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AHELP for CIAO 4.11 Sherpa v1

# 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:

### 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.

## See Also

models
devaucouleurs2d, hubblereynolds, sersic2d