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Дата изменения: Mon Jul 9 08:51:15 2007
Дата индексирования: Sat Dec 22 07:59:37 2007
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Constraints on the model components: XMM-Newton SAS Home Page
XMM-Newton Science Analysis System


bkgfit (ebkgmap-1.2) [xmmsas_20070708_1801-7.1.0]

Fitting algorithm: Fitting algorithm: Truncated Poisson fitting: Home Index

Meta Index / Home Page / Description / Fitting algorithm:


Constraints on the model components:

The fitting procedure will only converge to a unique solution if the components $b_i$ are linearly independent. A measure of this is the quantity


\begin{displaymath}
Q_{i,j} = \frac{\sum_{x=1}^{X}\sum_{y=1}^{Y} b_{x,y,i} \, b_...
... \big) \big(\sum_{x=1}^{X}\sum_{y=1}^{Y} b_{x,y,j}^2 \big) }}.
\end{displaymath} (4)

If one thinks of each image $b_i$ as a vector in an $X \times Y$ dimensional space, then $Q_{i,j}$ is the cosine of the angle between $b_i$ and $b_j$. The task calculates $Q$ for each pair of component images and fails with an error if any $Q$ is greater than 0.99. NOTE that the sums in equation 4 are carried out on unmasked pixels only. Hence components may be linearly independent in masked pixels yet still fail the $Q$ test within the task.

The task also fails if any of the components has only zero-valued pixels. Finally, since the Poisson image values are necessarily all $\ge 0$, negative values are not allowed in the model components.


Fitting algorithm: Fitting algorithm: Truncated Poisson fitting: Home Index

XMM-Newton SOC/SSC -- 2007-07-09