Synopsis
Two-dimensional gaussian function.
Syntax
gauss2d
Example
>>> create_model_component("gauss2d", "mdl") >>> print(mdl)
Create a component of the gauss2d 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 maximum peak of the model. |
Notes
The functional form of the model for points is:
f(x0,x1) = ampl * exp(-4 * log(2) * r(x0,x1)^2) 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.
See Also
- models
- gauss1d, normgauss2d, sigmagauss2d