Last modified: December 2018

URL: http://cxc.harvard.edu/sherpa/ahelp/normgauss2d.html
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AHELP for CIAO 4.11 Sherpa v1

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:

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


Bugs

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

See Also

models
gauss2d, normgauss1d, sigmagauss2d