Gaussian3D.h

Classes

Gaussian3D -- A three dimensional Gaussian class. (full description)

Gaussian3D_PS -- Partial specialization of Gaussian3D for AutoDiff (full description)

template<class T> class Gaussian3D : public Gaussian3DParam<T>

Interface

Public Members

Gaussian3D()

Gaussian3D(T height, const Vector<T>& center, const Vector<T>& width, T theta, T phi)

Gaussian3D(T &height, T &xCenter, T &yCenter, T &zCenter, T &xWidth, T &yWidth, T &zWidth, T &theta, T &phi)

Gaussian3D(const Gaussian3D<T> &other)

template <class W> Gaussian3D(const Gaussian3D<W> &other) : Gaussian3DParam<T>(other)

virtual ~Gaussian3D()

Gaussian3D<T> &operator=(const Gaussian3D<T> &other)

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

Private Members

T sq(T v) const

Description

Prerequisite

• Gaussian3DParam
• Function

Etymology

Synopsis

The width of the Gaussian is now specified in terms of the full width at half maximum (FWHM), like the 2D and 1D Gaussian functional classes.

The three axis values refer to the x, y, and z axes, and unlike with the 2D Gaussian any of the three axes may be the longest; instead, the position angles are restricted. The first position angle, theta, is the longitudinal angle, referring to the rotation (counterclockwise) around the z-axis. The second, phi, is the latidudinal angle, referring to the rotation around the theta-rotated y axis. The domain of both angles is -pi/4 < A < pi/4, although the angles are not constrained when fitting and can be set outside the domain by setting the parameters directly using Functional operator[]. (Note that the use of theta and phi corresponds to the mathematics convention for these angles, not the physics convention.)

The parameter interface (see Gaussian3DParam class), is used to provide an interface to the Fitting classes.

There are 9 parameters that are used to describe the Gaussian:

1. The height of the Gaussian. This is identical to the value returned using the height member function.
2. The center of the Gaussian in the x direction. This is identical to the value returned using the xCenter member function.
3. The center of the Gaussian in the y direction. This is identical to the value returned using the yCenter member function.
4. The center of the Gaussian in the z direction. This is identical to the value returned using the zCenter member function.
5. The width of the Gaussian along the x-axis.
6. The width of the Gaussian along the y-axis.
7. The width of the Gaussian along the z-axis.
8. The longitudinal position angle, theta (in radians)
9. The latitudinal position angle, phi (also 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

    Gaussian3D<Double> g(9.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 0.0, 0.0);
    Vector<Double> x(3);
    x(0) = 1.0; x(1) = 0.5; x(2) = 0.0
    cout << "g(" << x(0) << "," << x(1) << "," << x(2) << ")=" << g(x) << endl;
    

Motivation

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

• Optimize derivative calculations for faster fitting?

Member Description

Gaussian3D()
Gaussian3D(T height, const Vector<T>& center, const Vector<T>& width, T theta, T phi)
Gaussian3D(T &height, T &xCenter, T &yCenter, T &zCenter, T &xWidth, T &yWidth, T &zWidth, T &theta, T &phi)

Constructs the three-dimensional Gaussians. Defaults: height = 1, center = {0,0,0}, width = {1,1,1}, theta = phi = 0. The center and width vectors must have three elements.

Gaussian3D(const Gaussian3D<T> &other)
template <class W> Gaussian3D(const Gaussian3D<W> &other) : Gaussian3DParam<T>(other)

Copy constructor

virtual ~Gaussian3D()

Destructor

Gaussian3D<T> &operator=(const Gaussian3D<T> &other)

Assignment operator

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.

T sq(T v) const

template <class T> class Gaussian3D_PS<AutoDiff<T> > : public Gaussian3DParam<AutoDiff<T> >

Interface