MOPEX User's Guide - IRSA

8.6.1 Simplex Algorithm Modification
MOPEX User’s Guide
In order to do the minimization, the Simplex algorithm has been modified. The original downhill
Simplex algorithm minimizes a function by using the values of the function at several vertices
and trying to move away from the highest vertex. There are four basic ways in the original
Simplex to move a vertex: reflection, expansion, contraction and shrinkage. Two modifications
have been made. They are illustrated in Figure 8.24.
First, reflection is modified in the following way. If there is an indication that reflection is done
almost parallel to the lines of constant χ 2 , it is replaced with moving the highest vertex in the
direction perpendicular to the reflection direction. Second, contraction and shrinkage are replaced
with line minimization.
Figure 8.24: Illustration of the two modifications made to the original Simplex method.
8.7 Point Response Function
Point source detection and extraction in APEX rely upon a good measurement of the point
response function (PRF). The term PRF is not just an alternative way of saying point-spread
function (PSF). PSF-fitting is a commonly used term. However, PRF and PSF are two different
objects. A PSF is an image of a point-source, and it is often oversampled; i.e., the pixel size of the
PSF image is a fraction of the pixel size of the detector array or the mosaic image for which the
the PSF is applicable. A PRF, however, is not an image of a point source. One way to think of a
PRF image is as a kind of “table” of values of the responses of detector pixels to point source
“hits” at different sub-pixel positions of a central pixel, stored in a convenient, interleaved form
Basic Concepts in MOPEX 212
Point Response Function