Mimas linear algebra operations.
[Linear Algebra]

Collaboration diagram for Mimas linear algebra operations.:

This group contains Mimas operations, for vectors and matrices. More...

Functions
template<typename T>
boost::numeric::ublas::vector< T >	mimas::unit (const boost::numeric::ublas::vector< T > &x)
	Compute unit vector.
template<typename T>
T	mimas::scalar_cross_product (const boost::numeric::ublas::vector< T > &a, const boost::numeric::ublas::vector< T > &b)
	Scalar cross product.
template<typename T>
angle	mimas::getAngle (const boost::numeric::ublas::vector< T > &a, const boost::numeric::ublas::vector< T > &b)
	Compute angle between two 2-dimensional vectors.
template<typename T>
boost::numeric::ublas::vector< T >	mimas::rotate (const boost::numeric::ublas::vector< T > &v, const angle &a)
	2-dimensional rotation in the mathematical direction.
template<typename T>
boost::numeric::ublas::vector< T >	mimas::crossProduct (boost::numeric::ublas::vector< T > &a, boost::numeric::ublas::vector< T > &b)
	Cross product for 3-dimensional vectors.
template<typename T>
boost::numeric::ublas::vector< T >	mimas::rodrigues (boost::numeric::ublas::vector< T > const &u, boost::numeric::ublas::vector< T > const &v, double angle)
	Rodrigues' rotation formula.
template<typename T>
double	mimas::determinant (boost::numeric::ublas::matrix< T > const &M)
	Determinant of a matrix using the LU factorization.

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Detailed Description

This group contains Mimas operations, for vectors and matrices.

All functionality provided by mimas::vector formerly, should be provided here.

Author:

Stuart Meikle (stu@stumeikle.org)

Date:

Sat Mar 1 2003 BST

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Function Documentation

template<typename T>

boost::numeric::ublas::vector< T > mimas::crossProduct	(	boost::numeric::ublas::vector< T > &	a,
		boost::numeric::ublas::vector< T > &	b
	)

Cross product for 3-dimensional vectors.

Compute

Parameters:

	a	first vector.
	b	second vector.

Returns:

cross product of a and b.

template<typename T>

double mimas::determinant

(

boost::numeric::ublas::matrix< T > const &

M

)

Determinant of a matrix using the LU factorization.

The decomposition used is the one provided by uBLAS.

Parameters:

M

the matrix to compute the determinant of.

Author:

Julien Faucher (faucherj@gmail.com)

template<typename T>

angle mimas::getAngle	(	const boost::numeric::ublas::vector< T > &	a,
		const boost::numeric::ublas::vector< T > &	b
	)

Compute angle between two 2-dimensional vectors.

Parameters:

	a	first vector.
	b	second vector.

Returns:

angle to rotate a onto b

Definition at line 64 of file linalg.h.

template<typename T>

boost::numeric::ublas::vector< T > mimas::rodrigues	(	boost::numeric::ublas::vector< T > const &	u,
		boost::numeric::ublas::vector< T > const &	v,
		double	angle
	)

Rodrigues' rotation formula.

Computes the rotation of a point around an axis of given vector, and passing through the origin.

Parameters:

	u	the axis of the rotation (must be a unit 3-D vector)
	v	the vector to rotate
	angle	the angle of the rotation

Author:

Julien Faucher (faucherj@gmail.com)

template<typename T>

boost::numeric::ublas::vector< T > mimas::rotate	(	const boost::numeric::ublas::vector< T > &	v,
		const angle &	a
	)

2-dimensional rotation in the mathematical direction.

Attention! The direction of rotation is oposite to the one of vector::rotate.

template<typename T>

T mimas::scalar_cross_product	(	const boost::numeric::ublas::vector< T > &	a,
		const boost::numeric::ublas::vector< T > &	b
	)

Scalar cross product.

The scalar cross product for 2-dimensional vectors is . It is rotational invariant.

For scalar product see boost::inner_prod.

Parameters:

	a	first vector.
	b	second vector.

Definition at line 51 of file linalg.h.

template<typename T>

boost::numeric::ublas::vector< T > mimas::unit

(

const boost::numeric::ublas::vector< T > &

x

)

Compute unit vector.

Compute unit vector .

Parameters:

x

input vector (non-zero).

Returns:

Vector scaled to length 1.

Definition at line 37 of file linalg.h.

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