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Astronomical Data Analysis Software and Systems VII
ASP Conference Series, Vol. 145, 1998
R. Albrecht, R. N. Hook and H. A. Bushouse, e
Ö Copyright 1998 Astronomical Society of the Pacific. All rights reserved.
ds.
Fitting and Modeling of AXAF Data with the ASC
Fitting Application
S. Doe, M. Ljungberg, A. Siemiginowska and W. Joye
AXAF Science Center, MS 81, Smithsonian Astrophysical Observatory,
60 Garden Street, Cambridge, MA 02138 USA
Abstract. The AXAF mission will provide X­ray data with unprece­
dented spatial and spectral resolution. Because of the high quality of
these data, the AXAF Science Center will provide a new data analy­
sis system--including a new fitting application. Our intent is to enable
users to do fitting that is too awkward with, or beyond, the scope of
existing astronomical fitting software. Our main goals are: 1) to take
advantage of the full capabilities of the AXAF, we intend to provide a
more sophisticated modeling capability (i.e., models that are f(x, y, E, t),
models to simulate the response of AXAF instruments, and models that
enable ``joint­mode'' fitting, i.e., combined spatial­spectral or spectral­
temporal fitting); and 2) to provide users with a wide variety of models,
optimization methods, and fit statistics. In this paper, we discuss the
use of an object­oriented approach in our implementation, the current
features of the fitting application, and the features scheduled to be added
in the coming year of development. Current features include: an interac­
tive, command­line interface; a modeling language, which allows users to
build models from arithmetic combinations of base functions; a suite of
optimization and fit statistics; the ability to perform fits to multiple data
sets simultaneously; and, an interface with SM and SAOtng to plot or
image data, models, and/or residuals from a fit. We currently provide a
modeling capability in one or two dimensions, and have recently made an
e#ort to perform spectral fitting in a manner similar to XSPEC. We also
allow users to dynamically link the fitting application to their own algo­
rithms. Our goals for the coming year include incorporating the XSPEC
model library as a subset of models available in the application, enabling
``joint­mode'' analysis and adding support for new algorithms.
1. Introduction
The AXAF is NASA's ``Advanced X­ray Astrophysics Facility,'' scheduled for
launch on 27 August 1998. The AXAF Science Center Data Systems will provide
the astronomical community with software to reduce and analyze AXAF data.
In particular, our team is working on a fitting and modeling application suitable
for analysis of AXAF data. We have two main design goals: to provide modeling
in up to 4 dimensions, for functions truly f(E, x, y, t); and, to package together
157

158 Doe, Ljungberg, Siemiginowska and Joye
Generate
Model
Calculate
Fit Statistic
Search Parameter Space
FITTING ENGINE
Predicted
Data
Statistic
Fit
Parameters
Current
Figure 1. The main fitting process.
Method
Simplex Powell
MethodParam
char* name
int iterations
Method* parent
char* name
float value, min, max
function()
show()
help()
setValue()
getValue()
setMin()
setMax()
getMin()
getMax()
Simplex()
function()
help()
Powell()
function()
help()
float delta
Figure 2. The Method Class.
a wider variety of optimization algorithms and fit statistics. Meeting these goals
will enable users to take advantage of the quality of AXAF data.
2. Design of the Fitting Application
Figure 1 shows the main fitting process that occurs within the application. The
data are modeled by some function F ( #
X , #
P ), where #
X is the data space and #
P is
the vector of model parameters. A fit statistic is then calculated by comparing
the data to the predicted data calculated with the model. The fit statistic is used
by the optimization algorithm to determine the next #
P to try; the application
iterates through this process until the convergence criteria are reached, at which
point #
P contains the best fit parameters.
We have taken an object--oriented approach to the design of the fitting
application. Figure 2 shows an example; these are the classes associated with
the ``Search Parameter Space'' box shown in the previous figure. Since the design
for the classes associated with the other two boxes is substantially the same, we
show here only the ``Method'' class.

Fitting and Modeling of AXAF Data 159
MODEL MANAGER
FIT STATISTIC MANAGER
MANAGER
SRC BKGD INSTR
MODEL = SRC + BKGD * INSTR
MODELS MODELS MODELS
MANAGER
MANAGER
STATS
METHODS
OPTIMIZATION METHOD MANAGER
Figure 3. The Model, Method, and Statistic Managers.
We provide a number of di#erent optimization algorithms (e.g., the simplex
method, Powell minimization, grid search, etc.); each of these are contained
in their own separate derived class as shown in Figure 2. All of these classes
inherit from the base ``Method'' class, which contains information all the derived
classes use. This structure has made it particularly easy for us to ``plug--in'' new
algorithms as they are requested by our scientists. There is also a class associated
with the Method class called the ``MethodParam'' class; this class contains the
convergence criteria used by the various optimization algorithms.
Thus, we have three types of base classes to manage---the Method, Model
and Statistic classes. (A ``model'' is composed of an arithmetic combination
of functions f( #
X, #
P ) derived from the Model classes; the fit statistics of the
Statistic classes are used to compare the data with the ``predicted data'' gen­
erated by models.) Figure 3 shows the managers we use to keep track of the
algorithms and models currently in use. The Method and Statistic managers
need merely to point at the algorithm currently in use; the Model Manager, on
the other hand, needs to construct the model by evaluating three model stacks,
the source, background, and instrument model stacks, and then combining them
appropriately (i.e., the background model is added to the source model, and the
result is convolved with an instrument model). The source model alone may be
used, if no background or instrument models have been defined.
3. Current Implementation
We have implemented a version of the fitting application which is currently
undergoing alpha testing at the ASC. This version has capabilities which include
the following:
. Command­line interface
---Command completion, history, vi, emacs keymaps, escape to shell.
---Execute scripts, create logs.

160 Doe, Ljungberg, Siemiginowska and Joye
. Multiple data sets
---E.g., fit data from di#erent missions to the same model.
. Modeling in 1 and 2 dimensions
. Filtering of data in memory
. Modeling ``mini­language''
---Build model out of arithmetic combination of functions.
. Interaction with SAOtng, GNUPLOT, SM
. Selected XSPEC compatibility
. Dynamic linking to user algorithms
This version will serve as the foundation of the flight version.
4. Continuing Development
The first release of ASC software is scheduled for June 1998. For the June
release, we must add the following capabilities to the fitting application:
. Implementation of ``joint­mode'' analysis
. Modeling in up to 4 dimensions for functions truly f(E, x, y, t)
. Additional algorithms and statistical approaches
. Interface with ASC Data Model
. Support for X­ray gratings on AXAF
. Support for external AXAF simulators
. GUI
Adding this functionality to the fitting application will provide AXAF users
with a powerful tool for the analysis of AXAF data.
Acknowledgments. This project is supported by NASA contract NAS8­
39073 (ASC). We would like to thank Mark Birkinshaw for making his OPTIM
library available at the ASC.
References
Birkinshaw, M., 1995, CfA internal memo
Doe, S., Conroy, M., & McDowell, J., 1996, in ASP Conf. Ser., Vol. 101, Astro­
nomical Data Analysis Software and Systems V, ed. George H. Jacoby &
Jeannette Barnes (San Francisco: ASP), 155
Doe, S., Siemiginowska, A., Joye, W., & McDowell, J., 1997, in ASP Conf. Ser.,
Vol. 125, Astronomical Data Analysis Software and Systems VI, ed. Gareth
Hunt & H. E. Payne (San Francisco: ASP), 492