## Algorithms and techniques

The purpose of this section is to propose algorithms to solve some difficulties encountered during the data analysis and/or to permit a specific study/analysis

## Techniques to process big sets of data

Nowadays, analyzing and reducing the ever larger astronomical datasets is becoming a crucial challenge, especially for long cumulated observation times. The INTEGRAL/SPI X/gamma-ray spectrometer is an instrument for which it is essential to process many exposures at the same time in order to increase the low signal-to-noise ratio of the weakest sources. In this context, the conventional methods for data reduction are inefficient and sometimes not feasible at all.

Processing several years of data simultaneously requires computing not only the solution of a large system of equations, but also the associated uncertainties. We aim at reducing the computation time and the memory usage.

Since the SPI transfer function is sparse, we have used some popular methods for the solution of large sparse linear systems; we briefly review these methods. We use the Multifrontal Massively Parallel Solver (MUMPS) to compute the solution of the system of equations. We also need to compute the variance of the solution, which amounts to computing selected entries of the inverse of the sparse matrix corresponding to our linear system. This can be achieved through one of the latest features of the MUMPS software that has been partly motivated by this work. In this paper we provide a brief presentation of this feature and evaluate its effectiveness on astrophysical problems requiring the processing of large datasets simultaneously, such as the study of the entire emission of the Galaxy.

We used these algorithms to solve the large sparse systems arising from SPI data processing and to obtain both their solutions and the associated variances.

In conclusion, thanks to these newly developed tools, processing large datasets arising from SPI is now feasible with both a reasonable execution time and a low memory usage.

The algorithm is detailed in the paper "Simultaneous analysis of large INTEGRAL/SPI datasets:optimizing the computation of the solution and its variance usingsparse matrix algorithms" by L. Bouchet, P. R. Amestoy, A. Buttari, F.-H. Rouet and M. Chauvin, accepted for publication is Astronomy and Computing, 2013 [download here]

Contact : lbouchet@irap.omp.eu

## How to find the time-scales on which the intensity of sources varies

The INTEGRAL/SPI, X/gamma-ray spectrometer (20 keV - 8 MeV) is an instrument for which recovering source intensity variations is not straightforward and can constitute a difficulty for data analysis. In most cases, determining the source intensity changes between exposures is largely based on a-priori information. We propose techniques that help to overcome the difficulty related to source intensity variations, which make this step more rational. For this purpose, the time intensity variation of each source is modeled as a combination of piecewise segments of time during which a given source exhibits a constant intensity. To optimize the signal-to-noise ratios, the number of segments is minimized.

"Image-space" method

We present a first method that takes advantage of previous time series ("image-space") that can be obtained from another instrument onboard the INTEGRAL observatory; IBIS "imager". A data segmentation algorithm is then used to synthesize the time series into segments

\includegraphics{lc_gx339_27_36.eps}

GX 339-4 intensity variations. The 26-40 keV IBIS/INTEGRAL time-series (gray), which contains 1183 data points (one measurement per exposure), is segmented into 17 constant segments (green). The error bars of the IBIS light-curve are scaled (SNR scaling) in such way that GX 339-4 is detected with the same significance with both SPI and IBIS. These curves are plotted as a function of time (top) and the exposure number (bottom). The raw time series (without SNR scaling) is directly segmented into 46 segments (bottom blue curve).

The code for the "image-space" algorithm, written in IDL language, and the time-series of GX 339-4 to be used as input data can be downloaded here. This code and data allow to reproduce the main features of the figure shown above.

"Data-space" method

The second method no longer needs external light curves, but solely SPI raw data.For this, we developed a specific algorithm ("data-space") that involves the SPI transfer function.

\includegraphics{f10.eps}

"Data-space" method applied to V 0332+53. The source intensity variations (25-50 keV) is modeled by nine segments (red) and is compared with the IBIS/INTEGRAL: time-series (26-51 keV, gray). The green curve corresponds to the IBIS flux averaged on SPI-obtained segments. The insert is a zoom between exposure number 81 and 179. (Top) SPI intensity variations model (black) is compared with Swift/BAT time-series (24-50 keV, purple line). The scale between the different instruments is arbitrary and is chosen such that their measured total fluxes are equal. It should be noted that the Swift/BAT and IBIS data are not necessarily recorded at the same time as the SPI data, nor exactly in the same energy band.

The code for the "data-space" algorithm, written in Fortran language, and data for V0 332+53 to be used as input data can be downloaded here. The code is not fully optimized and does not have its full functionalities, but its purpose is to illustrate the algorithmic. The codes and data allow to reproduce the main features of the figure shown above.

Results

The algorithms permit us to obtain the intensity variations of sources between exposures, and they allow to obtain a sky model which better describes the data and optimizes the source signal-to-noise ratios. The algorithms are detailed (flowcharts, pseudo-codes) in the paper "INTEGRAL/SPI data segmentation to retrieve source intensity variations" by L. Bouchet, P. R. Amestoy, A. Buttari, F.-H. Rouet and M. Chauvin, 2013, accepted in Astronomy & Astrophysics [download here].

Contact : lbouchet@irap.omp.eu