Isis::LeastSquares Class Reference
[Math]

Generic least square fitting class. More...

#include <LeastSquares.h>

Public Types
enum	SolveMethod { SVD, QRD, SPARSE }
Public Member Functions
	LeastSquares (Isis::BasisFunction &basis, bool sparse=false, int sparseRows=0, int sparseCols=0, bool jigsaw=false)
	Creates a LeastSquares Object.
	~LeastSquares ()
	Destroys the LeastSquares object.
void	AddKnown (const std::vector< double > &input, double expected, double weight=1.0)
	Invoke this method for each set of knowns.
std::vector< double >	GetInput (int row) const
	This method returns the data at the given row.
double	GetExpected (int row) const
	This method returns the expected value at the given row.
int	Rows () const
	This methods returns the number of rows in the matrix.
int	Solve (Isis::LeastSquares::SolveMethod method=SVD)
	After all the data has been registered through AddKnown, invoke this method to solve the system of equations.
double	Evaluate (const std::vector< double > &input)
	Invokes the BasisFunction Evaluate method.
std::vector< double >	Residuals () const
	Returns a vector of residuals (errors).
double	Residual (int i) const
	Returns the ith residual.
void	Weight (int index, double weight)
	Reset the weight for the ith known.
int	Knowns () const
	The number of knowns (or times AddKnown was invoked) linear combination of the variables.
double	GetSigma0 ()
int	GetDegreesOfFreedom ()
void	Reset ()
void	ResetSparse ()
bool	SparseErrorPropagation ()
	Error propagation for sparse least-squares solution.
std::vector< double >	GetEpsilons () const
void	SetParameterWeights (const std::vector< double > weights)
void	SetNumberOfConstrainedParameters (int n)
const gmm::row_matrix < gmm::rsvector< double > > &	GetCovarianceMatrix () const

Detailed Description

Generic least square fitting class.

This class can be used to solved systems of linear equations through least squares fitting. The solution is derived through singular value decomposition or QR decomposition. For example:

$x + y = 3$

$-2x + 3y = 1$

$2x - y = 2$

Is a simple system of equations that can be solved using this class.

   Isis::BasisFunction b("Linear",2,2);
   Isis::LeastSquares lsq(b);

   std::vector<double> one;
   one.push_back(1.0);
   one.push_back(1.0);
   lsq.AddKnown(one,3.0);

   std::vector<double> two;
   two.push_back(-2.0);
   two.push_back(3.0);
   lsq.AddKnown(two,1.0);

   std::vector<double> tre;
   tre.push_back(2.0);
   tre.push_back(-1.0);
   lsq.AddKnown(tre,2.0);

   lsq.Solve();

   double out1 = lsq.Evaluate(one);
   double out2 = lsq.Evaluate(two);
   double out3 = lsq.Evaluate(tre);

See also:: PolynomialUnivariate; PolynomialBiVariate; BasisFunction

Author:: 2004-06-24 Jeff Anderson

Member Enumeration Documentation

enum Isis::LeastSquares::SolveMethod

Enumerator:

SVD	Singular Value Decomposition.
QRD	QR Decomposition.
SPARSE	Sparse.

Constructor & Destructor Documentation

Isis::LeastSquares::LeastSquares	(	Isis::BasisFunction &	basis,
		bool	sparse = `false`,
		int	sparseRows = `0`,
		int	sparseCols = `0`,
		bool	jigsaw = `false`
	)

Creates a LeastSquares Object.

Parameters:

basis

A BasisFunction. This parameter allows for the least squares fitting to be applied to arbitrary equations.

References _FILEINFO_, and Isis::IException::Programmer.

Isis::LeastSquares::~LeastSquares ( )

Destroys the LeastSquares object.

Member Function Documentation

void Isis::LeastSquares::AddKnown	(	const std::vector< double > &	data,
		double	result,
		double	weight = `1.0`
	)

Invoke this method for each set of knowns.

Given our example in the description, we have three knowns and expecteds. They are

$(1,1) = 3$

$(-2,3) = 1$

$(2,-1) = 2$

Parameters:

	data	A vector of knowns.
	result	The expected value for the knowns.
	weight	(Default = 1.0) How strongly to weight this known. Weight less than 1 increases residual for this known, while weight greater than 1 decreases the residual for this known.

Exceptions:

Isis::IException::Programmer

- Number of elements in data does not match basis requirements

References _FILEINFO_, Isis::BasisFunction::Name(), Isis::IException::Programmer, and Isis::BasisFunction::Variables().

Referenced by Isis::SurfaceModel::AddTriplet(), Isis::ReseauDistortionMap::SetFocalPlane(), Isis::VimsGroundMap::SetGround(), Isis::SpicePosition::SetPolynomial(), Isis::VimsSkyMap::SetSky(), Isis::ReseauDistortionMap::SetUndistortedFocalPlane(), Isis::OverlapNormalization::Solve(), and Isis::Affine::Solve().

double Isis::LeastSquares::Evaluate ( const std::vector< double > & data )

Invokes the BasisFunction Evaluate method.

Parameters:

data

The input variables to evaluate.

Returns:: The evaluation for the input variable.

Exceptions:

Isis::IException::Programmer

- Unable to evaluate until a solution has been computed

References _FILEINFO_, Isis::BasisFunction::Evaluate(), and Isis::IException::Programmer.

Referenced by Isis::SurfaceModel::Evaluate(), Isis::ReseauDistortionMap::SetFocalPlane(), Isis::VimsGroundMap::SetGround(), Isis::VimsSkyMap::SetSky(), and Isis::ReseauDistortionMap::SetUndistortedFocalPlane().

const gmm::row_matrix<gmm::rsvector<double> >& Isis::LeastSquares::GetCovarianceMatrix ( ) const [inline]

int Isis::LeastSquares::GetDegreesOfFreedom ( ) [inline]

Referenced by Isis::BundleAdjust::Solve().

std::vector<double> Isis::LeastSquares::GetEpsilons ( ) const [inline]

Referenced by Isis::BundleAdjust::GetSparseParameterCorrections().

double Isis::LeastSquares::GetExpected ( int row ) const

This method returns the expected value at the given row.

Parameters:

row

Returns:: double

References _FILEINFO_, Isis::IException::Programmer, Rows(), and Isis::toString().

std::vector< double > Isis::LeastSquares::GetInput ( int row ) const

This method returns the data at the given row.

Parameters:

row

Returns:: std::vector<double>

References _FILEINFO_, Isis::IException::Programmer, Rows(), and Isis::toString().

double Isis::LeastSquares::GetSigma0 ( ) [inline]

Referenced by Isis::BundleAdjust::Solve().

int Isis::LeastSquares::Knowns ( ) const [inline]

The number of knowns (or times AddKnown was invoked) linear combination of the variables.

Returns:: int The number of knowns

Referenced by Isis::VimsGroundMap::SetGround(), Isis::VimsSkyMap::SetSky(), and Isis::BundleAdjust::Solve().

void Isis::LeastSquares::Reset ( )

Referenced by ResetSparse(), and Isis::BundleAdjust::Solve().

void Isis::LeastSquares::ResetSparse ( ) [inline]

References Reset().

double Isis::LeastSquares::Residual ( int i ) const

Returns the ith residual.

That is, the difference between the evaluation of a known with the solution against the expected value. There is one residual for each time AddKnown was invoked.

Parameters:

i

The number of times AddKnown was invoked to be evaluated.

Returns:: The output value of the residual.

Exceptions:

Isis::IException::Programmer

- Unable to return residuals until a solution has been computed

References _FILEINFO_, and Isis::IException::Programmer.

std::vector< double > Isis::LeastSquares::Residuals ( ) const

Returns a vector of residuals (errors).

That is, the difference between the evaluation of a known with the solution against the expected value.

Returns:: The vector of residuals.

Exceptions:

Isis::IException::Programmer

- Unable to return residuals until a solution has been computed

References _FILEINFO_, and Isis::IException::Programmer.

Referenced by Isis::BundleAdjust::Solve().

int Isis::LeastSquares::Rows ( ) const

This methods returns the number of rows in the matrix.

Returns:: int

Referenced by GetExpected(), GetInput(), and Solve().

void Isis::LeastSquares::SetNumberOfConstrainedParameters ( int n ) [inline]

void Isis::LeastSquares::SetParameterWeights ( const std::vector< double > weights ) [inline]

Referenced by Isis::OverlapNormalization::Solve().

int Isis::LeastSquares::Solve ( Isis::LeastSquares::SolveMethod method = SVD )

After all the data has been registered through AddKnown, invoke this method to solve the system of equations.

You can then use the Evaluate and Residual methods freely.

References _FILEINFO_, QRD, Rows(), SPARSE, SVD, and Isis::IException::Unknown.

Referenced by Isis::ReseauDistortionMap::SetFocalPlane(), Isis::VimsGroundMap::SetGround(), Isis::SpicePosition::SetPolynomial(), Isis::VimsSkyMap::SetSky(), Isis::ReseauDistortionMap::SetUndistortedFocalPlane(), Isis::BundleAdjust::Solve(), Isis::SurfaceModel::Solve(), Isis::OverlapNormalization::Solve(), and Isis::Affine::Solve().

bool Isis::LeastSquares::SparseErrorPropagation ( )

Error propagation for sparse least-squares solution.

Computes the variance-covariance matrix of the parameters. This is the inverse of the normal equations matrix, scaled by the reference variance (also called variance of unit weight, etc).

Referenced by Isis::BundleAdjust::Solve().

void Isis::LeastSquares::Weight	(	int	index,
		double	weight
	)

Reset the weight for the ith known.

This weight will not be used unless the system is resolved using the Solve method.

Parameters:

	index	The position in the array to assign the given weight value
	weight	A weight factor to apply to the ith known. A weight less than one increase the residual for this known while a weight greater than one decrease the residual for this known.

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

src/base/objs/LeastSquares/LeastSquares.h
src/base/objs/LeastSquares/LeastSquares.cpp

Isis::LeastSquares Class Reference [Math]

Public Types

Public Member Functions

Detailed Description

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

Isis::LeastSquares Class Reference
[Math]