# Radial and elliptical profiles of Image Data

Sherpa Threads (CIAO 4.14 Sherpa)

## Overview

#### Synopsis:

This thread shows how you can use the sherpa_contrib package—part of the CIAO contributed scripts—to plot radial or elliptical profiles of your imaging fits. These can be used to visualize the fit results, and help you interpret the results—e.g. to see how well the model represents the data or to let you fine tune model parameters before a fit to try and reduce the fit time. The thread is based on the Fitting Imaging Data thread, which should be read before this thread.

**Last Update:** 28 Mar 2022 -
reviewed for CIAO 4.14, updated with data reprocessed with
CIAO 4.14 and CalDB 4.9.7.

## Contents

**Create and Read Fits Image Data****Initial fit to the data: Gaussian plus constant****Adding a Gaussian to model the core emission****Using elliptical models**-
**Overlays and data access** **Scripting It****Summary****History**-
**Images**- Figure 1: Initial radial profile of the data
- Figure 2: Initial radial profile of the model
- Figure 3: A Gaussian plus constant fit to the data
- Figure 4: Adding a second Gaussian component
- Figure 5: Residuals (in counts) about the fit
- Figure 6: Residuals (normalized by the error) about the fit
- Figure 7: Elliptical profile
- Figure 8: Over-riding the ellipticity

## Create and Read Fits Image Data

**Download the sample data:** 1838 (ACIS-S, G21.5-0.9)

unix% download_chandra_obsid 1838

This repeats the data creation step of the imaging thread, which should be read for an explanation of the steps.

unix% punlearn dmcopy unix% dmcopy \ "acisf01838_repro_evt2.fits[sky=box(4059.25,4235.75,521.5,431.5)][bin x=::2,y=::2]" \ image2.fits

After starting *Sherpa*, we load in both the radial-profile
code and the utility routines, then the data (the
from ... import line only has to be called once
per session):

sherpa> from sherpa_contrib.all import * sherpa> load_image("image2.fits")

An error message of

ImportError: No module named sherpa_contrib

means that the CIAO contributed scripts package has not been installed or is out of date.

We then set up the coordinate system we use for the fit, along with the statistic and optimization method:

sherpa> set_coord("physical") sherpa> set_stat("cash") sherpa> set_method("simplex")

We can review the current choices for these settings using the following commands or with the show_method and show_stat commands:

sherpa> get_coord() 'physical' sherpa> get_stat_name() 'cash' sherpa> get_method_name() 'neldermead'

We finish this section by restricting the region to be fitted:

## Initial fit to the data: Gaussian plus constant

We start with a single Gaussian component to represent the bulk of the emission, and restrict the range of the parameters to values appropriate to this dataset. We use values somewhat more restrictive than used in the original thread, the component name src rather than g1, and take advantage of the guess routine to set sensible limits on the parameter values:

sherpa> set_source(gauss2d.src) sherpa> print(src) gauss2d.src Param Type Value Min Max Units ----- ---- ----- --- --- ----- src.fwhm thawed 10 1.17549e-38 3.40282e+38 src.xpos thawed 0 -3.40282e+38 3.40282e+38 src.ypos thawed 0 -3.40282e+38 3.40282e+38 src.ellip frozen 0 0 0.999 src.theta frozen 0 -6.28319 6.28319 radians src.ampl thawed 1 -3.40282e+38 3.40282e+38 sherpa> guess(src) sherpa> print(src) gauss2d.src Param Type Value Min Max Units ----- ---- ----- --- --- ----- src.fwhm thawed 4 0.004 4000 src.xpos thawed 4061.5 3953.5 4167.5 src.ypos thawed 4240.5 4132.5 4346.5 src.ellip frozen 0 0 0.999 src.theta frozen 0 -6.28319 6.28319 radians src.ampl thawed 309 0.309 309000 sherpa> set_par(src.fwhm, min=0.1, max=300, val=20) sherpa> set_par(src.ampl, min=0.1, max=1000, val=20)

The last two sets of lines could also have been written:

sherpa> src.fwhm = 20 sherpa> src.fwhm.min = 0.1 sherpa> src.fwhm.max = 300 sherpa> src.ampl = 20 sherpa> src.ampl.min = 0.1 sherpa> src.ampl.max = 1000

The current source model definition may be displayed:

sherpa> show_model() Model: 1 gauss2d.src Param Type Value Min Max Units ----- ---- ----- --- --- ----- src.fwhm thawed 20 0.1 300 src.xpos thawed 4061.5 3953.5 4167.5 src.ypos thawed 4240.5 4132.5 4346.5 src.ellip frozen 0 0 0.999 src.theta frozen 0 -6.28319 6.28319 radians src.ampl thawed 20 0.1 1000

We now create our first radial plot of the data using the prof_data command:

sherpa> prof_data() sherpa> plt.xscale('log') sherpa> plt.yscale('log')

The resulting plot is shown in Figure 1:

### Figure 1: Initial radial profile of the data

We decide to include a background component before fitting, and so add in a constant model to the source expression. The value of the background model was estimated from Figure 1; this suggests a level of 0.05 counts per physical pixel. However, since the data has been binned by 2 in each direction (the cdelt field is 2), then we need to use a value of \(2 \times 2 \times 0.05\), as shown below:

sherpa> print(get_data().sky) physical crval = [3798.5,4019.5] crpix = [0.5,0.5] cdelt = [2.,2.] sherpa> set_source(src + const2d.bgnd) sherpa> bgnd.c0 = 0.2 sherpa> bgnd.c0.max = 100

The prof_fit command will produce a radial profile of the fit overlain on the data (similar to how plot_fit works). Before making this call we change the plot preferences so that both axes are drawn with log-scaling. We use the optional label argument of prof_fit to turn off display of the labels that show the profile center. The result is Figure 2.

sherpa> get_data_prof_prefs()["xlog"] = True sherpa> get_data_prof_prefs()["ylog"] = True sherpa> prof_fit(label=False)

### Figure 2: Initial radial profile of the model

It is obvious, from Figure 2, that the width of the Gaussian is too small. A value roughly twice the current size would be a better fit, so we change the src.fwhm value before our first fit.

sherpa> src.fwhm = src.fwhm.val * 2 sherpa> fit() Dataset = 1 Method = neldermead Statistic = cash Initial fit statistic = -31319 Final fit statistic = -49874.8 at function evaluation 496 Data points = 9166 Degrees of freedom = 9161 Change in statistic = 18555.9 src.fwhm 57.7364 src.xpos 4062 src.ypos 4241.4 src.ampl 23.6894 bgnd.c0 0.27316

Note that we had to say "src.fwhm.val * 2" rather than
"src.fwhm * 2" in the assignment operator. If we
did not include the trailing ".val" to get at the numeric
value of the parameter, *Sherpa* would have tried to create a
parameter link to itself, which
would have failed with the following error message:

ParameterError: requested parameter link creates a cyclic reference

We now use the prof_fit_resid and image_fit commands to see how well the model fits the data. The output of the prof_fit_resid command is shown in Figure 3.

sherpa> image_fit() sherpa> prof_fit_resid() sherpa> plt.savefig('fit.png')

### Figure 3: A Gaussian plus constant fit to the data

The y-axis of the top plot in Figure 3 is drawn with a logarithmic-scale since we earlier set the data plot preference for ylog to True. The x-axis has remained with a linear-scale because the preference for the residual plot has over-ridden the data setting. We change the x-axis preferences for both styles of residual plot (resid and delchi) so that future such plots (e.g. Figure 5) will have their x-axis drawn with a log-scale:

sherpa> get_resid_prof_prefs()["xlog"] = True sherpa> get_delchi_prof_prefs()["xlog"] = True

## Adding a Gaussian to model the core emission

We now add a second Gaussian component to represent the core emission.

sherpa> set_source(bgnd + src + gauss2d.core) sherpa> guess(core) sherpa> set_par(core.fwhm, 10, 0.1, 100) sherpa> set_par(core.ampl, 100, 0.1, 1000) sherpa> prof_fit(model=src)

The model profile now looks like Figure 4. Since the model expression now contains two components with xpos and ypos parameters we have to say which one should be used to define the profile center; in this case we choose the src component by adding model=src to the argumemt list of prof_fit. If no model had been specified the call would have failed with the error message:

ValueError: Multiple xpos parameters in source expression: ((const2d.bgnd + gauss2d.src) + gauss2d.core)

### Figure 4: Adding a second Gaussian component

We now fit the whole model. In the original thread only the core component, g2, is fit at this stage, but the results are similar. We then plot the fit results together with the residuals in two windows: Figure 5, where the residuals are measured as (data-model) and Figure 6, where they are measured as (data-model)/error.

sherpa> fit() Dataset = 1 Method = neldermead Statistic = cash Initial fit statistic = -54106.4 Final fit statistic = -55919.2 at function evaluation 1351 Data points = 9166 Degrees of freedom = 9157 Change in statistic = 1812.83 bgnd.c0 0.200978 src.fwhm 64.1228 src.xpos 4062.23 src.ypos 4241.83 src.ampl 17.3896 core.fwhm 6.50002 core.xpos 4062.35 core.ypos 4239.62 core.ampl 232.574 sherpa> prof_fit_resid(model=src, group_counts=200)

### Figure 5: Residuals (in counts) about the fit

sherpa> prof_fit_delchi(model=src, group_counts=200)

### Figure 6: Residuals (normalized by the error) about the fit

## Using elliptical models

Up until now the models have been circularly-symmetric (i.e. the ellipticity of the components has been zero). We now see what happens if we let the core emission be elliptical:

sherpa> thaw(core) sherpa> core.ellip = 0.1 sherpa> core.theta = 1 sherpa> fit() Dataset = 1 Method = neldermead Statistic = cash Initial fit statistic = -55969.3 Final fit statistic = -56099.7 at function evaluation 1196 Data points = 9166 Degrees of freedom = 9155 Change in statistic = 130.36 bgnd.c0 0.199319 src.fwhm 64.2921 src.xpos 4062.24 src.ypos 4241.84 src.ampl 17.2504 core.fwhm 8.02733 core.xpos 4062.29 core.ypos 4239.61 core.ellip 0.330437 core.theta 0.809444 core.ampl 233.588 sherpa> prof_fit(model=core, group_counts=200)

Since the range of the theta parameter of the models now defaults to -2π to 2π, rather than having a lower limit of 0, the theta parameter often does not need to be changed before starting a fit.

In earlier versions of CIAO (<4.6) this thread suggested setting

core.theta = 1

before the fit; changing this value before a fit can often be a sensible choice, as with any other parameter, to avoid getting trapped in local minima.

The resulting plot is shown in Figure 7.

### Figure 7: Elliptical profile

You can over-ride any of the component values used to define the profile: in the following we use the position of the core component but ignore the model's ellipticity, and use circular annuli instead. The result is shown in Figure 8.

sherpa> prof_fit(model=core, group_counts=200, ellip=0)

### Figure 8: Over-riding the ellipticity

## Overlays and data access

In this section we shall highlight some of the other features of the profiles package:

- plot preferences
- plot overlays
- data access

### Plot preferences

The individual plots—such as data, model, resid, and delchi—have preference settings. The current settings can be retrieved with the get_<type>_prof_prefs command: for example

sherpa> print(get_data_prof_prefs()) {'yerrorbars': True, 'ecolor': None, 'capsize': None, 'barsabove': False, 'xlog': True, 'ylog': True, 'linestyle': '', 'linecolor': None, 'color': None, 'marker': 'o', 'markerfacecolor': 'none', 'markersize': 4}

These values can be changed, and new ones added, either by saying

sherpa> get_data_prof_prefs()["markercolor"] = "green"

or by assigning a variable to the return value of the call and then changing the variable:

sherpa> p = get_data_prof_prefs() sherpa> p["markercolor"] = "green" sherpa> p["ecolor"] = "blue"

A full list of the preferences can be found in the following ahelp pages:

- get_data_prof_prefs()
- get_model_prof_prefs()
- get_source_prof_prefs()
- get_resid_prof_prefs()
- get_delchi_prof_prefs()

### Overlaying data

The overplot argument can be used to overlay data on an existing plot. The commands

sherpa> prof_data(model=core) sherpa> prof_model(model=core, overplot=True)

produce a plot similar to plot_fit. This capability extends to plot_fit, so you could say

sherpa> prof_fit(model=core) sherpa> prof_fit(2, model=core, overplot=True)

to overplot the data and model from dataset 2 onto the plot from the default dataset.

### Accessing the plot data

For the basic plot types—e.g. data, model, source, resid, delchi, and fit—there are corresponding get_<type>_prof() calls which return objects which contain the data used to create the plots. These routines can be called without having to call the corresponding prof_<type>() routine first.

## Scripting It

The commands used to run this thread may be saved in a text file such
as fit.py, which
can then be executed as a script:
%run -i fit.py. Alternatively, the *Sherpa*
session can be saved to a binary file with the
save command (restored with the
restore command), or to an
editable ASCII file with save_all.

The *Sherpa* script command may be used
to save *everything* typed on the command line in a
*Sherpa* session:

sherpa> script(filename="sherpa.log", clobber=False)

(Note that restoring a *Sherpa* session from such a file
could be problematic since it may include syntax errors,
unwanted fitting trials, et cetera.)

## Summary

This thread showed you how to use the plotting routines from the
sherpa_contrib.profiles
package.
These routines allow you to view a radial plot of your
two-dimensional data, model, fit, or residuals;
this allows you to inspect the fit parameters so that
you start closer to the best-fit solution or to
visually inspect the fit results. Since they radially
average the results you should *always*
also look at the image residuals too, using the
image_fit
command.

Both sets of routines can be loaded in one go using the sherpa_contrib module.

The ahelp pages for the individual commands provide more information:

- prof_data()
- prof_model()
- prof_source()
- prof_resid()
- prof_delchi()
- prof_fit()
- prof_fit_resid()
- prof_fit_delchi()

- get_data_prof_prefs()
- get_model_prof_prefs()
- get_source_prof_prefs()
- get_resid_prof_prefs()
- get_delchi_prof_prefs()

- get_data_prof()
- get_model_prof()
- get_source_prof()
- get_resid_prof()
- get_delchi_prof()
- get_fit_prof()

## History

15 Apr 2009 | new version for CIAO 4.1; based on the image-fitting thread |

24 Jul 2009 | replaced use of set_param_limits_from_image() by guess() |

06 Jan 2010 | updated for CIAO 4.2 |

13 Jul 2010 | updated for CIAO 4.2 Sherpa v2: removal of S-Lang version of thread. |

30 Jan 2012 | reviewed for CIAO 4.4. |

05 Dec 2013 | reviewed for CIAO 4.6: noted that the minimum value of the theta parameter is now -2π rather than 0. |

11 Dec 2014 | reviewed for CIAO 4.7: updated input file and fit results |

10 Dec 2015 | reviewed for CIAO 4.8, no content change. |

02 Dec 2016 | reviewed for CIAO 4.9, removed references to CIAO 3.4 functionality. |

01 Jun 2018 | reviewed for CIAO 4.10, added clarification on prof_fit grouping. |

12 Dec 2018 | reviewed for CIAO 4.11, no content change. |

11 Dec 2019 | Updated for CIAO 4.12, using Matplotlib rather than ChIPS. |

28 Mar 2022 | reviewed for CIAO 4.14, updated with data reprocessed with CIAO 4.14 and CalDB 4.9.7. |