AHELP for CIAO 4.13 Sherpa v1

# sigmagauss2d

Context: models

## Synopsis

Two-dimensional gaussian function (varying sigma).

## Syntax

`sigmagauss2d`

## Example

```>>> create_model_component("sigmagauss2d", "mdl")
>>> print(mdl)```

Create a component of the sigmagauss2d model and display its default parameters. The output is:

```mdl
Param        Type          Value          Min          Max      Units
-----        ----          -----          ---          ---      -----
mdl.sigma_a  thawed           10  1.17549e-38  3.40282e+38
mdl.sigma_b  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.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
sigma_a The sigma of the gaussian along the major axis.
sigma_b The sigma of the gaussian along the minor axis.
xpos The center of the gaussian on the x0 axis.
ypos The center of the gaussian on the x1 axis.
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(-r(x0,x1)^2 / 2)

r(x0,x1)^2 = xoff(x0,x1)^2 + yoff(x0,x1)^2
-------------   -------------
sigma_a^2       sigma_b^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.