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//#
//# Copyright (C) 2001,2002,2004,2005
//# 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: aips2-request@nrao.edu.
//# Postal address: AIPS++ Project Office
//# National Radio Astronomy Observatory
//# 520 Edgemont Road
//# Charlottesville, VA 22903-2475 USA
//#
//# $Id$
#ifndef SCIMATH_GENERICL2FIT_H
#define SCIMATH_GENERICL2FIT_H
//# Includes
#include <casacore/casa/aips.h>
#include <casacore/casa/Arrays/Matrix.h>
#include <casacore/casa/Arrays/Vector.h>
#include <casacore/casa/Containers/Block.h>
#include <casacore/scimath/Fitting/LSQaips.h>
#include <casacore/scimath/Fitting/LSQTraits.h>
#include <casacore/scimath/Functionals/Function.h>
#include <casacore/scimath/Functionals/FunctionTraits.h>
#include <casacore/scimath/Mathematics/AutoDiff.h>
namespace casacore { // begin namespace casa
//# Forward declarations
template <class T> class Array;
template <class T, class U> class Function;
// <summary> Generic base class for least-squares fit.
// </summary>
//
// <reviewed reviewer="wbrouw" date="2004/06/14" tests="tLinearFitSVD.cc"
// demos="">
// </reviewed>
//
// <prerequisite>
// <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 class acts as a generic base class for <src>L2</src> type
// fits.
// </etymology>
//
// <synopsis>
// NOTE: Constraints added. Documentation out of date at moment, check
// the tLinearFitSVD and tNonLinearFitLM programs for examples.
//
// The class acts as a base class for L2-type (least-squares) fitting.
// Actual classes (se e.g. <linkto class=LinearFit>LinearFit</linkto> and
// <linkto class=NonLinearFit>NonLinearFit</linkto>.
//
// 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: GenericL2Fit<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> The following data types can be used to instantiate the GenericL2Fit
// templated class:
// Known classes for FunctionTraits. I.e simple numerical like
// <src>Float</src>, <src>Double</src>, <src>Complex</src>,
// <src>DComplex</src>; and the <src>AutoDiff<></src> versions.
// </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
// <em> asSVD()</em> (which will also set the
// default collinearity to 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>
// 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(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;
// // Linear combination of functions describing 1 + x + x*x
// combination.setCoefficient(0, 1.0); // 1
// combination.setCoefficient(1, 1.0); // x
// combination.setCoefficient(2, 1.0); // x^2
// // Get the solution
// fitter.setFunction(combination);
// Vector<Double> solution = fitter.fit(x, primesTable, sigma);
// // Try with a function with automatic derivatives (note that default
// // polynomial has zero first guess)
// LinearFit<AutoDiffA<Double> > fitad;
// Polynomial<AutoDiffA<Double> > sqre(2);
// fitad.setFunction(sqre);
// solution = fitad.fit(x, 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 GenericL2Fit : public LSQaips {
public:
//# Constants
// Default collinearity test for SVD
const Double COLLINEARITY;
//# 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>
GenericL2Fit();
// Copy constructor (deep copy)
GenericL2Fit(const GenericL2Fit &other);
// Assignment (deep copy)
GenericL2Fit &operator=(const GenericL2Fit &other);
// Destructor
virtual ~GenericL2Fit();
// Sets the function to be fitted. Upon entry, the argument function object
// is cloned. The cloned copy is used in the later fitting process.
// A valid function should be an instance of the
// <linkto class="Function">Function</linkto> class,
// so that derivatives with respect to the adjustable parameters
// can be calculated. The current values of the "available" parameters
// of the function are taken as the initial guess for the non-linear fitting.
template <class U>
void setFunction(const Function<U,U> &function) { resetFunction();
ptr_derive_p = function.cloneAD(); setFunctionEx(); }
// Set the possible constraint functions. The <src>addConstraint</src>
// will add one; the <src>setConstraint</src> will [re-]set the
// <src>n</src>th constraint. If unsucessful, False returned.<br>
// Constraint functional can only be set when the function to be fitted
// has been set. It should have the same number of parameters as the function
// to be fitted. The <src>x</src> should have the correct dimension.
// <group>
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)) {
if (n >= constrFun_p.nelements() ||
!ptr_derive_p ||
ptr_derive_p->nparameters() != function.nparameters() ||
function.ndim() != x.nelements()) return False;
delete constrFun_p[n]; constrFun_p[n] = 0;
constrFun_p[n] = function.cloneAD(); return setConstraintEx(n, x, y); }
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));
// </group>
// 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)
void setCollinearity(const Double cln);
// Set sigma values to be interpreted as weight (i.e. 1/sigma/sigma).
// A value of zero or -1 will be skipped. The switch will stay in effect
// until set False again explicitly. Default is False.
void asWeight(const Bool aswgt) { asweight_p = aswgt; }
// Set the use of SVD or not (default). When set the default collinearity
// is set as well.
void asSVD(const Bool svd);
// Return a pointer to the function being fitted. Should
// never delete this pointer.
// <group>
Function<typename FunctionTraits<T>::DiffType,
typename FunctionTraits<T>::DiffType> *fittedFunction() {
return ptr_derive_p; }
const Function<typename FunctionTraits<T>::DiffType,
typename FunctionTraits<T>::DiffType>*
fittedFunction() const { return ptr_derive_p; }
// </group>
// Return the number of fitted parameters
uInt fittedNumber() const { return aCount_ai; }
// Return the number of constraints, and pointers to constraint functions.
// A <src>0-pointer</src> will be returned if no such constraint present.
// This pointer should never be destroyed.
// <group>
uInt NConstraints() { return constrFun_p.nelements(); }
Function<typename FunctionTraits<T>::DiffType,
typename FunctionTraits<T>::DiffType> *getConstraint(const uInt n) {
return (n >= constrFun_p.nelements() ? 0 : constrFun_p[n]); }
// </group>
// Return the nth constraint equation derived from SVD
// Note that the number present will be given by <src>getDeficiency()</src>
Vector<typename LSQTraits<typename FunctionTraits<T>::
BaseType>::base> getSVDConstraint(uInt n);
// Set the parameter values. The input is a vector of parameters; all
// or only the masked ones' values will be set, using the input values
// <group>
void setParameterValues
(const Vector<typename FunctionTraits<T>::BaseType> &parms);
void setMaskedParameterValues
(const Vector<typename FunctionTraits<T>::BaseType> &parms);
// </group>
// Fit the function to the data. If no sigma provided, all ones assumed.
// In the case of no x,y,sigma the fitting equations are supposed to be
// generated by previous calls to buildNormalMatrix. Note that the ones
// with a scalar sigma will assume sigma=1 (overloading problem). The mask
// assumes that if present, points with False will be skipped.
// <thrown>
// <li> AipsError if unmatched array sizes given
// <li> AipsError if equations cannot be inverted (not in SVD case and in
// the case of the Bool versions.)
// </thrown>
// <group>
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);
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);
// </group>
// Obtain the chi squared. It has already been calculated during the
// fitting process.
// <group>
Double chiSquare() const { return getChi(); }
// </group>
// Get the errors on the solved values
// <thrown>
// <li> AipsError if none present (or Bool returned)
// </thrown>
// <group>
const Vector<typename FunctionTraits<T>::BaseType> &errors() const;
Bool errors(Vector<typename FunctionTraits<T>::BaseType> &err) const;
// </group>
// Get covariance matrix
// <group>
Matrix<Double> compuCovariance();
void compuCovariance(Matrix<Double> &cov);
// </group>
// Generate the normal equations by one or more calls to the
// buildNormalMatrix(), before calling a fit() without arguments.
// The arguments are the same as for the fit(arguments) function.
// A False is returned if the Array sizes are unmatched.
// <group>
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);
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);
// </group>
// Return the residual after a fit in y. x can
// be a vector (if 1D function) or a matrix (ND functional), as in the
// fit() methods. If sol is given, it is the solution derived from
// a fit and its value will be used; otherwise only the parameters
// in the fitted functional will be used.
// If <src>model</src> is given as <src>True</src>, the model, rather
// the residual <src><data>-<model></src> will be returned in <src>y</src>.
// False is returned if residuals cannot be calculated.
// <thrown>
// <li> Aipserror if illegal array sizes
// </thrown>
// <group>
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);
Bool residual(Vector<typename FunctionTraits<T>::BaseType> &y,
const Array<typename FunctionTraits<T>::BaseType> &x,
const Bool model=False);
// </group>
// Get the rank of the solution (or zero of no fit() done yet). A
// valid solution will have the same rank as the number of unknowns (or
// double that number in the complex case). For SVD solutions the
// rank could be less.
uInt getRank() const {
return (solved_p ? nUnknowns()-getDeficiency() : 0); }
protected:
//#Data
// Adjustable
uInt aCount_ai;
// SVD indicator
Bool svd_p;
// Function to use in evaluating condition equation
Function<typename FunctionTraits<T>::DiffType,
typename FunctionTraits<T>::DiffType> *ptr_derive_p;
// List of functions describing the possible constraint equations
// e.g. The sum of 3 angles w`could be described by a
// <src>HyperPlane(3)</src> function with <src>[1,1,1]</src>
// as parameters; giving <src>[1,1,1]</src> as argument vector and
// <src>3.1415</src> as value.
// <group>
PtrBlock<Function<typename FunctionTraits<T>::DiffType,
typename FunctionTraits<T>::DiffType>*> constrFun_p;
// List of vectors describing the constraint equations' arguments
PtrBlock<Vector<typename FunctionTraits<T>::BaseType>*> constrArg_p;
// List of values describing the constraint equations' value
PtrBlock<typename FunctionTraits<T>::BaseType *> constrVal_p;
// </group>
// Number of available parameters
uInt pCount_p;
// Number of dimensions of input data
uInt ndim_p;
// No normal equations yet.
Bool needInit_p;
// Have solution
Bool solved_p;
// Have errors
Bool errors_p;
mutable Bool ferrors_p;
// Interpret as weights rather than as sigma the given values.
Bool asweight_p;
// The rank of the solution
uInt nr_p;
// Condition equation parameters (for number of adjustable parameters)
mutable Vector<typename FunctionTraits<T>::BaseType> condEq_p;
// Equation for all available parameters
mutable Vector<typename FunctionTraits<T>::BaseType> fullEq_p;
// Contiguous argument areas
// <group>
mutable Vector<typename FunctionTraits<T>::ArgType> arg_p;
mutable Vector<typename FunctionTraits<T>::ArgType> carg_p;
// </group>
// Local solution area
// <group>
mutable Vector<typename FunctionTraits<T>::BaseType> sol_p;
mutable Vector<typename FunctionTraits<T>::BaseType> fsol_p;
// </group>
// Local error area
// <group>
mutable Vector<typename FunctionTraits<T>::BaseType> err_p;
mutable Vector<typename FunctionTraits<T>::BaseType> ferr_p;
// </group>
// Local value and derivatives
mutable typename FunctionTraits<T>::DiffType valder_p;
// Local SVD constraints
mutable Vector<Vector<typename LSQTraits<typename FunctionTraits<T>::
BaseType>::base> > consvd_p;
//# 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) = 0;
// Build the normal matrix
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 constraint equations
void buildConstraint();
// Get the SVD constraints
void fillSVDConstraints();
// Calculate residuals
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);
// Function to get evaluated functional value
typename FunctionTraits<T>::BaseType
getVal_p(const Array<typename FunctionTraits<T>::BaseType> &x,
uInt j, uInt i) const;
// Initialise the fitter with number of solvable parameters
void initfit_p(uInt parcnt);
// Return number of condition equations and check sizes x, y, sigma
// <thrown>
// <li> Aipserror if size inconsistencies
// </thrown>
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);
// Reset all the input
void resetFunction();
private:
//# Data
//# Member functions
// Set function properties
void setFunctionEx();
// Set Constraint properties
Bool setConstraintEx(const uInt n,
const Vector<typename FunctionTraits<T>::BaseType> &x,
const typename FunctionTraits<T>::BaseType y);
};
} //# End namespace casacore
#ifndef CASACORE_NO_AUTO_TEMPLATES
#include <casacore/scimath/Fitting/GenericL2Fit.tcc>
#endif //# CASACORE_NO_AUTO_TEMPLATES
#endif
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