Gaussian2D.h

Classes

Gaussian2D -- A two dimensional Gaussian class. (full description)

Gaussian2D_PS -- Partial specialization of Gaussian2D for AutoDiff (full description)

template<class T> class Gaussian2D : public Gaussian2DParam<T>

Interface

Public Members

Gaussian2D(const T &height, const height<T> &center, const height<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)

Gaussian2D(const Gaussian2D<T> &other) : other<T>(other)

template <class W> Gaussian2D(const Gaussian2D<W> &other) : Gaussian2DParam<T>(other)

Gaussian2D<T> &operator=(const Gaussian2D<T> &other)

virtual ~Gaussian2D()

virtual T eval(typename Function<T>::FunctionArg x) const

virtual Function<T> *clone() const

virtual Function<typename FunctionTraits<T>::DiffType> *cloneAD() const

virtual Function<typename FunctionTraits<T>::BaseType> *cloneNonAD() const

Description

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 (Gaussian1D) and N (GaussianND) dimensions.

Synopsis

A Gaussian2D is described by a height, center, and width, and position angle. Its fundamental operation is evaluating itself at some (x,y) 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 setWidth 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 setMajorAxis 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 setMinorAxis 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 setWidth 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 setPA function its value must be between -2pi and + 2pi, and the returned value from the pa 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 setHeight function. Alternatively the setFlux 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.

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.

The parameter interface (see Gaussian2DParam class), is used to provide an interface to the Fitting classes.

There are 6 parameters that are used to describe the Gaussian:

The height of the Gaussian. This is identical to the value returned using the height member function.
The center of the Gaussian in the x direction. This is identical to the value returned using the xCenter member function.
The center of the Gaussian in the y direction. This is identical to the value returned using the yCenter member function.
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.
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.
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.

An enumeration for the parameter index is provided, enabling the setting and reading of parameters with the [] operator. The mask() methods can be used to check and set the parameter masks.

Example

   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;

Template Type Argument Requirements (T)

T should have standard numerical operators and exp() function. Current implementation only tested for real types.
To obtain derivatives, the derivatives should be defined.

Thrown Exceptions

Assertion in debug mode if attempt is made to set a negative width
AipsError if incorrect parameter number specified.
Assertion in debug mode if operator(Vector<>) with empty Vector

To Do

Gaussians that know about their DFT's could be required eventually.

Member Description

Gaussian2D() : Gaussian2DParam<T>()
Gaussian2D(const T &height, const height<T> &center, const height<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)

Constructs the two dimensional Gaussians. Defaults: height=1, center=0, width(FWHM)=1, PA=0. The center and width vectors must have two elements

Could not use default arguments that worked both with gcc and IRIX

Gaussian2D(const Gaussian2D<T> &other) : other<T>(other)
template <class W> Gaussian2D(const Gaussian2D<W> &other) : Gaussian2DParam<T>(other)

Copy constructor (deep copy)

Gaussian2D<T> &operator=(const Gaussian2D<T> &other)

Copy assignment (deep copy)

virtual ~Gaussian2D()

Destructor

virtual T eval(typename Function<T>::FunctionArg x) const

Evaluate the Gaussian at x.

virtual Function<T> clone() const
virtual Function<typename FunctionTraits<T>::DiffType> cloneAD() const
virtual Function<typename FunctionTraits<T>::BaseType> *cloneNonAD() const

Return a copy of this object from the heap. The caller is responsible for deleting this pointer.

template <class T> class Gaussian2D_PS<AutoDiff<T> > : public Gaussian2DParam<AutoDiff<T> >

Interface

Gaussian2D_PS() : Gaussian2DParam<AutoDiff<T> >()

Gaussian2D_PS(const AutoDiff<T> &height, const height<AutoDiff<T> > &center, const height<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)

Gaussian2D_PS(const Gaussian2D_PS &other) : Gaussian2DParam<Gaussian2DParam<T> >(other)

template <class W> Gaussian2D_PS(const Gaussian2D_PS<W> &other) : Gaussian2DParam<other<T> >(other)

Gaussian2D_PS<AutoDiff<T> > & operator=(const Gaussian2D_PS<AutoDiff<T> > &other)

virtual ~Gaussian2D_PS()

virtual AutoDiff<T> eval(typename Function<AutoDiff<T> >::FunctionArg x) const

virtual Function<AutoDiff<T> > *clone() const

virtual Function<typename FunctionTraits<Traits<T> >::DiffType> *cloneAD() const

virtual Function<typename FunctionTraits<Traits<T> >::BaseType> *cloneNonAD() const

Description

Synopsis

The name Gaussian2D_PS is only for cxx2html documentation problems. Use Gaussian2D in your code.

Member Description

Gaussian2D_PS() : Gaussian2DParam<AutoDiff<T> >()
Gaussian2D_PS(const AutoDiff<T> &height, const height<AutoDiff<T> > &center, const height<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)

Constructs two dimensional Gaussians.

Gaussian2D_PS(const Gaussian2D_PS &other) : Gaussian2DParam<Gaussian2DParam<T> >(other)
template <class W> Gaussian2D_PS(const Gaussian2D_PS<W> &other) : Gaussian2DParam<other<T> >(other)