Changing the grouping scheme of a data set within Sherpa
Sherpa Threads (CIAO 4.14 Sherpa)
Overview
Synopsis:
In order to use Gaussian statistics to fit a model to a data set, it is often necessary to "group" the data—i.e., combine channels until you have enough counts—before use. It is possible to set and change the grouping of a file after it has been read into Sherpa by using the group commands: set_grouping, group, group_counts, group_snr, group_adapt, group_adapt_snr, group_bins, and group_width.
This thread shows how you can use these functions when fitting PHA data.
Last Update: 3 Mar 2022 - reviewed for CIAO 4.14; typos fixed.
Contents
- Getting Started
- Grouping the data
- Fitting the data
- Grouping within a filter
- Scripting It
- Summary
- History
- Images
Getting Started
Loading the data
This thread uses the same data set as used in the Introduction to Fitting PHA Spectra thread. We load the data set twice—using load_pha—so that we can easily see the effect of changing the grouping scheme (the screen output has been omitted for clarity):
sherpa> load_pha(1, "3c273.pi") ... sherpa> load_pha(2, "3c273.pi") ...
We note that the data in 3c273.pi was created so that each group contained at least 15 counts—by using the NUM_CTS grouptype option of dmgroup—as can be seen by using the dmhistory tool.
sherpa> !dmhistory 3c273.pi dmgroup | tr ' ' "\012" dmgroup infile="3c273.pi" outfile="./3c273.tmp" grouptype="NUM_CTS" grouptypeval="15" binspec="" xcolumn="channel" ycolumn="counts" tabspec="" tabcolumn="" stopspec="" stopcolumn="" errcolumn="" clobber="no" verbose="0" maxlength="0"
The command was preceded by "!" to tell Sherpa to execute it as a shell command, and "| tr ' ' "\012"" was used to add a new-line character between parameter values (to make the screen output easier to read).
Grouping the data
We use the group_counts function to group the second data set by 30 counts per group, which is double that of the first data set. The two data sets are then plotted using logarithmic scaling on both axes:
sherpa> group_counts(2, 30)
sherpa> set_xlog()
sherpa> set_ylog()
sherpa> plot("data", 1, "data", 2)
We now use Matplotlib functions to tweak the plot: in this case to hide the X-axis label from the top plot and the title of the second plot (as they overlap with the default plot size) and to set the X-axis range for both plots:
sherpa> axes = plt.gcf().axes sherpa> axes[0].set_xlabel('') sherpa> axes[1].set_title('') sherpa> axes[0].set_xlim(0.1, 20) sherpa> axes[1].set_xlim(0.1, 20)
The resulting plot (Figure 1) shows how the data looks before and after re-grouping.
Figure 1: Data grouped by 15 and 30 counts per group
In this thread, we use the group_counts command as an example. The other available grouping commands are:
- group_bins() — this function divides the channels into the specified number ("num") of bins.
- group_width() — this function divides the channels such that there are "num" bins in each group.
- group_snr() — this function allows the user to adaptively group PHA spectral data by signal-to-noise ratio, i.e., group bins of data until each group exceeds at least the minimum specified signal-to-noise ratio.
- group_adapt() — this function allows the user to adaptively group PHA spectral data by counts, i.e., group bins of data until the number of counts in each group exceeds the minimum number of counts specified in the 'min' argument, keeping bright features ungrouped while grouping low signal-to-noise regions.
- group_adapt_snr() — this function allows the user to adaptively group PHA spectral data by signal-to-noise ratio, i.e., group bins of data until each group exceeds at least the minimum specified signal-to-noise ratio.
The group_counts and related functions can also be used on data that was not grouped before being read into Sherpa; this can be useful for two reasons:
- You can use the functions to find the best grouping scheme for your data without having to re-run the dmgroup tool and re-load the data into Sherpa.
- You can fit the un-grouped data with the Cash statistic and then use the functions to make it easier to compare the fit to the data in plots.
Fitting the data
Once the data has been re-grouped you can use it just like any other data set. Here we repeat the fit made in the Introduction to fitting PHA spectra to see what difference the alternate grouping scheme makes.
sherpa> notice_id(2, 0.3, 6.0) sherpa> subtract(2) sherpa> set_source(2, xsphabs.abs1 * powlaw1d.p1) sherpa> abs1.nh = 0.07 sherpa> freeze(abs1) sherpa> guess(2, p1) sherpa> fit(2) Dataset = 2 Method = levmar Statistic = chi2gehrels Initial fit statistic = 997.017 Final fit statistic = 27.5501 at function evaluation 19 Data points = 22 Degrees of freedom = 20 Probability [Q-value] = 0.120485 Reduced statistic = 1.3775 Change in statistic = 969.467 p1.gamma 2.15315 +/- 0.0724515 p1.ampl 0.000230433 +/- 1.3657e-05 sherpa> show_fit() Optimization Method: LevMar name = levmar ftol = 1.1920928955078125e-07 xtol = 1.1920928955078125e-07 gtol = 1.1920928955078125e-07 maxfev = None epsfcn = 1.1920928955078125e-07 factor = 100.0 numcores = 1 verbose = 0 Statistic: Chi2Gehrels Chi Squared with Gehrels variance. The variance is estimated from the number of counts in each bin, but unlike `Chi2DataVar`, the Gaussian approximation is not used. This makes it more-suitable for use with low-count data. The standard deviation for each bin is calculated using the approximation from [1]_: sigma(i,S) = 1 + sqrt(N(i,s) + 0.75) where the higher-order terms have been dropped. This is accurate to approximately one percent. For data where the background has not been subtracted then the error term is: sigma(i) = sigma(i,S) whereas with background subtraction, sigma(i)^2 = sigma(i,S)^2 + [A(S)/A(B)]^2 sigma(i,B)^2 A(B) is the off-source "area", which could be the size of the region from which the background is extracted, or the length of a background time segment, or a product of the two, etc.; and A(S) is the on-source "area". These terms may be defined for a particular type of data: for example, PHA data sets A(B) to `BACKSCAL * EXPOSURE` from the background data set and A(S) to `BACKSCAL * EXPOSURE` from the source data set. See Also -------- Chi2DataVar, Chi2ModVar, Chi2XspecVar Notes ----- The accuracy of the error term when the background has been subtracted has not been determined. A preferable approach to background subtraction is to model the background as well as the source signal. References ---------- .. [1] "Confidence limits for small numbers of events in astrophysical data", Gehrels, N. 1986, ApJ, vol 303, p. 336-346. http://adsabs.harvard.edu/abs/1986ApJ...303..336G Fit:Dataset = 2 Method = levmar Statistic = chi2gehrels Initial fit statistic = 997.017 Final fit statistic = 27.5501 at function evaluation 19 Data points = 22 Degrees of freedom = 20 Probability [Q-value] = 0.120485 Reduced statistic = 1.3775 Change in statistic = 969.467 p1.gamma 2.15315 +/- 0.0724515 p1.ampl 0.000230433 +/- 1.3657e-05 sherpa> covar(2) Dataset = 2 Confidence Method = covariance Iterative Fit Method = None Fitting Method = levmar Statistic = chi2gehrels covariance 1-sigma (68.2689%) bounds: Param Best-Fit Lower Bound Upper Bound ----- -------- ----------- ----------- p1.gamma 2.15315 -0.0758287 0.0758287 p1.ampl 0.000230433 -1.3896e-05 1.3896e-05
which can be compared to the original results:
sherpa> notice_id(1, 0.3, 6.0) sherpa> subtract(1) sherpa> set_source(1, abs1 * p1) sherpa> guess(p1) sherpa> fit(1) Dataset = 1 Method = levmar Statistic = chi2gehrels Initial fit statistic = 70.6886 Final fit statistic = 29.3673 at function evaluation 13 Data points = 43 Degrees of freedom = 41 Probability [Q-value] = 0.9124 Reduced statistic = 0.716276 Change in statistic = 41.3213 p1.gamma 2.13926 +/- 0.0788122 p1.ampl 0.00022098 +/- 1.44103e-05 sherpa> covar(1) Dataset = 1 Confidence Method = covariance Iterative Fit Method = None Fitting Method = levmar Statistic = chi2gehrels covariance 1-sigma (68.2689%) bounds: Param Best-Fit Lower Bound Upper Bound ----- -------- ----------- ----------- p1.gamma 2.13926 -0.0815619 0.0815619 p1.ampl 0.00022098 -1.46038e-05 1.46038e-05
The following shows both fits (the extra commands are used to make the two plots have the same X-axis, and to add plot labels):
sherpa> plot("fit", 1, "fit", 2) sherpa> import matplotlib.ticker as mtick sherpa> tformatter = mtick.FormatStrFormatter("%g") sherpa> fig = plt.gcf() sherpa> plt.sca(fig.axes[0]) sherpa> plt.xlabel("") sherpa> plt.gca().set(xticklabels=[]) sherpa> plt.gca().yaxis.set_major_formatter(tformatter) sherpa> plt.tick_params(which="both",direction="in",bottom=True,top=True,right=True,left=True,labelbottom=False) sherpa> plt.sca(fig.axes[1]) sherpa> plt.title("") sherpa> plt.gca().xaxis.set_major_formatter(tformatter) sherpa> plt.gca().yaxis.set_major_formatter(tformatter) sherpa> plt.tick_params(which="both",direction="in",bottom=True,top=True,right=True,left=True,labelbottom=True) sherpa> fig.subplots_adjust(hspace=0) sherpa> fig.axes[0].get_shared_x_axes().join(fig.axes[0],fig.axes[1]) sherpa> fig.axes[1].autoscale() sherpa> plt.xlim(0.1, 10) sherpa> plt.sca(fig.axes[0]) sherpa> plt.text(0.5,0.0006,"15 counts per group",color="lime",fontsize=8) sherpa> plt.sca(fig.axes[1]) sherpa> plt.text(0.5,0.0006,"30 counts per group",color="lime",fontsize=8)
which creates this plot (Figure 2).
Figure 2: Fit to both data sets
Grouping within a filter
If we look at both datasets we can see that even though we were interested in the 0.3 - 6 keV range, the grouped and filtered ranges are different:
sherpa> get_filter() '0.248199999332:6.570000171661' sherpa> get_filter(2) '0.001460000058:6.540800094604'
This has happened because the grouping has been applied to all the channels in the PHA file, which will often result in the requested boundary (such as 0.3 keV) to fall within a bin. For bright sources this does not make much of a difference, but it can greatly enhance the data that gets included in a fit.
One solution is to change the filter from notice to ignore, since this would exclude those bins that cover the end points. An example would be:
sherpa> ignore_id(2, None, 0.3) sherpa> ignore_id(2, 6, None) sherpa> get_filter(2) '0.306600004435:5.372799873352'
However, this also leads to a loss of information. In this case channels that contain information we are interested in. A solution is to tell the grouping commands what channels we should use, which is done with the tabstops argument to group_counts and friends.
The first step is to ungroup the dataset and apply the requested filter (we first clear out any filter on the dataset to ensure we are setting the right range):
sherpa> ungroup(2) sherpa> notice_id(2) sherpa> notice_id(2, 0.3, 6) sherpa> plot_data(2, xlog=False, ylog=False)
Figure 3: The ungrouped and filtered data set
We can now access the mask attribute of the dataset, which indicates whether a channel is included (True) or excluded (False) from the filter:
sherpa> d2 = get_data(2) sherpa> mask = d2.mask sherpa> plt.clf() sherpa> plt.plot(d2.channel, mask) sherpa> plt.xlabel("Channel") sherpa> plt.ylabel("Mask")
Figure 4: The mask array
We can now run group_counts, noting that the tabstops array must be the inverse of the mask array (so set to 1 or True for those bins which we do not want to group). This can be achieved using the syntax ~mask, which is a short form for the Numpy invert function. For this example we use a grouping of 25 because there are 660 counts in the 0.3 to 6 keV range, and this divides nicely by 30 (the previous binning scheme):
sherpa> group_counts(2, 25, tabStops=~mask) sherpa> get_filter(2) '0.291999995708:6.000599861145'
Since each channel has a finite width, the bins that overlap 0.3 and 6 keV end up being removed in this approach, which is why the filter expression starts at an enery greater than 0.3 keV and ends before 6 keV.
We can plot this, using a linear scale for the X-axis, with:
sherpa> plot_fit(2, xlog=True) sherpa> plt.axvline(0.3, color='k') sherpa> plt.axvline(6, color='k')
Figure 5: The grouped data
The choice of 25 for the binning scheme was to ensure that the last bin was incomplete (i.e. contains less that 25 counts). We can look for such bins as they have a "quality" value of 2:
sherpa> q2 = get_quality(2) sherpa> print(q2[q2 > 0]) [2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2.] sherpa> print(d2.channel[q2 > 0]) [395. 396. 397. 398. 399. 400. 401. 402. 403. 404. 405. 406. 407. 408. 409. 410. 411.]
We can see that these are the last channels in the noticed range (Figure 4). One option is to use the data as is, so with one bin that is incomplete. An alternative is to exclude this bin, which can be done with the ignore_bad function. Unfortunately this requires re-creating the filter, as shown below.
sherpa> ignore_bad(2) WARNING: filtering grouped data with quality flags, previous filters deleted sherpa> notice_id(2, 0.3, 6) sherpa> get_filter(2) '0.291999995708:5.460399866104'
sherpa> plot_fit(2)
Figure 6: The grouped data
Scripting It
The file fit.py is a Python script which performs the primary commands used above; it can be executed by typing %run -i fit.py on the Sherpa command line.
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 shows how you can use the grouping functionality in Sherpa to change the grouping scheme of a PHA file once it has been read into Sherpa. This allows you to see how sensitive the fit results are to the grouping scheme by changing the number of counts per group or using a different method for grouping the data.
History
14 Dec 2004 | updated for CIAO 3.2: script version and path |
17 Jun 2005 | updated information in Get Started on loading the script |
21 Dec 2005 | reviewed for CIAO 3.3: no changes |
01 Dec 2006 | reviewed for CIAO 3.4: no changes |
14 Dec 2008 | updated for CIAO 4.1: sherpa_utils.sl script replaced by new Sherpa 4.1 grouping functionality |
29 Apr 2009 | new script command is available with CIAO 4.1.2 |
17 Dec 2009 | updated for CIAO 4.2: new group_bins and group_width commands |
13 Jul 2010 | updated for CIAO 4.2 Sherpa v2: removal of S-Lang version of thread. |
15 Dec 2010 | updated for CIAO 4.3: new set_xlog and set_ylog commands are available for setting the axis scale of plots to logarithmic |
15 Dec 2011 | reviewed for CIAO 4.4: added a warning about filtering/grouping source and background data sets |
13 Dec 2012 | updated for CIAO 4.5: noted that grouping a data set in Sherpa no longer clears the existing data filter; removed an outdated warning about filtering/grouping source and background data sets, as the associated bug has been fixed. |
03 Dec 2013 | reviewed for CIAO 4.6: no changes |
02 Dec 2015 | reviewed for CIAO 4.8: no content change. |
09 Nov 2016 | reviewed for CIAO 4.9: updated screen outputs and moved closing notes to admonition block in "Grouping the data" section; no new content. |
12 Apr 2018 | reviewed for CIAO 4.10: no content change. |
06 Dec 2018 | reviewed for CIAO 4.11: screen output revised. |
12 Dec 2019 | reviewed for CIAO 4.12: replaced ChIPS with matplotlib syntax. |
15 Dec 2020 | reviewed for CIAO 4.13: plots updated to the latest scheme; noticed energy range has been updated to 0.3 to 6 keV; added a section on using tab stops to group the data. |
03 Mar 2022 | reviewed for CIAO 4.14; typos fixed. |