gaussian2d - Function

Calculate two-dimensional Gaussian

Synopsis
gaussian2d(x, y, height, center, fwhm, pa)

include "gaussian.g"

Description

The gaussian2d function evaluates two-dimensional Gaussians. You can specify the peak height of the Gaussian, the center of the Gaussian, the width of the major and minor axes and the position-angle of the Gaussian.

The width of the Gaussian is defined to be the full width at half-maximum (FWHM). If you prefer to use ``natural'' widths a constant fwhm_to_natural is provided^1.5. To get a natural width, multiply the FWHM by this constant ^1.6. Similarly the FWHM is derived by dividing the natural width by this constant.

The ``position angle'' is the angle, measured counter-clockwise, between the ``x'' axis and the major axis of the Gaussian. This angle is in radians.

The major axis of the Gaussian is considered to be the first axis of the specified FWHM, whether or not that width is in fact wider than the second axis. If you care about this, you should be careful to ensure that the first width is not smaller than the second.

You can evaluate the Gaussian at a number of positions by passing the function a vector for ``x'' and ``y'' instead of just scalars.

Arguments

x	in	values at which to evaluate the Gaussian
		Allowed:	double
		Default:	no default
y	in	values at which to evaluate the Gaussian
		Allowed:	numeric
		Default:	no default
height	in	maximum value of the Gaussian
		Allowed:	double
		Default:	1.0
center	in	location of the maximum value of the Gaussian
		Allowed:	double vector
		Default:	[0.0,0.0]
fwhm	in	width of the gaussian
		Allowed:	double vector
		Default:	[1.0,1.0]/fwhm_to_natural
pa	in	position angle (from y-axis to major-axis) (radians)
		Allowed:	double
		Default:	0.0

Returns
The ``z'' values or fail

Example
First evaluate a 2-D Gaussian onto a [100,100] array.

      include 'gaussian.g';
      z := array(0, 100, 100);
      x := 1:100
      for (i in 1:100) {
        y := array(x[i], 100);
        z[,i] := gaussian2d(x, y, center=[50, 50], fwhm=[30, 15], pa=30*pi/180)
      }

And then show it in a plotter:

      include 'pgplotter.g';
      pg := pgplotter();
      pg.env(1, 100, 1, 100, 1, 0);
      pg.gray(z, 1, 0, [0, 1, 0, 0, 0, 1])

See Also
gaussian1d

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	Package	utility
	Module	mathematics