Last modified: December 2023

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AHELP for CIAO 4.16 Sherpa


Context: models


Two-dimensional normalised gaussian function.




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

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

   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           


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.


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] ).



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

See Also

gauss2d, normgauss1d, sigmagauss2d