normgauss2d

Context: models

Synopsis

Two-dimensional normalised gaussian function.

Syntax

normgauss2d

Example

>>> create_model_component("normgauss2d", "mdl")
>>> print(mdl)

Create a component of the normgauss2d model and display its default parameters. The output is:

mdl
   Param        Type          Value          Min          Max      Units
   -----        ----          -----          ---          ---      -----
   mdl.fwhm     thawed           10  1.17549e-38  3.40282e+38           
   mdl.xpos     thawed            0 -3.40282e+38  3.40282e+38           
   mdl.ypos     thawed            0 -3.40282e+38  3.40282e+38           
   mdl.ellip    frozen            0            0        0.999           
   mdl.theta    frozen            0     -6.28319      6.28319    radians
   mdl.ampl     thawed            1 -3.40282e+38  3.40282e+38

ATTRIBUTES

The attributes for this object are:

Attribute	Definition
fwhm	The Full-Width Half Maximum of the gaussian along the major axis. It is related to the sigma value by: FWHM = sqrt(8 * log(2)) * sigma.
xpos	The center of the gaussian on the x0 axis.
ypos	The center of the gaussian on the x1 axis.
ellip	The ellipticity of the gaussian.
theta	The angle of the major axis. It is in radians, measured counter-clockwise from the X0 axis (i.e. the line X1=0).
ampl	The amplitude refers to the integral of the model over the range -infinity to infinity for both axes.

Notes

The functional form of the model for points is:

f(x0,x1) = 4 * log(2) * ampl * exp(-4 * log(2) * r(x0,x1)^2)
           -------------------------------------------------
               pi * fwhm * fwhm * sqrt(1 - ellip * ellip)

r(x0,x1)^2 = xoff(x0,x1)^2 * (1-ellip)^2 + yoff(x0,x1)^2
             -------------------------------------------
                         fwhm^2 * (1-ellip)^2

xoff(x0,x1) = (x0 - xpos) * cos(theta) + (x1 - ypos) * sin(theta)

yoff(x0,x1) = (x1 - ypos) * cos(theta) - (x0 - xpos) * sin(theta)

The grid version is evaluated by adaptive multidimensional integration scheme on hypercubes using cubature rules, based on code from HIntLib ( [1] ) and GSL ( [2] ).

References

[1] HIntLib - High-dimensional Integration Library http://mint.sbg.ac.at/HIntLib/
[2] GSL - GNU Scientific Library http://www.gnu.org/software/gsl/

Bugs

See the bugs pages on the Sherpa website for an up-to-date listing of known bugs.