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Gaussian2D.h
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//# Gaussian2D.h: A two-dimensional Gaussian class
//# Copyright (C) 1995,1996,1997,2001,2002,2005
//# 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: casa-feedback@nrao.edu.
//# Postal address: AIPS++ Project Office
//# National Radio Astronomy Observatory
//# 520 Edgemont Road
//# Charlottesville, VA 22903-2475 USA
#ifndef SCIMATH_GAUSSIAN2D_H
#define SCIMATH_GAUSSIAN2D_H
//# Includes
#include <casacore/casa/aips.h>
#include <casacore/casa/Arrays/ArrayFwd.h>
#include <casacore/scimath/Functionals/Gaussian2DParam.h>
#include <casacore/scimath/Functionals/Function.h>
#include <casacore/scimath/Mathematics/AutoDiff.h>
#include <casacore/scimath/Mathematics/AutoDiffMath.h>
namespace casacore { //# NAMESPACE CASACORE - BEGIN
// <summary> A two dimensional Gaussian class.</summary>
// <use visibility=export>
// <reviewed reviewer="tcornwel" date="1996/02/22" tests="tGaussian2D"
// demos="">
// </reviewed>
// <prerequisite>
// <li> <linkto class="Gaussian2DParam">Gaussian2DParam</linkto>
// <li> <linkto class="Function">Function</linkto>
// </prerequisite>
// <etymology>
// A Gaussian2D functional is designed exclusively for calculating a
// Gaussian (or Normal) distribution in two dimensions. Other classes exist
// for calculating these functions in two
// (<linkto class=Gaussian1D>Gaussian1D</linkto>) and N
// (<linkto class=GaussianND>GaussianND</linkto>) dimensions.
// </etymology>
// <synopsis>
// A <src>Gaussian2D</src> is described by a height, center, and width,
// and position angle. Its fundamental operation is evaluating itself
// at some <src>(x,y)</src>
// coordinate. Its parameters (height, center and width, position angle) may
// be changed at run time.
//
// The width of the Gaussian (for the constructors or the <src> setWidth
// </src> function) is always specified in terms of the full width at half
// maximum (FWHM). The major axis is parallel with the y axis when the
// position angle is zero. The major axis will always have a larger width
// than the minor axis.
//
// It is not possible to set the width of the major axis (using the <src>
// setMajorAxis </src> function) smaller than the width of the current minor
// axis. Similarly it is not possible to set the width of the minor axis
// (using the <src> setMinorAxis </src> function) to be larger than the
// current major axis. Exceptions are thrown if these rules are violated or
// if the either the major or minor axis is set to a non-positive width. To
// set both axis in one hit use the <src> setWidth </src> function. All
// these restrictions can be overcome when the parameters interface is used
// (see below).
//
// The position angle is the angle between the y axis and the major axis and
// is measured counterclockwise, so a position angle of 45 degrees rotates
// the major axis to the line where y=-x. The position angle is always
// specified and returned in radians. When using the <src> setPA </src>
// function its value must be between -2pi and + 2pi, and the returned value
// from the <src> pa </src> function will always be a value between 0 and
// pi.
//
// The axial ratio can be used as an alternative to specifying the width of
// the minor axis. It is the ratio between the minor and major axis
// widths. The axial ratio is constrained to be between zero and one, and
// specifying something different (using setAxialRatio) will throw an
// exception.
//
// The peak height of the Gaussian can be specified at construction time or
// by using the <src> setHeight </src> function. Alternatively the <src>
// setFlux </src> function can be used to implicitly set the peak height by
// specifying the integrated area under the Gaussian. The height (or flux)
// can be positive, negative or zero, as this class makes no assumptions on
// what quantity the height represents.
//
// <note role=tip> Changing the width of the Gaussian will not affect
// its peak height but will change its flux. So you should always set the
// width before setting the flux. </note>
//
// The parameter interface (see
// <linkto class="Gaussian2DParam">Gaussian2DParam</linkto> class),
// is used to provide an interface to the
// <linkto module="Fitting">Fitting</linkto> classes.
//
// There are 6 parameters that are used to describe the Gaussian:
// <ol>
// <li> The height of the Gaussian. This is identical to the value
// returned using the <src> height </src> member function.
// <li> The center of the Gaussian in the x direction. This is identical to
// the value returned using the <src> xCenter </src> member function.
// <li> The center of the Gaussian in the y direction. This is identical to
// the value returned using the <src> yCenter </src> member function.
// <li> The width (FWHM) of the Gaussian on one axis. Initially this will be
// the major axis, but if the parameters are adjusted by a Fitting
// class, it may become the axis with the smaller width. To aid
// convergence of the non-linear fitting routines this parameter is
// allowed to be negative. This does not affect the shape of the
// Gaussian as the squares of the widths are used when evaluating the
// function.
// <li> A modified axial ratio. This parameter is the ratio of the width on
// the 'other' axis (which initially is the minor axis) and axis given
// by parameter YWIDTH. Because these internal widths are allowed to be
// negative and because there is no constraints on which axis is the
// larger one the modified axial ratio is not constrained to be between
// zero and one.
// <li> The position angle. This represents the angle (in radians) between
// the axis used by parameter 4, and the y axis, measured
// counterclockwise. If parameter 4 represents the major axis width
// then this parameter will be identical to the position angle,
// otherwise it will be different by 90 degrees. The tight constraints
// on the value of the rotation angle enforced by the setPA() function
// are relaxed so that any value between -6000 and 6000 is allowed. It
// is still interpreted in radians.
// </ol>
//
// An enumeration for the parameter index is provided, enabling the setting
// and reading of parameters with the <src>[]</src> operator. The
// <src>mask()</src> methods can be used to check and set the parameter masks.
//
// </synopsis>
// <example>
// <srcblock>
// Gaussian2D<Double> g(10.0, 0.0, 0.0, 2.0, 1.0, 0.0);
// Vector<Double> x(2);
// x(0) = 1.0; x(1) = 0.5;
// cout << "g(" << x(0) << "," << x(1) << ") = " << g(x) << endl;
// </srcblock>
// </example>
// <templating arg=T>
// <li> T should have standard numerical operators and exp() function. Current
// implementation only tested for real types.
// <li> To obtain derivatives, the derivatives should be defined.
// </templating>
// <thrown>
// <li> Assertion in debug mode if attempt is made to set a negative width
// <li> AipsError if incorrect parameter number specified.
// <li> Assertion in debug mode if operator(Vector<>) with empty Vector
// </thrown>
// <todo asof="2001/08/19">
// <li> Gaussians that know about their DFT's could be required eventually.
// </todo>
template<class T> class Gaussian2D : public Gaussian2DParam<T>
{
public:
//# Enumerations
//# Constructors
// Constructs the two dimensional Gaussians. Defaults:
// height=1, center=0, width(FWHM)=1, PA=0. The center and width vectors
// must have two elements
// <note role=warning> Could not use default arguments
// that worked both with gcc and IRIX </note>
// <group>
Gaussian2D() : Gaussian2DParam<T>() {}
Gaussian2D(const T &height, const Vector<T> &center,
const Vector<T> &width, const T &pa) :
Gaussian2DParam<T>(height, center, width, pa) {}
Gaussian2D(const T &height, const T &xCenter, const T &yCenter,
const T &majorAxis, const T &axialRatio, const T &pa) :
Gaussian2DParam<T>(height, xCenter, yCenter, majorAxis,
axialRatio, pa) {}
// </group>
// Copy constructor (deep copy)
// <group>
Gaussian2D(const Gaussian2D<T> &other) : Gaussian2DParam<T>(other) {}
template <class W>
Gaussian2D(const Gaussian2D<W> &other) : Gaussian2DParam<T>(other) {}
// </group>
// Copy assignment (deep copy)
Gaussian2D<T> &operator=(const Gaussian2D<T> &other) {
Gaussian2DParam<T>::operator=(other); return *this; }
// Destructor
virtual ~Gaussian2D() {}
//# Operators
// Evaluate the Gaussian at <src>x</src>.
// <group>
virtual T eval(typename Function<T>::FunctionArg x) const;
// </group>
//# Member functions
// Return a copy of this object from the heap. The caller is responsible
// for deleting this pointer.
// <group>
virtual Function<T> *clone() const { return new Gaussian2D<T>(*this); }
virtual Function<typename FunctionTraits<T>::DiffType> *cloneAD() const {
return new Gaussian2D<typename FunctionTraits<T>::DiffType>(*this); }
virtual Function<typename FunctionTraits<T>::BaseType> *cloneNonAD() const {
return new Gaussian2D<typename FunctionTraits<T>::BaseType>(*this); }
// </group>
//# Make members of parent classes known.
protected:
using Gaussian2DParam<T>::param_p;
using Gaussian2DParam<T>::thePA;
using Gaussian2DParam<T>::theCpa;
using Gaussian2DParam<T>::theSpa;
using Gaussian2DParam<T>::theXwidth;
public:
using Gaussian2DParam<T>::HEIGHT;
using Gaussian2DParam<T>::XCENTER;
using Gaussian2DParam<T>::YCENTER;
using Gaussian2DParam<T>::YWIDTH;
using Gaussian2DParam<T>::RATIO;
using Gaussian2DParam<T>::PANGLE;
using Gaussian2DParam<T>::fwhm2int;
};
#define Gaussian2D_PS Gaussian2D
// <summary> Partial specialization of Gaussian2D for <src>AutoDiff</src>
// </summary>
// <synopsis>
// <note role=warning> The name <src>Gaussian2D_PS</src> is only for cxx2html
// documentation problems. Use <src>Gaussian2D</src> in your code.</note>
// </synopsis>
template <class T> class Gaussian2D_PS<AutoDiff<T> > :
public Gaussian2DParam<AutoDiff<T> >
{
public:
//# Constructors
// Constructs two dimensional Gaussians.
// <group>
Gaussian2D_PS() : Gaussian2DParam<AutoDiff<T> >() {}
Gaussian2D_PS(const AutoDiff<T> &height,
const Vector<AutoDiff<T> > &center,
const Vector<AutoDiff<T> > &width,
const AutoDiff<T> &pa) :
Gaussian2DParam<AutoDiff<T> >(height, center, width, pa) {}
Gaussian2D_PS(const AutoDiff<T> &height, const AutoDiff<T> &xCenter,
const AutoDiff<T> &yCenter, const AutoDiff<T> &majorAxis,
const AutoDiff<T> &axialRatio, const AutoDiff<T> &pa) :
Gaussian2DParam<AutoDiff<T> >(height, xCenter, yCenter, majorAxis,
axialRatio, pa) {}
// </group>
// Copy constructor (deep copy)
// <group>
Gaussian2D_PS(const Gaussian2D_PS &other) :
Gaussian2DParam<AutoDiff<T> >(other) {}
template <class W>
Gaussian2D_PS(const Gaussian2D_PS<W> &other) :
Gaussian2DParam<AutoDiff<T> >(other) {}
// </group>
// Copy assignment (deep copy)
Gaussian2D_PS<AutoDiff<T> > &
operator=(const Gaussian2D_PS<AutoDiff<T> > &other) {
Gaussian2DParam<AutoDiff<T> >::operator=(other); return *this; }
// Destructor
virtual ~Gaussian2D_PS() {}
//# Operators
// Evaluate the Gaussian and its derivatives at <src>x</src>.
// <group>
virtual AutoDiff<T> eval(typename Function<AutoDiff<T> >::FunctionArg x) const;
// </group>
//# Member functions
// Return a copy of this object from the heap. The caller is responsible
// for deleting this pointer.
// <group>
virtual Function<AutoDiff<T> > *clone() const {
return new Gaussian2D<AutoDiff<T> >(*this); }
virtual Function<typename FunctionTraits<AutoDiff<T> >::DiffType>
*cloneAD() const {
return new Gaussian2D<typename FunctionTraits<AutoDiff<T> >::DiffType>
(*this); }
virtual Function<typename FunctionTraits<AutoDiff<T> >::BaseType>
*cloneNonAD() const {
return new Gaussian2D<typename FunctionTraits<AutoDiff<T> >::BaseType>
(*this); }
// </group>
//# Make members of parent classes known.
protected:
using Gaussian2DParam<AutoDiff<T> >::param_p;
using Gaussian2DParam<AutoDiff<T> >::thePA;
using Gaussian2DParam<AutoDiff<T> >::theCpa;
using Gaussian2DParam<AutoDiff<T> >::theSpa;
using Gaussian2DParam<AutoDiff<T> >::theXwidth;
public:
using Gaussian2DParam<AutoDiff<T> >::HEIGHT;
using Gaussian2DParam<AutoDiff<T> >::XCENTER;
using Gaussian2DParam<AutoDiff<T> >::YCENTER;
using Gaussian2DParam<AutoDiff<T> >::YWIDTH;
using Gaussian2DParam<AutoDiff<T> >::RATIO;
using Gaussian2DParam<AutoDiff<T> >::PANGLE;
using Gaussian2DParam<AutoDiff<T> >::fwhm2int;
};
#undef Gaussian2D_PS
} //# NAMESPACE CASACORE - END
#ifndef CASACORE_NO_AUTO_TEMPLATES
#include <casacore/scimath/Functionals/Gaussian2D.tcc>
#include <casacore/scimath/Functionals/Gaussian2D2.tcc>
#endif //# CASACORE_NO_AUTO_TEMPLATES
#endif
Gaussian2D_PS
#define Gaussian2D_PS
Definition Gaussian2D.h:245
casacore::AutoDiff
Definition AutoDiff.h:254
casacore::Function
Definition Function.h:200
casacore::Function::param_p
FunctionParam< T > param_p
The parameters and masks.
Definition Function.h:330
casacore::Function::FunctionArg
const ArgType * FunctionArg
Definition Function.h:205
casacore::Gaussian2DParam
Definition Gaussian2DParam.h:191
casacore::Gaussian2DParam::theXwidth
T theXwidth
cached vale of the Xwidth = ratio*theYwidth;
Definition Gaussian2DParam.h:286
casacore::Gaussian2DParam::height
T height() const
Get or set the peak height of the Gaussian.
Definition Gaussian2DParam.h:235
casacore::Gaussian2DParam::thePA
T thePA
cached vale of the PA
Definition Gaussian2DParam.h:279
casacore::Gaussian2DParam::majorAxis
T majorAxis() const
casacore::Gaussian2DParam::yCenter
T yCenter() const
Definition Gaussian2DParam.h:252
casacore::Gaussian2DParam::center
Vector< T > center() const
Get or set the center ordinate of the Gaussian.
casacore::Gaussian2DParam::theCpa
T theCpa
Definition Gaussian2DParam.h:283
casacore::Gaussian2DParam::width
Vector< T > width() const
Set or get the FWHM of the Gaussian.
casacore::Gaussian2DParam::fwhm2int
T fwhm2int
Constant to scale halfwidth at 1/e to FWHM.
Definition Gaussian2DParam.h:277
casacore::Gaussian2DParam::Gaussian2DParam
Gaussian2DParam()
Constructs the two dimensional Gaussians.
casacore::Gaussian2DParam::theSpa
T theSpa
cached values of the cos and sine of thePA
Definition Gaussian2DParam.h:282
casacore::Gaussian2DParam::operator=
Gaussian2DParam< T > & operator=(const Gaussian2DParam< T > &other)
Copy assignment (deep copy).
casacore::Gaussian2DParam::axialRatio
T axialRatio() const
casacore::Gaussian2DParam::xCenter
T xCenter() const
Definition Gaussian2DParam.h:250
casacore::Gaussian2DParam::PANGLE
@ PANGLE
Definition Gaussian2DParam.h:194
casacore::Gaussian2DParam::HEIGHT
@ HEIGHT
Definition Gaussian2DParam.h:194
casacore::Gaussian2DParam::XCENTER
@ XCENTER
Definition Gaussian2DParam.h:194
casacore::Gaussian2DParam::RATIO
@ RATIO
Definition Gaussian2DParam.h:194
casacore::Gaussian2DParam::YCENTER
@ YCENTER
Definition Gaussian2DParam.h:194
casacore::Gaussian2DParam::YWIDTH
@ YWIDTH
Definition Gaussian2DParam.h:194
casacore::Gaussian2D_PS< AutoDiff< T > >::cloneNonAD
virtual Function< typename FunctionTraits< AutoDiff< T > >::BaseType > * cloneNonAD() const
Definition Gaussian2D.h:308
casacore::Gaussian2D_PS< AutoDiff< T > >::~Gaussian2D_PS
virtual ~Gaussian2D_PS()
Destructor.
Definition Gaussian2D.h:289
casacore::Gaussian2D_PS< AutoDiff< T > >::Gaussian2D_PS
Gaussian2D_PS()
Constructs two dimensional Gaussians.
Definition Gaussian2D.h:261
casacore::Gaussian2D_PS< AutoDiff< T > >::operator=
Gaussian2D_PS< AutoDiff< T > > & operator=(const Gaussian2D_PS< AutoDiff< T > > &other)
Copy assignment (deep copy).
Definition Gaussian2D.h:285
casacore::Gaussian2D_PS< AutoDiff< T > >::Gaussian2D_PS
Gaussian2D_PS(const AutoDiff< T > &height, const Vector< AutoDiff< T > > &center, const Vector< AutoDiff< T > > &width, const AutoDiff< T > &pa)
Definition Gaussian2D.h:262
casacore::Gaussian2D_PS< AutoDiff< T > >::Gaussian2D_PS
Gaussian2D_PS(const AutoDiff< T > &height, const AutoDiff< T > &xCenter, const AutoDiff< T > &yCenter, const AutoDiff< T > &majorAxis, const AutoDiff< T > &axialRatio, const AutoDiff< T > &pa)
Definition Gaussian2D.h:267
casacore::Gaussian2D_PS< AutoDiff< T > >::Gaussian2D_PS
Gaussian2D_PS(const Gaussian2D_PS &other)
Copy constructor (deep copy).
Definition Gaussian2D.h:276
casacore::Gaussian2D_PS< AutoDiff< T > >::Gaussian2D_PS
Gaussian2D_PS(const Gaussian2D_PS< W > &other)
Definition Gaussian2D.h:279
casacore::Gaussian2D_PS< AutoDiff< T > >::cloneAD
virtual Function< typename FunctionTraits< AutoDiff< T > >::DiffType > * cloneAD() const
Definition Gaussian2D.h:304
casacore::Gaussian2D_PS< AutoDiff< T > >::clone
virtual Function< AutoDiff< T > > * clone() const
Return a copy of this object from the heap.
Definition Gaussian2D.h:301
casacore::Gaussian2D_PS< AutoDiff< T > >::eval
virtual AutoDiff< T > eval(typename Function< AutoDiff< T > >::FunctionArg x) const
Evaluate the Gaussian and its derivatives at x.
casacore::Gaussian2D
Definition Gaussian2D.h:176
casacore::Gaussian2D::cloneAD
virtual Function< typename FunctionTraits< T >::DiffType > * cloneAD() const
Definition Gaussian2D.h:222
casacore::Gaussian2D::~Gaussian2D
virtual ~Gaussian2D()
Destructor.
Definition Gaussian2D.h:209
casacore::Gaussian2D::Gaussian2D
Gaussian2D(const T &height, const T &xCenter, const T &yCenter, const T &majorAxis, const T &axialRatio, const T &pa)
Definition Gaussian2D.h:191
casacore::Gaussian2D::Gaussian2D
Gaussian2D()
Constructs the two dimensional Gaussians.
Definition Gaussian2D.h:187
casacore::Gaussian2D::operator=
Gaussian2D< T > & operator=(const Gaussian2D< T > &other)
Copy assignment (deep copy).
Definition Gaussian2D.h:205
casacore::Gaussian2D::cloneNonAD
virtual Function< typename FunctionTraits< T >::BaseType > * cloneNonAD() const
Definition Gaussian2D.h:224
casacore::Gaussian2D::Gaussian2D
Gaussian2D(const Gaussian2D< W > &other)
Definition Gaussian2D.h:201
casacore::Gaussian2D::clone
virtual Function< T > * clone() const
Return a copy of this object from the heap.
Definition Gaussian2D.h:221
casacore::Gaussian2D::Gaussian2D
Gaussian2D(const T &height, const Vector< T > &center, const Vector< T > &width, const T &pa)
Definition Gaussian2D.h:188
casacore::Gaussian2D::Gaussian2D
Gaussian2D(const Gaussian2D< T > &other)
Copy constructor (deep copy).
Definition Gaussian2D.h:199
casacore::Gaussian2D::eval
virtual T eval(typename Function< T >::FunctionArg x) const
Evaluate the Gaussian at x.
casacore::Vector
Definition Vector.h:82
casacore
this file contains all the compiler specific defines
Definition mainpage.dox:28
casacore::pa
LatticeExprNode pa(const LatticeExprNode &left, const LatticeExprNode &right)
This function finds 180/pi*atan2(left,right)/2.