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gaussian1d - Function

	Package	utility
	Module	mathematics

Calculate a one-dimensional Gaussian

Synopsis
gaussian1d(x, height, center, fwhm)

include "gaussian.g"

Description

The gaussian1d function evaluates one-dimensional Gaussians. You can specify the peak height of the Gaussian, the center of the Gaussian and the width 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^1.3. To get a natural width, multiply the FWHM by this constant ^1.4. Similarly the FWHM is derived by dividing the natural width by this constant.

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

Arguments

x	in	values at which to evaluate the Gaussian
		Allowed:	double
		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
		Default:	0.0
fwhm	in	width of the gaussian
		Allowed:	double
		Default:	1/fwhm_to_natural

Returns
The ``y'' values or fail

Example
This simple example calculates and plots a Gaussian.

      include 'gaussian.g';
      x := 1:100;
      y := gaussian1d(x, height=3, center=30, fwhm=20);

And then plot the example, marking the peak and FWHM of the Gaussian.

      include 'pgplotter.g';
      pg := pgplotter();
      pg.env(1, 100, 0, 3, 0, 0);
      pg.line(x,y);                   # Plot the Gaussian
      pg.line([30,30], [0, 3]);       # Show the center

      # Show the FWHM
      pg.line([30-20/2, 30-20/2, 30+20/2, 30+20/2],   # x
	      [0,       3/2,     3/2,     0]);        # y

See Also
gaussian2d