Matrix decompositions

Classes to perform matrix decompositions, used to solve linear equations and provide information about matrices. More...

Classes
class	TooN::Cholesky< Size, Precision >
	Decomposes a positive-semidefinite symmetric matrix A (such as a covariance) into L*D*L^T, where L is lower-triangular and D is diagonal. More...
class	TooN::Lapack_Cholesky< Size, Precision >
	Decomposes a positive-semidefinite symmetric matrix A (such as a covariance) into L*L^T, where L is lower-triangular. More...
class	TooN::LU< Size, Precision >
	Performs LU decomposition and back substitutes to solve equations. More...
class	TooN::QR< Rows, Cols, Precision >
	Performs QR decomposition. More...
class	TooN::QR_Lapack< Rows, Cols, Precision >
	Performs QR decomposition. More...
struct	TooN::SQSVD< Size, Precision >
	version of SVD forced to be square princiapally here to allow use in WLS More...
class	TooN::SymEigen< Size, Precision >
	Performs eigen decomposition of a matrix. More...
class	TooN::GR_SVD< M, N, Precision, WANT_U, WANT_V >
	Performs SVD and back substitute to solve equations. More...
class	TooN::SVD< Rows, Cols, Precision >
	Performs SVD and back substitute to solve equations. More...

Functions
template<int R, int C, class Precision , class Base >
void	TooN::gauss_jordan (Matrix< R, C, Precision, Base > &m)
	Perform Gauss-Jordan reduction on m. More...
Matrix< 2 >	TooN::inv (const Matrix< 2 > &m)
	Invert a matrix. More...

Detailed Description

Classes to perform matrix decompositions, used to solve linear equations and provide information about matrices.

Some of these are wrappers around LAPACK, others are built in. provided by the LAPACK library.

Function Documentation

gauss_jordan()

template<int R, int C, class Precision , class Base >

void TooN::gauss_jordan

(

Matrix< R, C, Precision, Base > &

m

)

Perform Gauss-Jordan reduction on m.

If m is of the form \([A | I ]\), then after reduction, m will be \([ I | A^{-1}]\). There is no restriction on the input, in that the matrix augmenting A does not need to be I, or square. The reduction is performed using elementary row operations and partial pivoting.

Parameters

m	The matrix to be reduced.

inv()

Matrix<2> TooN::inv ( const Matrix< 2 > &  m )

inline

Invert a matrix.

For sizes other than 2x2, decompositions provide a suitable solition.

Parameters

m	Matrix to invert.