Class for linear least-squares fit. More...

#include <LinearFit.h>

Inheritance diagram for casacore::LinearFit< T >:

Public Member Functions
	LinearFit ()
	Create a fitter: the normal way to generate a fitter object. More...

	LinearFit (const LinearFit &other)
	Copy constructor (deep copy) More...

LinearFit &	operator= (const LinearFit &other)
	Assignment (deep copy) More...

virtual	~LinearFit ()
	Destructor. More...

Public Member Functions inherited from casacore::GenericL2Fit< T >
	GenericL2Fit ()
	Create a fitter: the normal way to generate a fitter object. More...

	GenericL2Fit (const GenericL2Fit &other)
	Copy constructor (deep copy) More...

GenericL2Fit &	operator= (const GenericL2Fit &other)
	Assignment (deep copy) More...

virtual	~GenericL2Fit ()
	Destructor. More...

template<class U >
void	setFunction (const Function< U, U > &function)
	Sets the function to be fitted. More...

template<class U >
Bool	setConstraint (const uInt n, const Function< U, U > &function, const Vector< typename FunctionTraits< T >::BaseType > &x, const typename FunctionTraits< T >::BaseType y=typename FunctionTraits< T >::BaseType(0))
	Set the possible constraint functions. More...

Bool	setConstraint (const uInt n, const Vector< typename FunctionTraits< T >::BaseType > &x, const typename FunctionTraits< T >::BaseType y=typename FunctionTraits< T >::BaseType(0))

Bool	setConstraint (const uInt n, const typename FunctionTraits< T >::BaseType y=typename FunctionTraits< T >::BaseType(0))

Bool	addConstraint (const Function< typename FunctionTraits< T >::DiffType, typename FunctionTraits< T >::DiffType > &function, const Vector< typename FunctionTraits< T >::BaseType > &x, const typename FunctionTraits< T >::BaseType y=typename FunctionTraits< T >::BaseType(0))

Bool	addConstraint (const Vector< typename FunctionTraits< T >::BaseType > &x, const typename FunctionTraits< T >::BaseType y=typename FunctionTraits< T >::BaseType(0))

Bool	addConstraint (const typename FunctionTraits< T >::BaseType y=typename FunctionTraits< T >::BaseType(0))

void	setCollinearity (const Double cln)
	Set the collinearity factor as the square of the sine of the minimum angle allowed between input vectors (default zero for non-SVD, 1e-8 for SVD) More...

void	asWeight (const Bool aswgt)
	Set sigma values to be interpreted as weight (i.e. More...

void	asSVD (const Bool svd)
	Set the use of SVD or not (default). More...

Function< typename FunctionTraits< T >::DiffType, typename FunctionTraits< T > ::DiffType > *	fittedFunction ()
	Return a pointer to the function being fitted. More...

const Function< typename FunctionTraits< T >::DiffType, typename FunctionTraits< T > ::DiffType > *	fittedFunction () const

uInt	fittedNumber () const
	Return the number of fitted parameters. More...

uInt	NConstraints ()
	Return the number of constraints, and pointers to constraint functions. More...

Function< typename FunctionTraits< T >::DiffType, typename FunctionTraits< T > ::DiffType > *	getConstraint (const uInt n)

Vector< typename LSQTraits < typename FunctionTraits< T > ::BaseType >::base >	getSVDConstraint (uInt n)
	Return the nth constraint equation derived from SVD Note that the number present will be given by `getDeficiency()` More...

void	setParameterValues (const Vector< typename FunctionTraits< T >::BaseType > &parms)
	Set the parameter values. More...

void	setMaskedParameterValues (const Vector< typename FunctionTraits< T >::BaseType > &parms)

Vector< typename FunctionTraits< T >::BaseType >	fit (const Vector< typename FunctionTraits< T >::BaseType > &x, const Vector< typename FunctionTraits< T >::BaseType > &y, const Vector< typename FunctionTraits< T >::BaseType > &sigma, const Vector< Bool > *const mask=0)
	Fit the function to the data. More...

Vector< typename FunctionTraits< T >::BaseType >	fit (const Matrix< typename FunctionTraits< T >::BaseType > &x, const Vector< typename FunctionTraits< T >::BaseType > &y, const Vector< typename FunctionTraits< T >::BaseType > &sigma, const Vector< Bool > *const mask=0)

Vector< typename FunctionTraits< T >::BaseType >	fit (const Vector< typename FunctionTraits< T >::BaseType > &x, const Vector< typename FunctionTraits< T >::BaseType > &y, const Vector< Bool > *const mask=0)

Vector< typename FunctionTraits< T >::BaseType >	fit (const Matrix< typename FunctionTraits< T >::BaseType > &x, const Vector< typename FunctionTraits< T >::BaseType > &y, const Vector< Bool > *const mask=0)

Vector< typename FunctionTraits< T >::BaseType >	fit (const Vector< Bool > *const mask=0)

Bool	fit (Vector< typename FunctionTraits< T >::BaseType > &sol, const Vector< typename FunctionTraits< T >::BaseType > &x, const Vector< typename FunctionTraits< T >::BaseType > &y, const Vector< typename FunctionTraits< T >::BaseType > &sigma, const Vector< Bool > *const mask=0)

Bool	fit (Vector< typename FunctionTraits< T >::BaseType > &sol, const Matrix< typename FunctionTraits< T >::BaseType > &x, const Vector< typename FunctionTraits< T >::BaseType > &y, const Vector< typename FunctionTraits< T >::BaseType > &sigma, const Vector< Bool > *const mask=0)

Bool	fit (Vector< typename FunctionTraits< T >::BaseType > &sol, const Vector< typename FunctionTraits< T >::BaseType > &x, const Vector< typename FunctionTraits< T >::BaseType > &y, const typename FunctionTraits< T >::BaseType &sigma, const Vector< Bool > *const mask=0)

Bool	fit (Vector< typename FunctionTraits< T >::BaseType > &sol, const Matrix< typename FunctionTraits< T >::BaseType > &x, const Vector< typename FunctionTraits< T >::BaseType > &y, const typename FunctionTraits< T >::BaseType &sigma, const Vector< Bool > *const mask=0)

Bool	fit (Vector< typename FunctionTraits< T >::BaseType > &sol, const Vector< Bool > *const mask=0)

Double	chiSquare () const
	Obtain the chi squared. More...

const Vector< typename FunctionTraits< T >::BaseType > &	errors () const
	Get the errors on the solved values. More...

Bool	errors (Vector< typename FunctionTraits< T >::BaseType > &err) const

Matrix< Double >	compuCovariance ()
	Get covariance matrix. More...

void	compuCovariance (Matrix< Double > &cov)

void	buildNormalMatrix (const Vector< typename FunctionTraits< T >::BaseType > &x, const Vector< typename FunctionTraits< T >::BaseType > &y, const Vector< typename FunctionTraits< T >::BaseType > &sigma, const Vector< Bool > *const mask=0)
	Generate the normal equations by one or more calls to the buildNormalMatrix(), before calling a fit() without arguments. More...

void	buildNormalMatrix (const Matrix< typename FunctionTraits< T >::BaseType > &x, const Vector< typename FunctionTraits< T >::BaseType > &y, const Vector< typename FunctionTraits< T >::BaseType > &sigma, const Vector< Bool > *const mask=0)

void	buildNormalMatrix (const Vector< typename FunctionTraits< T >::BaseType > &x, const Vector< typename FunctionTraits< T >::BaseType > &y, const Vector< Bool > *const mask=0)

void	buildNormalMatrix (const Matrix< typename FunctionTraits< T >::BaseType > &x, const Vector< typename FunctionTraits< T >::BaseType > &y, const Vector< Bool > *const mask=0)

Bool	residual (Vector< typename FunctionTraits< T >::BaseType > &y, const Array< typename FunctionTraits< T >::BaseType > &x, const Vector< typename FunctionTraits< T >::BaseType > &sol, const Bool model=False)
	Return the residual after a fit in y. More...

Bool	residual (Vector< typename FunctionTraits< T >::BaseType > &y, const Array< typename FunctionTraits< T >::BaseType > &x, const Bool model=False)

uInt	getRank () const
	Get the rank of the solution (or zero of no fit() done yet). More...

Public Member Functions inherited from casacore::LSQaips
	LSQaips (uInt nUnknowns, uInt nConstraints=0)
	Construct an object with the number of unknown, knowns and constraints, and type, using the default collinearity factor and the default Levenberg-Marquardt adjustment factor. More...

	LSQaips (uInt nUnknowns, const LSQReal &, uInt nConstraints=0)
	Allow explicit complex/real specification. More...

	LSQaips (uInt nUnknowns, const LSQComplex &, uInt nConstraints=0)

	LSQaips ()
	Default constructor (empty, real, only usable after a set(nUnknowns)) More...

	LSQaips (const LSQaips &other)
	Copy constructor (deep copy) More...

LSQaips &	operator= (const LSQaips &other)
	Assignment (deep copy) More...

	~LSQaips ()

template<class U >
void	solve (U *sol)
	Solve normal equations. More...

template<class U >
void	solve (std::complex< U > *sol)

template<class U >
void	solve (U &sol)

template<class U >
void	solve (Vector< U > &sol)

template<class U >
Bool	solveLoop (uInt &nRank, U *sol, Bool doSVD=False)
	Solve a Levenberg-Marquardt loop. More...

template<class U >
Bool	solveLoop (uInt &nRank, std::complex< U > *sol, Bool doSVD=False)

template<class U >
Bool	solveLoop (uInt &nRank, U &sol, Bool doSVD=False)

template<class U >
Bool	solveLoop (uInt &nRank, Vector< U > &sol, Bool doSVD=False)

template<class U >
Bool	solveLoop (Double &fit, uInt &nRank, U *sol, Bool doSVD=False)

template<class U >
Bool	solveLoop (Double &fit, uInt &nRank, std::complex< U > *sol, Bool doSVD=False)

template<class U >
Bool	solveLoop (Double &fit, uInt &nRank, U &sol, Bool doSVD=False)

template<class U >
Bool	solveLoop (Double &fit, uInt &nRank, Vector< U > &sol, Bool doSVD=False)

template<class U >
Bool	getCovariance (U *covar)
	Get the covariance matrix. More...

template<class U >
Bool	getCovariance (std::complex< U > *covar)

template<class U >
Bool	getCovariance (Array< U > &covar)

template<class U >
Bool	getErrors (U *errors)
	Get main diagonal of covariance function (of size `nUnknowns`) More...

template<class U >
Bool	getErrors (std::complex< U > *errors)

template<class U >
Bool	getErrors (U &errors)

template<class U >
Bool	getErrors (Vector< U > &errors)

Public Member Functions inherited from casacore::LSQFit
	LSQFit (uInt nUnknowns, uInt nConstraints=0)
	Construct an object with the number of unknowns and constraints, using the default collinearity factor and the default Levenberg-Marquardt adjustment factor. More...

	LSQFit (uInt nUnknowns, const LSQReal &, uInt nConstraints=0)
	Allow explicit Real specification. More...

	LSQFit (uInt nUnknowns, const LSQComplex &, uInt nConstraints=0)
	Allow explicit Complex specification. More...

	LSQFit ()
	Default constructor (empty, only usable after a `set(nUnknowns)`) More...

	LSQFit (const LSQFit &other)
	Copy constructor (deep copy) More...

LSQFit &	operator= (const LSQFit &other)
	Assignment (deep copy) More...

	~LSQFit ()

Bool	invert (uInt &nRank, Bool doSVD=False)
	Triangularize the normal equations and determine the rank `nRank` of the normal equations and, in the case of an `SVD` solution, the constraint equations. More...

template<class U >
void	copy (const Double beg, const Double end, U &sol, LSQReal)
	Copy date from beg to end; converting if necessary to complex data. More...

template<class U >
void	copy (const Double beg, const Double end, U &sol, LSQComplex)

template<class U >
void	copy (const Double beg, const Double end, U *sol, LSQReal)

template<class U >
void	copy (const Double beg, const Double end, U *sol, LSQComplex)

template<class U >
void	uncopy (Double beg, const Double end, U &sol, LSQReal)

template<class U >
void	uncopy (Double beg, const Double end, U &sol, LSQComplex)

template<class U >
void	uncopy (Double beg, const Double end, U *sol, LSQReal)

template<class U >
void	uncopy (Double beg, const Double end, U *sol, LSQComplex)

template<class U >
void	copyDiagonal (U &errors, LSQReal)

template<class U >
void	copyDiagonal (U &errors, LSQComplex)

template<class U >
void	solve (U *sol)
	Solve normal equations. More...

template<class U >
void	solve (std::complex< U > *sol)

template<class U >
void	solve (U &sol)

template<class U >
Bool	solveLoop (uInt &nRank, U *sol, Bool doSVD=False)
	Solve a loop in a non-linear set. More...

template<class U >
Bool	solveLoop (uInt &nRank, std::complex< U > *sol, Bool doSVD=False)

template<class U >
Bool	solveLoop (uInt &nRank, U &sol, Bool doSVD=False)

template<class U >
Bool	solveLoop (Double &fit, uInt &nRank, U *sol, Bool doSVD=False)

template<class U >
Bool	solveLoop (Double &fit, uInt &nRank, std::complex< U > *sol, Bool doSVD=False)

template<class U >
Bool	solveLoop (Double &fit, uInt &nRank, U &sol, Bool doSVD=False)

template<class U , class V >
void	makeNorm (const V &cEq, const U &weight, const U &obs, Bool doNorm=True, Bool doKnown=True)
	Make normal equations using the `cEq` condition equation (cArray) (with `nUnknowns` elements) and a weight `weight`, given the known observed value `obs`. More...

template<class U , class V >
void	makeNorm (const V &cEq, const U &weight, const U &obs, LSQFit::Real, Bool doNorm=True, Bool doKnown=True)

template<class U , class V >
void	makeNorm (const V &cEq, const U &weight, const std::complex< U > &obs, Bool doNorm=True, Bool doKnown=True)

template<class U , class V >
void	makeNorm (const V &cEq, const U &weight, const std::complex< U > &obs, LSQFit::Complex, Bool doNorm=True, Bool doKnown=True)

template<class U , class V >
void	makeNorm (const V &cEq, const U &weight, const std::complex< U > &obs, LSQFit::Separable, Bool doNorm=True, Bool doKnown=True)

template<class U , class V >
void	makeNorm (const V &cEq, const U &weight, const std::complex< U > &obs, LSQFit::AsReal, Bool doNorm=True, Bool doKnown=True)

template<class U , class V >
void	makeNorm (const V &cEq, const U &weight, const std::complex< U > &obs, LSQFit::Conjugate, Bool doNorm=True, Bool doKnown=True)

template<class U , class V , class W >
void	makeNorm (uInt nIndex, const W &cEqIndex, const V &cEq, const U &weight, const U &obs, Bool doNorm=True, Bool doKnown=True)

template<class U , class V , class W >
void	makeNorm (uInt nIndex, const W &cEqIndex, const V &cEq, const V &cEq2, const U &weight, const U &obs, const U &obs2, Bool doNorm=True, Bool doKnown=True)

template<class U , class V , class W >
void	makeNorm (uInt nIndex, const W &cEqIndex, const V &cEq, const U &weight, const U &obs, LSQFit::Real, Bool doNorm=True, Bool doKnown=True)

template<class U , class V , class W >
void	makeNorm (uInt nIndex, const W &cEqIndex, const V &cEq, const U &weight, const std::complex< U > &obs, Bool doNorm=True, Bool doKnown=True)

template<class U , class V , class W >
void	makeNorm (uInt nIndex, const W &cEqIndex, const V &cEq, const U &weight, const std::complex< U > &obs, LSQFit::Complex, Bool doNorm=True, Bool doKnown=True)

template<class U , class V , class W >
void	makeNorm (uInt nIndex, const W &cEqIndex, const V &cEq, const U &weight, const std::complex< U > &obs, LSQFit::Separable, Bool doNorm=True, Bool doKnown=True)

template<class U , class V , class W >
void	makeNorm (uInt nIndex, const W &cEqIndex, const V &cEq, const U &weight, const std::complex< U > &obs, LSQFit::AsReal, Bool doNorm=True, Bool doKnown=True)

template<class U , class V , class W >
void	makeNorm (uInt nIndex, const W &cEqIndex, const V &cEq, const U &weight, const std::complex< U > &obs, LSQFit::Conjugate, Bool doNorm=True, Bool doKnown=True)

template<class U , class V >
void	makeNorm (const std::vector< std::pair< uInt, V > > &cEq, const U &weight, const U &obs, Bool doNorm=True, Bool doKnown=True)

template<class U , class V >
void	makeNorm (const std::vector< std::pair< uInt, V > > &cEq, const U &weight, const U &obs, LSQFit::Real, Bool doNorm=True, Bool doKnown=True)

template<class U , class V >
void	makeNorm (const std::vector< std::pair< uInt, V > > &cEq, const U &weight, const std::complex< U > &obs, Bool doNorm=True, Bool doKnown=True)

template<class U , class V >
void	makeNorm (const std::vector< std::pair< uInt, V > > &cEq, const U &weight, const std::complex< U > &obs, LSQFit::Complex, Bool doNorm=True, Bool doKnown=True)

template<class U , class V >
void	makeNorm (const std::vector< std::pair< uInt, V > > &cEq, const U &weight, const std::complex< U > &obs, LSQFit::Separable, Bool doNorm=True, Bool doKnown=True)

template<class U , class V >
void	makeNorm (const std::vector< std::pair< uInt, V > > &cEq, const U &weight, const std::complex< U > &obs, LSQFit::AsReal, Bool doNorm=True, Bool doKnown=True)

template<class U , class V >
void	makeNorm (const std::vector< std::pair< uInt, V > > &cEq, const U &weight, const std::complex< U > &obs, LSQFit::Conjugate, Bool doNorm=True, Bool doKnown=True)

template<class U , class V , class W >
void	makeNormSorted (uInt nIndex, const W &cEqIndex, const V &cEq, const U &weight, const U &obs, Bool doNorm=True, Bool doKnown=True)

template<class U , class V , class W >
void	makeNormSorted (uInt nIndex, const W &cEqIndex, const V &cEq, const V &cEq2, const U &weight, const U &obs, const U &obs2, Bool doNorm=True, Bool doKnown=True)

template<class U >
Bool	getConstraint (uInt n, U *cEq) const
	Get the `n-th` (from 0 to the rank deficiency, or missing rank, see e.g. More...

template<class U >
Bool	getConstraint (uInt n, std::complex< U > *cEq) const

template<class U >
Bool	getConstraint (uInt n, U &cEq) const

template<class U , class V >
Bool	setConstraint (uInt n, const V &cEq, const U &obs)
	Add a new constraint equation (updating nConstraints); or set a numbered constraint equation (0..nConstraints-1). More...

template<class U , class V >
Bool	setConstraint (uInt n, const V &cEq, const std::complex< U > &obs)

template<class U , class V , class W >
Bool	setConstraint (uInt n, uInt nIndex, const W &cEqIndex, const V &cEq, const U &obs)

template<class U , class V , class W >
Bool	setConstraint (uInt n, uInt nIndex, const W &cEqIndex, const V &cEq, const std::complex< U > &obs)

template<class U , class V >
Bool	addConstraint (const V &cEq, const U &obs)

template<class U , class V >
Bool	addConstraint (const V &cEq, const std::complex< U > &obs)

template<class U , class V , class W >
Bool	addConstraint (uInt nIndex, const W &cEqIndex, const V &cEq, const U &obs)

template<class U , class V , class W >
Bool	addConstraint (uInt nIndex, const W &cEqIndex, const V &cEq, const std::complex< U > &obs)

Bool	merge (const LSQFit &other)
	Merge other `LSQFit` object (i.e. More...

Bool	merge (const LSQFit &other, uInt nIndex, const uInt *nEqIndex)

Bool	merge (const LSQFit &other, uInt nIndex, const std::vector< uInt > &nEqIndex)

template<class W >
Bool	merge (const LSQFit &other, uInt nIndex, const W &nEqIndex)

void	reset ()
	Reset status to empty. More...

void	set (uInt nUnknowns, uInt nConstraints=0)
	Set new sizes (default is for Real) More...

void	set (Int nUnknowns, Int nConstraints=0)

void	set (uInt nUnknowns, const LSQReal &, uInt nConstraints=0)

void	set (Int nUnknowns, const LSQReal &, Int nConstraints=0)

void	set (uInt nUnknowns, const LSQComplex &, uInt nConstraints=0)

void	set (Int nUnknowns, const LSQComplex &, Int nConstraints=0)

void	set (Double factor=1e-6, Double LMFactor=1e-3)
	Set new factors (collinearity `factor`, and Levenberg-Marquardt `LMFactor`) More...

void	setEpsValue (Double epsval=1e-8)
	Set new value solution test. More...

void	setEpsDerivative (Double epsder=1e-8)
	Set new derivative test. More...

void	setMaxIter (uInt maxiter=0)
	Set maximum number of iterations. More...

uInt	nIterations () const
	Get number of iterations done. More...

void	setBalanced (Bool balanced=False)
	Set the expected form of the normal equations. More...

LSQFit::ReadyCode	isReady () const
	Ask the state of the non-linear solutions. More...

const std::string &	readyText () const

template<class U >
Bool	getCovariance (U *covar)
	Get the covariance matrix (of size `nUnknowns * nUnknowns`) More...

template<class U >
Bool	getCovariance (std::complex< U > *covar)

template<class U >
Bool	getErrors (U *errors)
	Get main diagonal of covariance function (of size `nUnknowns`) More...

template<class U >
Bool	getErrors (std::complex< U > *errors)

template<class U >
Bool	getErrors (U &errors)

uInt	nUnknowns () const
	Get the number of unknowns. More...

uInt	nConstraints () const
	Get the number of constraints. More...

uInt	getDeficiency () const
	Get the rank deficiency Warning: Note that the number is returned assuming real values; For complex values it has to be halved More...

Double	getChi () const
	Get chi^2 (both are identical); the standard deviation (per observation) and the standard deviation per weight unit. More...

Double	getChi2 () const

Double	getSD () const

Double	getWeightedSD () const

void	debugIt (uInt &nun, uInt &np, uInt &ncon, uInt &ner, uInt &rank, Double &nEq, Double &known, Double &constr, Double &er, uInt &piv, Double &sEq, Double *&sol, Double &prec, Double &nonlin) const
	Debug: More...

Bool	fromRecord (String &error, const RecordInterface &in)
	Create an LSQFit object from a record. More...

Bool	toRecord (String &error, RecordInterface &out) const
	Create a record from an LSQFit object. More...

const String &	ident () const
	Get identification of record. More...

void	toAipsIO (AipsIO &) const
	Save or restore using AipsIO. More...

void	fromAipsIO (AipsIO &)

Protected Member Functions
virtual Bool	fitIt (Vector< typename FunctionTraits< T >::BaseType > &sol, const Array< typename FunctionTraits< T >::BaseType > &x, const Vector< typename FunctionTraits< T >::BaseType > &y, const Vector< typename FunctionTraits< T >::BaseType > const sigma, const Vector< Bool > const mask=0)
	Generalised fitter. More...

Protected Member Functions inherited from casacore::GenericL2Fit< T >
void	buildMatrix (const Array< typename FunctionTraits< T >::BaseType > &x, const Vector< typename FunctionTraits< T >::BaseType > &y, const Vector< typename FunctionTraits< T >::BaseType > const sigma, const Vector< Bool > const mask=0)
	Build the normal matrix. More...

void	buildConstraint ()
	Build the constraint equations. More...

void	fillSVDConstraints ()
	Get the SVD constraints. More...

Bool	buildResidual (Vector< typename FunctionTraits< T >::BaseType > &y, const Array< typename FunctionTraits< T >::BaseType > &x, const Vector< typename FunctionTraits< T >::BaseType > *const sol, const Bool model=False)
	Calculate residuals. More...

FunctionTraits< T >::BaseType	getVal_p (const Array< typename FunctionTraits< T >::BaseType > &x, uInt j, uInt i) const
	Function to get evaluated functional value. More...

void	initfit_p (uInt parcnt)
	Initialise the fitter with number of solvable parameters. More...

uInt	testInput_p (const Array< typename FunctionTraits< T >::BaseType > &x, const Vector< typename FunctionTraits< T >::BaseType > &y, const Vector< typename FunctionTraits< T >::BaseType > *const sigma)
	Return number of condition equations and check sizes x, y, sigma. More...

void	resetFunction ()
	Reset all the input. More...

Protected Member Functions inherited from casacore::LSQFit
Double *	rowrt (uInt i) const
	Get pointer in rectangular array. More...

Double *	rowru (uInt i) const

void	init ()
	Initialise areas. More...

void	clear ()
	Clear areas. More...

void	deinit ()
	De-initialise area. More...

void	solveIt ()
	Solve normal equations. More...

Bool	solveItLoop (Double &fit, uInt &nRank, Bool doSVD=False)
	One non-linear LM loop. More...

void	solveMR (uInt nin)
	Solve missing rank part. More...

Bool	invertRect ()
	Invert rectangular matrix (i.e. More...

Double	normSolution (const Double *sol) const
	Get the norm of the current solution vector. More...

Double	normInfKnown (const Double *known) const
	Get the infinite norm of the known vector. More...

Bool	mergeIt (const LSQFit &other, uInt nIndex, const uInt *nEqIndex)
	Merge sparse normal equations. More...

void	save (Bool all=True)
	Save current status (or part) More...

void	restore (Bool all=True)
	Restore current status. More...

void	copy (const LSQFit &other, Bool all=True)
	Copy data. More...

void	extendConstraints (uInt n)
	Extend the constraint equation area to the specify number of equations. More...

void	createNCEQ ()
	Create the solution equation area nceq_p and fill it. More...

void	getWorkSOL ()
	Get work areas for solutions, covariance. More...

void	getWorkCOV ()

Additional Inherited Members
Public Types inherited from casacore::LSQFit
enum	ReadyCode { NONREADY, SOLINCREMENT, DERIVLEVEL, MAXITER, NOREDUCTION, SINGULAR, N_ReadyCode }
	State of the non-linear solution. More...

enum	ErrorField { NC, SUMWEIGHT, SUMLL, CHI2, N_ErrorField }
	Offset of fields in error_p data area. More...

Public Attributes inherited from casacore::GenericL2Fit< T >
const Double	COLLINEARITY
	Default collinearity test for SVD. More...

Static Public Attributes inherited from casacore::LSQFit
static Real	REAL
	And values to use. More...

static Complex	COMPLEX

static Separable	SEPARABLE

static AsReal	ASREAL

static Conjugate	CONJUGATE

Protected Types inherited from casacore::LSQFit
enum	StateBit { INVERTED, TRIANGLE, NONLIN, N_StateBit }
	Bits that can be set/referenced. More...

Static Protected Member Functions inherited from casacore::LSQFit
static Double	realMC (const std::complex< Double > &x, const std::complex< Double > &y)
	Calculate the real or imag part of `x*conj(y)` More...

static Double	imagMC (const std::complex< Double > &x, const std::complex< Double > &y)

static Float	realMC (const std::complex< Float > &x, const std::complex< Float > &y)

static Float	imagMC (const std::complex< Float > &x, const std::complex< Float > &y)

Protected Attributes inherited from casacore::GenericL2Fit< T >
uInt	aCount_ai
	Adjustable. More...

Bool	svd_p
	SVD indicator. More...

Function< typename FunctionTraits< T >::DiffType, typename FunctionTraits< T > ::DiffType > *	ptr_derive_p
	Function to use in evaluating condition equation. More...

PtrBlock< Function< typename FunctionTraits< T >::DiffType, typename FunctionTraits< T > ::DiffType > * >	constrFun_p
	List of functions describing the possible constraint equations e.g. More...

PtrBlock< Vector< typename FunctionTraits< T >::BaseType > * >	constrArg_p
	List of vectors describing the constraint equations' arguments. More...

PtrBlock< typename FunctionTraits< T >::BaseType * >	constrVal_p
	List of values describing the constraint equations' value. More...

uInt	pCount_p
	Number of available parameters. More...

uInt	ndim_p
	Number of dimensions of input data. More...

Bool	needInit_p
	No normal equations yet. More...

Bool	solved_p
	Have solution. More...

Bool	errors_p
	Have errors. More...

Bool	ferrors_p

Bool	asweight_p
	Interpret as weights rather than as sigma the given values. More...

uInt	nr_p
	The rank of the solution. More...

Vector< typename FunctionTraits< T >::BaseType >	condEq_p
	Condition equation parameters (for number of adjustable parameters) More...

Vector< typename FunctionTraits< T >::BaseType >	fullEq_p
	Equation for all available parameters. More...

Vector< typename FunctionTraits< T >::ArgType >	arg_p
	Contiguous argument areas. More...

Vector< typename FunctionTraits< T >::ArgType >	carg_p

Vector< typename FunctionTraits< T >::BaseType >	sol_p
	Local solution area. More...

Vector< typename FunctionTraits< T >::BaseType >	fsol_p

Vector< typename FunctionTraits< T >::BaseType >	err_p
	Local error area. More...

Vector< typename FunctionTraits< T >::BaseType >	ferr_p

FunctionTraits< T >::DiffType	valder_p
	Local value and derivatives. More...

Vector< Vector< typename LSQTraits< typename FunctionTraits< T >::BaseType > ::base > >	consvd_p
	Local SVD constraints. More...

Protected Attributes inherited from casacore::LSQFit
uInt	state_p
	Bits set to indicate state. More...

uInt	nun_p
	Number of unknowns. More...

uInt	ncon_p
	Number of constraints. More...

uInt	n_p
	Matrix size (will be n_p = nun_p + ncon_p) More...

uInt	r_p
	Rank of normal equations (normally n_p) More...

Double	prec_p
	Collinearity precision. More...

Double	startnon_p
	Levenberg start factor. More...

Double	nonlin_p
	Levenberg current factor. More...

Double	stepfactor_p
	Levenberg step factor. More...

Double	epsval_p
	Test value for [incremental] solution in non-linear loop. More...

Double	epsder_p
	Test value for known vector in non-linear loop. More...

Bool	balanced_p
	Indicator for a well balanced normal equation. More...

uInt	maxiter_p
	Maximum number of iterations for non-linear solution. More...

uInt	niter_p
	Iteration count for non-linear solution. More...

ReadyCode	ready_p
	Indicate the non-linear state. More...

uInt *	piv_p
	Pivot table (n_p) More...

LSQMatrix *	norm_p
	Normal equations (triangular nun_p * nun_p) More...

uInt	nnc_p
	Current length nceq_p. More...

LSQMatrix *	nceq_p
	Normal combined with constraint equations for solutions (triangular nnc_p*nnc_p) More...

Double *	known_p
	Known part equations (n_p) More...

Double *	error_p
	Counts for errors (N_ErrorField) More...

Double *	constr_p
	Constraint equation area (nun_p*ncon_p)) More...

Double *	sol_p
	Solution area (n_p) More...

LSQFit *	nar_p
	Save area for non-linear case (size determined internally) More...

Double *	lar_p
	Save area for non-symmetric (i.e. More...

Double *	wsol_p
	Work areas for interim solutions and covariance. More...

Double *	wcov_p

Static Protected Attributes inherited from casacore::LSQFit
static const String	recid
	Record field names. More...

static const String	state

static const String	nun

static const String	ncon

static const String	prec

static const String	startnon

static const String	nonlin

static const String	rank

static const String	nnc

static const String	piv

static const String	constr

static const String	known

static const String	errors

static const String	sol

static const String	lar

static const String	wsol

static const String	wcov

static const String	nceq

static const String	nar

Detailed Description

template<class T>
class casacore::LinearFit< T >

Class for linear least-squares fit.

Review Status

Reviewed By:: wbrouw
Date Reviewed:: 2004/06/15
Test programs:: tLinearFitSVD

Prerequisite

Etymology

A set of data point is fit with some functional equation. The equations solved are linear equations. The functions themselves however can be wildly nonlinear.

Synopsis

NOTE: Constraints added. Documentation out of date at moment, check the tLinearFitSVD and tNonLinearFirLM programs for examples.

The following is a brief summary of the linear least-squares fit problem. See module header, Fitting, for a more complete description.

Given a set of N data points (measurements), (x(i), y(i)) i = 0,...,N-1, along with a set of standard deviations, sigma(i), for the data points, and M specified functions, f(j)(x) j = 0,...,M-1, we form a linear combination of the functions:

z(i) = a(0)f(0)(x(i)) + a(1)f(1)(x(i)) +... + a(M-1)f(M-1)(x(i)),

where a(j) j = 0,...,M-1 are a set of parameters to be determined. The linear least-squares fit tries to minimize

chi-square = [(y(0)-z(0))/sigma(0)]^2 + [(y(1)-z(1))/sigma(1)]^2 +..\.

+ [(y(N-1)-z(N-1))/sigma(N-1)]^2.

by adjusting {a(j)} in the equation.

For complex numbers, [(y(i)-z(i))/sigma(i)]^2 in chi-square is replaced by [(y(i)-z(i))/sigma(i)]*conjugate([(y(i)-z(i))/sigma(i)])

For multidimensional functions, x(i) is a vector, and

f(j)(x(i)) = f(j)(x(i,0), x(i,1), x(i,2),...)

Normally, it is necessary that N > M for the solutions to be valid, since there must be more data points than model parameters to be solved.

If the measurement errors (standard deviation sigma) are not known at all, they can all be set to one initially. In this case, we assume all measurements have the same standard deviation, after minimizing chi-square, we recompute

sigma^2 = {(y(0)-z(0))^2 + (y(1)-z(1))^2 +..\.

+ (y(N-1)-z(N-1))^2}/(N-M) = chi-square/(N-M).

A statistic weight can also be assigned to each measurement if the standard deviation is not available. sigma can be calculated from

sigma = 1/ sqrt(weight)

Alternatively a 'weight' switch can be set with asWeight(). For best arithmetic performance, weight should be normalized to a maximum value of one. Having a large weight value can sometimes lead to overflow problems.

The function to be fitted to the data can be given as an instance of the Function class. One can also form a sum of functions using the CompoundFunction.

For small datasets the usage of the calls is:

Create a functional description of the parameters
Create a fitter: LinearFit<T> fitter();
Set the functional representation: fitter.setFunction()
Do the fit to the data: fitter.fit(x, data, sigma) (or do a number of calls to buildNormalMatrix(x, data, sigma) and finish of with fitter.fit() or fitter.sol())
if needed the covariance; residuals; chiSquared, parameter errors can all be obtained

Note that the fitter is reusable. An example is given in the following.

The solution of a fit always produces the total number of parameters given to the fitter. I.e. including any parameters that were fixed. In the latter case the solution returned will be the fixed value.

Template Type Argument Requirements (T)

Float
Double
Complex
DComplex

If there are a large number of unknowns or a large number of data points machine memory limits (or timing reasons) may not allow a complete in-core fitting to be performed. In this case one can incrementally build the normal equation (see buildNormalMatrix()).

The normal operation of the class tests for real inversion problems only. If tests are needed for almost collinear columns in the solution matrix, the collinearity can be set as the square of the sine of the minimum angle allowed.

Singular Value Decomposition is supported by the LinearFitSVD class, which has a behaviour completely identical to this class (apart from a default collinearity of 1e-8).

Other information (see a.o. LSQFit) can be set and obtained as well.

Motivation

The creation of this class was driven by the need to write code to perform baseline fitting or continuum subtraction.

Example

In the following a polynomial is fitted through the first 20 prime numbers. The data is given in the x vector (1 to 20) and in the primesTable (2, 3,..., 71) (see tLinearFitSVD test program). In the following all four methods to calculate a polynomial through the data is used

// The list of coordinate x-values
Vector<Double> x(nPrimes);
indgen((Array<Double>&)x, 1.0);  // 1, 2,..\.
Vector<Double> primesTable(nPrimes);
for (uInt i=1; i < nPrimes; i++) {
primesTable(i) =
Primes::nextLargerPrimeThan(Int(primesTable(i-1)+0.01));
};   
Vector<Double> sigma(nPrimes);
sigma = 1.0;
// The fitter
LinearFit<Double> fitter;
Polynomial<AutoDiff<Double> > combination(2);
// Get the solution
fitter.setFunction(combination);
Vector<Double> solution = fitter.fit(x, primesTable, sigma);
// create a special function (should probably at beginning)
static void myfnc(Vector<Double> &y, const Double x) {
y(0) = 1; for (uInt i=1; i<y.nelements(); i++) y(i) = y(i-1)*x; };
fitter.setFunction(3, &myfnc);
solution = fitter.fit(x, primesTable, sigma);
// Create the direct coefficients table
fitter.setFunction(3);
Matrix<Double> xx(nPrimes, 3);
for (uInt i=0; i<nPrimes; i++) {
xx(i,0) = 1;
for (uInt j=1; j<3; j++) xx(i,j) = xx(i,j-1)*Double(i+1);
};
solution = fitter.fit(xx, primesTable, sigma);

In the test program examples are given on how to get the other information, and other examples.

Definition at line 207 of file LinearFit.h.

Constructor & Destructor Documentation

template<class T>

casacore::LinearFit< T >::LinearFit ( )

Create a fitter: the normal way to generate a fitter object.

Necessary data will be deduced from the Functional provided with setFunction()

template<class T>

casacore::LinearFit< T >::LinearFit ( const LinearFit< T > & other )

Copy constructor (deep copy)

template<class T>

virtual casacore::LinearFit< T >::~LinearFit ( )

virtual

Destructor.

Member Function Documentation

template<class T>

virtual Bool casacore::LinearFit< T >::fitIt	(	Vector< typename FunctionTraits< T >::BaseType > &	sol,
		const Array< typename FunctionTraits< T >::BaseType > &	x,
		const Vector< typename FunctionTraits< T >::BaseType > &	y,
		const Vector< typename FunctionTraits< T >::BaseType > *const	sigma,
		const Vector< Bool > *const	mask = `0`
	)

protectedvirtual

Generalised fitter.

Implements casacore::GenericL2Fit< T >.

template<class T>

LinearFit& casacore::LinearFit< T >::operator= ( const LinearFit< T > & other )

Assignment (deep copy)

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

casa/casacore/scimath/Fitting/LinearFit.h

Public Member Functions

Protected Member Functions

Additional Inherited Members

Detailed Description

template<class T> class casacore::LinearFit< T >

Review Status

Prerequisite

Etymology

Synopsis

Template Type Argument Requirements (T)

Motivation

Example

Constructor & Destructor Documentation

Member Function Documentation

template<class T>
class casacore::LinearFit< T >