Gaussian3DParam.h

Classes

Gaussian3DParam -- Parameter handling for 3 dimensional Gaussian class (full description)

template<class Type> class Gaussian3DParam : public Function<Type>

Interface

Public Members

Gaussian3DParam()

Gaussian3DParam(Type height, const Vector<Type>& center, const Vector<Type>& width, Type theta, Type phi)

Gaussian3DParam(Type &height, Type &xCenter, Type &yCenter, Type &zCenter, Type &xWidth, Type &yWidth, Type &zWidth, Type &theta, Type &phi)

Gaussian3DParam(const Gaussian3DParam<Type> &other)

Gaussian3DParam<Type> &operator=(const Gaussian3DParam<Type> &other)

virtual ~Gaussian3DParam()

virtual uInt ndim() const

Type height() const

void setHeight(const Type & height)

Type flux() const

void setFlux(const Type & flux)

Vector<Type> center() const

void setCenter(const Vector<Type>& center)

Type xCenter() const

void setXcenter(const Type & xcenter)

Type yCenter() const

void setYcenter(const Type & ycenter)

Type zCenter() const

void setZcenter(const Type & zcenter)

Vector<Type> width() const

void setWidth(const Vector<Type>& width)

void setXwidth(const Type & xwidth)

Type xWidth() const

void setYwidth(const Type & ywidth)

Type yWidth() const

void setZwidth(const Type & zwidth)

Type zWidth() const

Type theta() const

void settheta(const Type & sT)

Type phi() const

void setphi(const Type & sP)

Protected Members

void settrigvals() const

Description

Review Status

Programs:

Tests:

• tGaussian3DParam

Prerequisite

• FunctionParam class
• Function class

Etymology

Synopsis

A Gaussian3D is described by a height, center, width, and two position angles.

The width of the Gaussian is now specified in terms of the full width at half maximum (FWHM), as with the 1D and 2D 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. (Note that the use of theta and phi corresponds to the mathematical convention for these angles, not the physics convention.)

The parameter interface (see FunctionParam 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 H, CX, CY,CZ, AX, AY, AZ, THETA, PHI 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.

This class is in general used implicitly by the Gaussian3D class only.

Other points to bear in mind when fitting this class to measured data are:

• If you need to fit a circular Gaussian to data you should mask one or both position angles. This avoids rank deficiency in the fitting routines as the position angle is meaningless when the axes are equal.

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;
    

Template Type Argument Requirements (T)

• T should have standard numerical operators and exp() function. Current implementation only tested for real types (and AutoDiff of them).

Thrown Exceptions

• Assertion in debug mode if attempt is made to set a negative width
• AipsError if incorrect parameter number specified.
• others?

To Do

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

Member Description

Gaussian3DParam()
Gaussian3DParam(Type height, const Vector<Type>& center, const Vector<Type>& width, Type theta, Type phi)
Gaussian3DParam(Type &height, Type &xCenter, Type &yCenter, Type &zCenter, Type &xWidth, Type &yWidth, Type &zWidth, Type &theta, Type &phi)

Gaussian3DParam(const Gaussian3DParam<Type> &other)

Copy construcor

Gaussian3DParam<Type> &operator=(const Gaussian3DParam<Type> &other)

Copy assignment

virtual ~Gaussian3DParam()

Destructor

virtual uInt ndim() const

Return dimensionality

Type height() const
void setHeight(const Type & height)

Type flux() const
void setFlux(const Type & flux)

Get or set the total flux of the Gaussian. (Note: Since this changes the height of the Gaussian but not its width, always set the width before setting the flux.)

Vector<Type> center() const
void setCenter(const Vector<Type>& center)
Type xCenter() const
void setXcenter(const Type & xcenter)
Type yCenter() const
void setYcenter(const Type & ycenter)
Type zCenter() const
void setZcenter(const Type & zcenter)

Get or cet the center coordinates of the Gaussian

Vector<Type> width() const
void setWidth(const Vector<Type>& width)
void setXwidth(const Type & xwidth)
Type xWidth() const
void setYwidth(const Type & ywidth)
Type yWidth() const
void setZwidth(const Type & zwidth)
Type zWidth() const

Get or set the sigma-width of the Gaussian

Type theta() const
void settheta(const Type & sT)
Type phi() const
void setphi(const Type & sP)

Get or set the rotation angles of the Gaussian. Theta=logitude, phi=latitude

void settrigvals() const