye2f

Definition at line 64 of file identity.h.

typedef Eye<double,3> fiber::Eye3d

Definition at line 61 of file identity.h.

typedef Eye<float,3> fiber::Eye3f

Definition at line 65 of file identity.h.

typedef Eye<double,4> fiber::Eye4d

Definition at line 62 of file identity.h.

typedef Eye<float,4> fiber::Eye4f

Definition at line 66 of file identity.h.

typedef int fiber::Index

Definition at line 31 of file fiber.h.

typedef Matrix<double,2,2> fiber::Matrix2d

Definition at line 140 of file matrix.h.

typedef Matrix<float,2,2> fiber::Matrix2f

Definition at line 148 of file matrix.h.

typedef Matrix<double,3,3> fiber::Matrix3d

Definition at line 141 of file matrix.h.

typedef Matrix<float,3,3> fiber::Matrix3f

Definition at line 149 of file matrix.h.

typedef Matrix<double,4,4> fiber::Matrix4d

Definition at line 142 of file matrix.h.

typedef Matrix<float,4,4> fiber::Matrix4f

Definition at line 150 of file matrix.h.

typedef Quaternion<double> fiber::Quaterniond

Definition at line 182 of file quaternion.h.

typedef Quaternion<float> fiber::Quaternionf

Definition at line 183 of file quaternion.h.

typedef unsigned int fiber::Size

Definition at line 32 of file fiber.h.

typedef Matrix<double,2,1> fiber::Vector2d

Definition at line 144 of file matrix.h.

typedef Matrix<float,2,1> fiber::Vector2f

Definition at line 152 of file matrix.h.

typedef Matrix<double,3,1> fiber::Vector3d

Definition at line 145 of file matrix.h.

typedef Matrix<float,3,1> fiber::Vector3f

Definition at line 153 of file matrix.h.

typedef Matrix<double,4,1> fiber::Vector4d

Definition at line 146 of file matrix.h.

typedef Matrix<float,4,1> fiber::Vector4f

Definition at line 154 of file matrix.h.

Function Documentation

template<typename Scalar , class Exp >

void fiber::AxisAngleToQuaternion	(	const fiber::_RValue< Scalar, Exp > &	axis,
		const Scalar	angle,
		Quaternion< Scalar > *	q
	)

We follow the counter-clockwise right hand convention. For example, if r is a vector in the x-y plane and the axis of rotation is the z-axis, then | q * [0 r]' * q |(1-3) is a vector in the x-y plane corresponding to r rotated by the angle, theta, in the counter-clockwise direction.

Definition at line 50 of file rotation_conversions.h.

template<typename Scalar >

void fiber::AxisAngleToQuaternion	(	const AxisAngle< Scalar > &	axis_angle,
		Quaternion< Scalar > *	q
	)

We follow the counter-clockwise right hand convention. For example, if r is a vector in the x-y plane and the axis of rotation is the z-axis, then | q * [0 r]' * q |(1-3) is a vector in the x-y plane corresponding to r rotated by the angle, theta, in the counter-clockwise direction.

Definition at line 68 of file rotation_conversions.h.

template<typename Scalar , class Exp >

void fiber::AxisAngleToRotationMatrix	(	const AxisAngle< Scalar > &	axis_angle,
		_LValue< Scalar, Exp > *	R
	)

We follow the counter-clockwise right hand convention. For example, if r is a vector in the x-y plane and the axis of rotation is the z-axis, then R*r is a vector in the x-y plane corresponding to r rotated by the angle, theta, in the counter-clockwise direction.

Definition at line 80 of file rotation_conversions.h.

template<int rows, int cols, typename Scalar , class Exp >

LView<Scalar, Exp, rows, cols> fiber::Block	(	_LValue< Scalar, Exp > &	A,
		int	i,
		int	j
	)

inline

Definition at line 161 of file view.h.

template<typename Scalar , class Exp >

LView<Scalar, Exp, Exp::ROWS_, 1> fiber::Column	(	_LValue< Scalar, Exp > &	A,
		int	j
	)

inline

Definition at line 178 of file view.h.

template<int cols, typename Scalar , class Exp >

LView<Scalar, Exp, Exp::ROWS_, cols> fiber::Columns	(	_LValue< Scalar, Exp > &	A,
		int	j
	)

inline

Definition at line 184 of file view.h.

template<typename Scalar >

Quaternion<Scalar> fiber::Conjugate ( Quaternion< Scalar > const & q )

inline

Definition at line 150 of file quaternion.h.

template<typename Scalar , int Axis>

void fiber::CoordinateAxisAngleToQuaternion	(	const CoordinateAxisAngle< Scalar, Axis > &	axis_angle,
		Quaternion< Scalar > *	q
	)

We follow the counter-clockwise right hand convention. For example, if r is a vector in the x-y plane and the axis of rotation is the z-axis, then | q * [0 r]' * q |(1-3) is a vector in the x-y plane corresponding to r rotated by the angle, theta, in the counter-clockwise direction.

Definition at line 97 of file rotation_conversions.h.

template<typename Scalar , int Axis, class Exp >

void fiber::CoordinateAxisAngleToRotationMatrix	(	const CoordinateAxisAngle< Scalar, Axis > &	axis_angle,
		_LValue< Scalar, Exp > *	R
	)

We follow the counter-clockwise right hand convention. For example, if r is a vector in the x-y plane and the axis of rotation is the z-axis, then R*r is a vector in the x-y plane corresponding to r rotated by the angle, theta, in the counter-clockwise direction.

Definition at line 116 of file rotation_conversions.h.

template<typename Scalar , class Exp >

_CrossMatrix<Scalar, Exp> fiber::CrossMatrix ( _RValue< Scalar, Exp > const & A )

inline

cross-product matrix of a vector

Given a vector v, the CrossMatrix of v is the skew symmetric 3x3 matrix given by: | 0 -v[2] v[1] | | v[2] 0 -v[0] | | -v[1] v[0] 0 |

Definition at line 101 of file cross_matrix.h.

template<typename Scalar , class Exp1 , class Exp2 >

Scalar fiber::Dot	(	_RValue< Scalar, Exp1 > const &	A,
		_RValue< Scalar, Exp2 > const &	B
	)

inline

Dot product of two vectors.

Definition at line 50 of file product.h.

template<typename Scalar , int Axis1, int Axis2, int Axis3>

void fiber::EulerAnglesToQuaternion	(	const euler::Angles< Scalar, Axis1, Axis2, Axis3 > &	euler,
		Quaternion< Scalar > *	q
	)

Definition at line 305 of file rotation_conversions.h.

template<typename Scalar , class Exp >

_RView<Scalar, Exp, Exp::ROWS_, 1> fiber::GetColumn	(	_RValue< Scalar, Exp > const &	A,
		int	j
	)

inline

Definition at line 89 of file view.h.

template<int cols, typename Scalar , class Exp >

_RView<Scalar, Exp, Exp::ROWS_, cols> fiber::GetColumns	(	_RValue< Scalar, Exp > const &	A,
		int	j
	)

inline

Definition at line 95 of file view.h.

template<typename Scalar , class Exp >

_RView<Scalar, Exp, 1, Exp::COLS_> fiber::GetRow	(	_RValue< Scalar, Exp > const &	A,
		int	i
	)

inline

Definition at line 76 of file view.h.

template<int rows, typename Scalar , class Exp >

_RView<Scalar, Exp, rows, Exp::COLS_> fiber::GetRows	(	_RValue< Scalar, Exp > const &	A,
		int	i
	)

inline

Definition at line 82 of file view.h.

template<typename Scalar , class Exp >

_LValue<Scalar, Exp>& fiber::LValue ( _LValue< Scalar, Exp > & exp )

Explicitly expose _LValue of an expressions, can be used to help the compiler disambiguate overloads.

Definition at line 77 of file lvalue.h.

template<typename Scalar , class Exp >

Scalar fiber::Norm ( _RValue< Scalar, Exp > const & A )

inline

Return the 2-norm of a vector.

Definition at line 41 of file normalize.h.

template<typename Scalar , class Exp >

Scalar fiber::Norm	(	_RValue< Scalar, Exp > const &	A,
		int	n
	)

inline

Return the n-norm of a vector.

Definition at line 47 of file normalize.h.

template<typename Scalar , class Exp >

_Normalize<Scalar, Exp> fiber::Normalize ( _RValue< Scalar, Exp > const & A )

inline

Prresents a view of a matrix or vector where each element is normalized, such that the sum of the elements is 1.0.

Definition at line 87 of file normalize.h.

template<typename Scalar , class Exp1 , class Exp2 >

Matrix<Scalar, Exp1::ROWS_, Exp2::COLS_> fiber::operator*	(	_RValue< Scalar, Exp1 > const &	A,
		_RValue< Scalar, Exp2 > const &	B
	)

inline

Matrix multiplication.

Definition at line 34 of file product.h.

template<typename Scalar , class Exp >

_Scale<Scalar, Exp> fiber::operator*	(	Scalar	s,
		_RValue< Scalar, Exp > const &	A
	)

inline

Definition at line 54 of file scale.h.

template<typename Scalar , class Exp >

_Scale<Scalar, Exp> fiber::operator*	(	_RValue< Scalar, Exp > const &	A,
		Scalar	s
	)

inline

Definition at line 59 of file scale.h.

template<typename Scalar >

Quaternion<Scalar> fiber::operator*	(	Quaternion< Scalar > const &	q_A,
		Quaternion< Scalar > const &	q_B
	)

inline

We define quaternion multiplication as in Diebel.

The quaternion multiplication q*p is equivalent to the matrix left-multiply of Q(q)*p where Q(q) =

*   | q0 -q1 -q2 -q3 |
*   | q1  q0 -q3  q2 |
*   | q2  q3  q0 -q1 |
*   | q3 -q2  q1  q0 |
*

Definition at line 166 of file quaternion.h.

template<typename Scalar , class Exp1 , class Exp2 >

_Sum<Scalar, Exp1, Exp2> fiber::operator+	(	_RValue< Scalar, Exp1 > const &	A,
		_RValue< Scalar, Exp2 > const &	B
	)

inline

Definition at line 65 of file sum.h.

template<typename Scalar , class Exp1 , class Exp2 >

_Difference<Scalar, Exp1, Exp2> fiber::operator-	(	_RValue< Scalar, Exp1 > const &	A,
		_RValue< Scalar, Exp2 > const &	B
	)

inline

Definition at line 65 of file difference.h.

template<typename Scalar , class Mat >

std::ostream& fiber::operator<<	(	std::ostream &	out,
		_RValue< Scalar, Mat > const &	M
	)

Definition at line 37 of file ostream.h.

template<typename Scalar , class Exp >

void fiber::QuaternionToAxisAngle	(	const Quaternion< Scalar > &	q,
		fiber::_LValue< Scalar, Exp > *	axis,
		Scalar *	angle
	)

TODO(bialkowski): need scalar traits to determine this threshold

Definition at line 137 of file rotation_conversions.h.

template<typename Scalar , class Exp >

void fiber::QuaternionToRotationMatrix	(	const Quaternion< Scalar > &	q,
		fiber::_LValue< Scalar, Exp > *	R
	)

Definition at line 152 of file rotation_conversions.h.

template<typename Scalar , class Exp >

void fiber::RotationMatrixToQuaternion	(	const fiber::_RValue< Scalar, Exp > &	R,
		Quaternion< Scalar > *	q
	)

Definition at line 172 of file rotation_conversions.h.

template<typename Scalar , class Exp >

LView<Scalar, Exp, 1, Exp::COLS_> fiber::Row	(	_LValue< Scalar, Exp > &	A,
		int	i
	)

inline

Definition at line 167 of file view.h.

template<int rows, typename Scalar , class Exp >

LView<Scalar, Exp, rows, Exp::COLS_> fiber::Rows	(	_LValue< Scalar, Exp > &	A,
		int	i
	)

inline

Definition at line 172 of file view.h.

template<typename Scalar , class Exp >

const _RValue<Scalar, Exp>& fiber::RValue ( const _RValue< Scalar, Exp > & exp )

Explicitly expose _RValue of an expressions, can be used to help the compiler disambiguate overloads.

Definition at line 51 of file rvalue.h.

template<typename Scalar , class Exp >

Scalar fiber::SquaredNorm ( _RValue< Scalar, Exp > const & A )

inline

Return the squared 2-norm of a vector.

Definition at line 35 of file normalize.h.

template<typename Scalar , class Exp >

_Transpose<Scalar, Exp> fiber::Transpose ( _RValue< Scalar, Exp > const & A )

inline

Definition at line 54 of file transpose.h.

template<int rows, int cols, typename Scalar , class Exp >

_RView<Scalar, Exp, rows, cols> fiber::View	(	_RValue< Scalar, Exp > const &	A,
		Index	i,
		Index	j
	)

inline

Definition at line 70 of file view.h.

Namespaces

Classes

Typedefs

Functions

Detailed Description

Typedef Documentation

Function Documentation