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LinearFit.h
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//# LinearFit.h: Class for linear least-squares fit.
//#
//# Copyright (C) 1995,1999,2000,2001,2002,2004
//# Associated Universities, Inc. Washington DC, USA.
//#
//# This library is free software; you can redistribute it and/or modify it
//# under the terms of the GNU Library General Public License as published by
//# the Free Software Foundation; either version 2 of the License, or (at your
//# option) any later version.
//#
//# This library is distributed in the hope that it will be useful, but WITHOUT
//# ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
//# FITNESS FOR A PARTICULAR PURPOSE. See the GNU Library General Public
//# License for more details.
//#
//# You should have received a copy of the GNU Library General Public License
//# along with this library; if not, write to the Free Software Foundation,
//# Inc., 675 Massachusetts Ave, Cambridge, MA 02139, USA.
//#
//# Correspondence concerning AIPS++ should be addressed as follows:
//# Internet email: casa-feedback@nrao.edu.
//# Postal address: AIPS++ Project Office
//# National Radio Astronomy Observatory
//# 520 Edgemont Road
//# Charlottesville, VA 22903-2475 USA
#ifndef SCIMATH_LINEARFIT_H
#define SCIMATH_LINEARFIT_H
//# Includes
#include <casacore/casa/aips.h>
#include <casacore/scimath/Fitting/GenericL2Fit.h>
namespace casacore { //# NAMESPACE CASACORE - BEGIN
//# Forward declarations
// <summary> Class for linear least-squares fit.
// </summary>
//
// <reviewed reviewer="wbrouw" date="2004/06/15" tests="tLinearFitSVD.cc"
// demos="">
// </reviewed>
//
// <prerequisite>
// <li> <linkto class="Functional">Functional</linkto>
// <li> <linkto class="Function">Function</linkto>
// <li> <linkto module="Fitting">Fitting</linkto>
// </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.
// </etymology>
//
// <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 Documentation out of date at moment, check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, <linkto module="Fitting">Fitting</linkto>,
// 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:
// <srcblock>
// z(i) = a(0)f(0)(x(i)) + a(1)f(1)(x(i)) + ... + a(M-1)f(M-1)(x(i)),
// </srcblock>
// where a(j) j = 0,...,M-1 are a set of parameters to be determined.
// The linear least-squares fit tries to minimize
// <srcblock>
// 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.
// </srcblock>
// by adjusting {a(j)} in the equation.
//
// For complex numbers, <code>[(y(i)-z(i))/sigma(i)]^2</code> in chi-square
// is replaced by
// <code>[(y(i)-z(i))/sigma(i)]*conjugate([(y(i)-z(i))/sigma(i)])</code>
//
// For multidimensional functions, x(i) is a vector, and
// <srcblock>
// f(j)(x(i)) = f(j)(x(i,0), x(i,1), x(i,2), ...)
// </srcblock>
//
// 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
// <srcblock>
// 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).
// </srcblock>
//
// A statistic weight can also be assigned to each measurement if the
// standard deviation is not available. sigma can be calculated from
// <srcblock>
// sigma = 1/ sqrt(weight)
// </srcblock>
// Alternatively a 'weight' switch can be set with <src>asWeight()</src>.
// 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
// <linkto class="Function">Function</linkto> class.
// One can also form a sum of functions using the
// <linkto class="CompoundFunction">CompoundFunction</linkto>.
//
// For small datasets the usage of the calls is:
// <ul>
// <li> Create a functional description of the parameters
// <li> Create a fitter: LinearFit<T> fitter();
// <li> Set the functional representation: fitter.setFunction()
// <li> 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())
// <li> if needed the covariance; residuals; chiSquared, parameter errors
// can all be obtained
// </ul>
// 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.
//
// <templating arg=T>
// <li> Float
// <li> Double
// <li> Complex
// <li> DComplex
// </templating>
//
// 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
// <linkto class=LinearFitSVD>LinearFitSVD</linkto> class,
// which has a behaviour completely identical to this class (apart from a
// default collinearity of 1e-8).
//
// Other information (see a.o. <linkto class=LSQFit>LSQFit</linkto>) can
// be set and obtained as well.
// </synopsis>
//
// <motivation>
// The creation of this class was driven by the need to write code
// to perform baseline fitting or continuum subtraction.
// </motivation>
// <example>
//# /// redo 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
// <srcblock>
// // 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);
// </srcblock>
// In the test program examples are given on how to get the other
// information, and other examples.
// </example>
template<class T> class LinearFit : public GenericL2Fit<T>
{
public:
//# Constructors
// Create a fitter: the normal way to generate a fitter object. Necessary
// data will be deduced from the Functional provided with
// <src>setFunction()</src>
LinearFit();
// Copy constructor (deep copy)
LinearFit(const LinearFit &other);
// Assignment (deep copy)
LinearFit &operator=(const LinearFit &other);
// Destructor
virtual ~LinearFit();
//# Member functions
protected:
//#Data
//# Member functions
// Generalised fitter
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);
private:
//# Data
//# Member functions
protected:
//# Make members of parent classes known.
using GenericL2Fit<T>::pCount_p;
using GenericL2Fit<T>::ptr_derive_p;
using GenericL2Fit<T>::sol_p;
using GenericL2Fit<T>::solved_p;
using GenericL2Fit<T>::nr_p;
using GenericL2Fit<T>::svd_p;
using GenericL2Fit<T>::condEq_p;
using GenericL2Fit<T>::err_p;
using GenericL2Fit<T>::errors_p;
using GenericL2Fit<T>::COLLINEARITY;
using GenericL2Fit<T>::buildConstraint;
using GenericL2Fit<T>::fillSVDConstraints;
};
} //# NAMESPACE CASACORE - END
#ifndef CASACORE_NO_AUTO_TEMPLATES
#include <casacore/scimath/Fitting/LinearFit.tcc>
#endif //# CASACORE_NO_AUTO_TEMPLATES
#endif
casacore::Array
Definition Array.h:155
casacore::FunctionTraits::BaseType
T BaseType
Template base type.
Definition FunctionTraits.h:142
casacore::GenericL2Fit::solved_p
Bool solved_p
Have solution.
Definition GenericL2Fit.h:484
casacore::GenericL2Fit::fillSVDConstraints
void fillSVDConstraints()
Get the SVD constraints.
casacore::GenericL2Fit::nr_p
uInt nr_p
The rank of the solution.
Definition GenericL2Fit.h:491
casacore::GenericL2Fit::condEq_p
Vector< typename FunctionTraits< T >::BaseType > condEq_p
Condition equation parameters (for number of adjustable parameters).
Definition GenericL2Fit.h:493
casacore::GenericL2Fit::COLLINEARITY
const Double COLLINEARITY
Default collinearity test for SVD.
Definition GenericL2Fit.h:215
casacore::GenericL2Fit::err_p
Vector< typename FunctionTraits< T >::BaseType > err_p
Local error area.
Definition GenericL2Fit.h:508
casacore::GenericL2Fit::buildConstraint
void buildConstraint()
Build the constraint equations.
casacore::GenericL2Fit::pCount_p
uInt pCount_p
Number of available parameters.
Definition GenericL2Fit.h:478
casacore::GenericL2Fit::sol_p
Vector< typename FunctionTraits< T >::BaseType > sol_p
Local solution area.
Definition GenericL2Fit.h:503
casacore::GenericL2Fit::GenericL2Fit
GenericL2Fit()
Create a fitter: the normal way to generate a fitter object.
casacore::GenericL2Fit::svd_p
Bool svd_p
SVD indicator.
Definition GenericL2Fit.h:460
casacore::GenericL2Fit::errors_p
Bool errors_p
Have errors.
Definition GenericL2Fit.h:486
casacore::GenericL2Fit::ptr_derive_p
Function< typename FunctionTraits< T >::DiffType, typename FunctionTraits< T >::DiffType > * ptr_derive_p
Function to use in evaluating condition equation.
Definition GenericL2Fit.h:463
casacore::LSQFit::sol
static const String sol
Definition LSQFit.h:855
casacore::LinearFit::~LinearFit
virtual ~LinearFit()
Destructor.
casacore::LinearFit::operator=
LinearFit & operator=(const LinearFit &other)
Assignment (deep copy).
casacore::LinearFit::LinearFit
LinearFit(const LinearFit &other)
Copy constructor (deep copy).
casacore::LinearFit::LinearFit
LinearFit()
Create a fitter: the normal way to generate a fitter object.
casacore::LinearFit::fitIt
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.
casacore::Vector
Definition Vector.h:82
casacore
this file contains all the compiler specific defines
Definition mainpage.dox:28
casacore::mask
LatticeExprNode mask(const LatticeExprNode &expr)
This function returns the mask of the given expression.
casacore::Bool
bool Bool
Define the standard types used by Casacore.
Definition aipstype.h:40