Matrix decompositions

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

Classes
class	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	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	LU< Size, Precision >
	Performs LU decomposition and back substitutes to solve equations. More...
class	QR< Rows, Cols, Precision >
	Performs QR decomposition. More...
class	QR_Lapack< Rows, Cols, Precision >
	Performs QR decomposition. More...
struct	SQSVD< Size, Precision >
	version of SVD forced to be square princiapally here to allow use in WLS More...
class	SymEigen< Size, Precision >
	Performs eigen decomposition of a matrix. More...
class	GR_SVD< M, N, Precision, WANT_U, WANT_V >
	Performs SVD and back substitute to solve equations. More...
class	SVD< Rows, Cols, Precision >
	Performs SVD and back substitute to solve equations. More...
Functions
template<int R, int C, class Precision , class Base >
void	gauss_jordan (Matrix< R, C, Precision, Base > &m)
Matrix< 2 >	inv (const Matrix< 2 > &m)

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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.

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Function Documentation

void TooN::gauss_jordan

(

Matrix< R, C, Precision, Base > &

m

)

Perform Gauss-Jordan reduction on m.

If m is of the form , then after reduction, m will be . 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.

References Matrix< Rows, Cols, Precision, Layout >::num_cols(), and Matrix< Rows, Cols, Precision, Layout >::num_rows().

Matrix<2> TooN::inv

(

const Matrix< 2 > &

m

)

Invert a matrix.

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

Parameters:

m	Matrix to invert.

References TooN::Data().