# Sersic2D¶

class sherpa.astro.models.Sersic2D(name='sersic2d')[source] [edit on github]

Two-dimensional Sersic model.

This is a generalization of the `DeVaucouleurs2D` model, in which the exponent `n` can vary (1, 2, and 3).

r0

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.

n

The Sersic index (n=4 replicates the `DeVaucouleurs2D` model).

Notes

The functional form of the model for points is can be expressed as the following:

```f(x0,x1) = ampl * exp(-b(n) * (r(x0,x1)^(1/n) - 1))

b(n) = 2 * n - 1 / 3 + 4 / (405 * n) + 46 / (25515 * n^2)

r(x0,x1)^2 = xoff(x0,x1)^2 * (1-ellip)^2 + yoff(x0,x1)^2
-------------------------------------------
r0^2 * (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 (4) and GSL (5).

References

1

http://ned.ipac.caltech.edu/level5/March05/Graham/Graham2.html

2

Graham, A. & Driver, S., 2005, PASA, 22, 118 http://adsabs.harvard.edu/abs/2005PASA…22..118G

3

Ciotti, L. & Bertin, G., A&A, 1999, 352, 447-451 http://adsabs.harvard.edu/abs/1999A%26A…352..447C

4

HIntLib - High-dimensional Integration Library http://mint.sbg.ac.at/HIntLib/

5

GSL - GNU Scientific Library http://www.gnu.org/software/gsl/

Attributes Summary

 `cache` The maximum size of the cache. `ndim` A two-dimensional model. `thawedparhardmaxes` The hard maximum values for the thawed parameters. `thawedparhardmins` The hard minimum values for the thawed parameters. `thawedparmaxes` The maximum limits of the thawed parameters. `thawedparmins` The minimum limits of the thawed parameters. `thawedpars` The thawed parameters of the model.

Methods Summary

 `apply`(outer, *otherargs, **otherkwargs) Clear the cache. Display the cache status. `calc`(*args, **kwargs) Evaluate the model on a grid. `guess`(dep, *args, **kwargs) Set an initial guess for the parameter values. `regrid`(*args, **kwargs) Reset the parameter values. `set_center`(xpos, ypos, *args, **kwargs) `startup`([cache]) Called before a model may be evaluated multiple times. Called after a model may be evaluated multiple times.

Attributes Documentation

cache = 5

The maximum size of the cache.

ndim = 2

A two-dimensional model.

thawedparhardmaxes

The hard maximum values for the thawed parameters.

The minimum and maximum range of the parameters can be changed with thawedparmins and thawedparmaxes but only within the range given by thawedparhardmins to thawparhardmaxes.

thawedparhardmins

The hard minimum values for the thawed parameters.

The minimum and maximum range of the parameters can be changed with thawedparmins and thawedparmaxes but only within the range given by thawedparhardmins to thawparhardmaxes.

thawedparmaxes

The maximum limits of the thawed parameters.

Get or set the maximum limits of the thawed parameters of the model as a list of numbers. If there are no thawed parameters then [] is used. The ordering matches that of the pars attribute.

`thawedpars`, `thawedarhardmaxes`, `thawedparmins`

thawedparmins

The minimum limits of the thawed parameters.

Get or set the minimum limits of the thawed parameters of the model as a list of numbers. If there are no thawed parameters then [] is used. The ordering matches that of the pars attribute.

`thawedpars`, `thawedarhardmins`, `thawedparmaxes`

thawedpars

The thawed parameters of the model.

Get or set the thawed parameters of the model as a list of numbers. If there are no thawed parameters then [] is used. The ordering matches that of the pars attribute.

Methods Documentation

apply(outer, *otherargs, **otherkwargs) [edit on github]
cache_clear() [edit on github]

Clear the cache.

cache_status() [edit on github]

Display the cache status.

Information on the cache - the number of “hits”, “misses”, and “requests” - is displayed at the INFO logging level.

Example

```>>> pl.cache_status()
powlaw1d.pl                size:    5  hits:   633  misses:   240  check=  873
```
calc(*args, **kwargs)[source] [edit on github]

Evaluate the model on a grid.

Parameters
• p (sequence of numbers) – The parameter values to use. The order matches the `pars` field.

• *args – The model grid. The values can be scalar or arrays, and the number depends on the dimensionality of the model and whether it is being evaluated over an integrated grid or at a point (or points).

get_center()[source] [edit on github]
guess(dep, *args, **kwargs)[source] [edit on github]

Set an initial guess for the parameter values.

Attempt to set the parameter values, and ranges, for the model to match the data values. This is intended as a rough guess, so it is expected that the model is only evaluated a small number of times, if at all.

regrid(*args, **kwargs) [edit on github]
reset() [edit on github]

Reset the parameter values.

Restores each parameter to the last value it was set to. This allows the parameters to be easily reset after a fit.

set_center(xpos, ypos, *args, **kwargs)[source] [edit on github]
startup(cache=False) [edit on github]

Called before a model may be evaluated multiple times.

Parameters

cache (bool, optional) – Should a cache be used when evaluating the models.

teardown() [edit on github]

Called after a model may be evaluated multiple times.