AHELP for CIAO 4.15 Sherpa

# lorentz2d

Context: models

## Synopsis

Two-dimensional un-normalised Lorentz function.

## Syntax

`lorentz2d`

## Example

```>>> create_model_component("lorentz2d", "mdl")
>>> print(mdl)```

Create a component of the lorentz2d 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.
xpos The center of the model on the x0 axis.
ypos The center of the model on the x1 axis.
ellip The ellipticity of the model.
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 / (1 + 4 * 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)```

and for an integrated grid it is the integral of this over the bin.

## Bugs

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