cvr::linearLeastSquares Class Reference
[Linear Algebra]

#include <cvrLinearLeastSquares.h>

Inheritance diagram for cvr::linearLeastSquares:

Collaboration diagram for cvr::linearLeastSquares:

List of all members.

Classes

class parameters

The parameters for the class linearLeastSquares. More...

Public Types

enum eAlgorithm { QR, CompleteFactorization, SVD, DCSVD }

Public Member Functions

linearLeastSquares ()

linearLeastSquares (const parameters &par)

linearLeastSquares (const linearLeastSquares &other)

virtual ~linearLeastSquares ()

bool apply (const fmatrix &A, const fvector &b, fvector &x) const

bool apply (const dmatrix &A, const dvector &b, dvector &x) const

bool apply (const fmatrix &A, const fmatrix &b, fmatrix &x) const

bool apply (const dmatrix &A, const dmatrix &b, dmatrix &x) const

linearLeastSquares & copy (const linearLeastSquares &other)

linearLeastSquares & operator= (const linearLeastSquares &other)

virtual const std::string & name () const

virtual linearLeastSquares * clone () const

virtual linearLeastSquares * newInstance () const

const parameters & getParameters () const

Detailed Description

Class linearLeastSquares.

Solving the linear least squares problem means to find a solution $x$ for

$A x = b$

by minimizing the Euclidean norm squared of the residual $Ax-b$ . Here $A$ is a m x n matrix, with m>n, $x$ is an n-dimensional vector, and $b$ is a m-dimensional vector.

This class is usually used to solve an over-determined system of linear equations, where there is more equations than variables. If the LAPACK library is used, this method can also be employed to solve under-determined system, choosing the solution of minimal norm.

If LAPACK is enabled, the functor provides several algorithms for the same task, which vary in speed and robustness against the ill-conditionness of the matrix A. Please refer to the LAPACK documentation for more details:

QR: uses the QR (or LQ) decomposition of the matrix A. This method can be employed if and only if the matrix A has full rank.
CompleteFactorization: performs a complete orthogonal factorization
SVD: uses a singular value decomposition. This is the recomended method if the matrix A is ill-conditioned, and the only one used if LAPACK is not found.
DCSVD: uses a divide-and-conquer singular value decomposition.

See also:: linearLeastSquares::parameters.

Member Enumeration Documentation

enum cvr::linearLeastSquares::eAlgorithm

Enumeration for the algorithms available.

Enumerator:

QR	QR decomposition: slower but more robust.
CompleteFactorization	Complete Orthogonal Factorization.
SVD	Singular Value Decomposition: slowest but works even with ill-conditioned matrices.
DCSVD	Divide-and-conquer singular value decomposition.

Constructor & Destructor Documentation

cvr::linearLeastSquares::linearLeastSquares ( )

Default constructor.

cvr::linearLeastSquares::linearLeastSquares ( const parameters & par )

Construct a functor using the given parameters.

cvr::linearLeastSquares::linearLeastSquares ( const linearLeastSquares & other )

Copy constructor.

Parameters:

other

the object to be copied

virtual cvr::linearLeastSquares::~linearLeastSquares ( ) [virtual]

Destructor.

Member Function Documentation

bool cvr::linearLeastSquares::apply	(	const dmatrix &	A,
		const dmatrix &	b,
		dmatrix &	x
	)			const

Find the solution $x$ for

$A x = b$

.

Parameters:

	A	matrix A
	b	each column is a vector b
	x	each column is a vector x where the solution is stored for the corresponding column in b.

The dimension of b and the number of rows of A must be identical. The resulting dimension of x will be identical to the number of columns of A.

The internal state of the class will store the decomposition of the matrix A, so that the other apply methods with other b vectors can be used.

Returns:: true if apply successful or false otherwise.

bool cvr::linearLeastSquares::apply	(	const fmatrix &	A,
		const fmatrix &	b,
		fmatrix &	x
	)			const

Find the solution $x$ for

$A x = b$

.

Parameters:

	A	matrix A
	b	each column is a vector b
	x	each column is a vector x where the solution is stored for the corresponding column in b.

The dimension of b and the number of rows of A must be identical. The resulting dimension of x will be identical to the number of columns of A.

The internal state of the class will store the decomposition of the matrix A, so that the other apply methods with other b vectors can be used.

Returns:: true if apply successful or false otherwise.

bool cvr::linearLeastSquares::apply	(	const dmatrix &	A,
		const dvector &	b,
		dvector &	x
	)			const

Find the solution $x$ for

$A x = b$

.

Parameters:

	A	matrix A
	b	vector b
	x	vector x where the solution is stored.

The dimension of b and the number of rows of A must be identical. The resulting dimension of x will be identical to the number of columns of A.

The internal state of the class will store the decomposition of the matrix A, so that the other apply methods with other b vectors can be used.

Returns:: true if apply successful or false otherwise.

bool cvr::linearLeastSquares::apply	(	const fmatrix &	A,
		const fvector &	b,
		fvector &	x
	)			const

Find the solution $x$ for

$A x = b$

.

Parameters:

	A	matrix A
	b	vector b
	x	vector x where the solution is stored.

The dimension of b and the number of rows of A must be identical. The resulting dimension of x will be identical to the number of columns of A.

The internal state of the class will store the decomposition of the matrix A, so that the other apply methods with other b vectors can be used.

Returns:: true if apply successful or false otherwise.

virtual linearLeastSquares* cvr::linearLeastSquares::clone ( ) const [virtual]

Returns a pointer to a clone of this functor.

Implements cvr::functor.

linearLeastSquares& cvr::linearLeastSquares::copy ( const linearLeastSquares & other )

Copy data of "other" functor.

Parameters:

other

the functor to be copied

Returns:: a reference to this functor object

const parameters& cvr::linearLeastSquares::getParameters ( ) const

Returns used parameters.

Reimplemented from cvr::linearAlgebraFunctor.

virtual const std::string& cvr::linearLeastSquares::name ( ) const [virtual]

Returns the complete name of the functor class.

Implements cvr::functor.

virtual linearLeastSquares* cvr::linearLeastSquares::newInstance ( ) const [virtual]

Returns a pointer to a new instance of this functor.

Implements cvr::functor.

linearLeastSquares& cvr::linearLeastSquares::operator= ( const linearLeastSquares & other )

Alias for copy member.

Parameters:

other

the functor to be copied

Returns:: a reference to this functor object

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

cvrLinearLeastSquares.h


Classes
class	parameters
	The parameters for the class linearLeastSquares. More...
Public Types
enum	eAlgorithm { QR, CompleteFactorization, SVD, DCSVD }
Public Member Functions
	linearLeastSquares ()
	linearLeastSquares (const parameters &par)
	linearLeastSquares (const linearLeastSquares &other)
virtual	~linearLeastSquares ()
bool	apply (const fmatrix &A, const fvector &b, fvector &x) const
bool	apply (const dmatrix &A, const dvector &b, dvector &x) const
bool	apply (const fmatrix &A, const fmatrix &b, fmatrix &x) const
bool	apply (const dmatrix &A, const dmatrix &b, dmatrix &x) const
linearLeastSquares &	copy (const linearLeastSquares &other)
linearLeastSquares &	operator= (const linearLeastSquares &other)
virtual const std::string &	name () const
virtual linearLeastSquares *	clone () const
virtual linearLeastSquares *	newInstance () const
const parameters &	getParameters () const

cvr::linearLeastSquares Class Reference [Linear Algebra]

Classes

Public Types

Public Member Functions

Detailed Description

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

cvr::linearLeastSquares Class Reference
[Linear Algebra]