<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<html>
<head>
<meta content="text/html; charset=ISO-8859-1"
http-equiv="Content-Type">
<title></title>
</head>
<body text="#000000" bgcolor="#ffffff">
Richard et al.,<br>
<br>
A general comment: it seems some of these correlations are weak and
in fact we may never have sensible values for them. If we are going
for a compact format, we might think about initially dropping the
off-diagonal elements that are only non-zero in principle.<br>
<br>
I'm worried about keeping a significant amount of zero-valued data
as a place-holder for future use and having that future never
arrive.<br>
<br>
As an extreme version of this, you can imagine a near-diagonal
representation where none of the off-diagonal elements are kept.
Don't know if this is actually possible. It likely would mean a
parametrization aligned with detector geometry rather than an
abstract global coordinate system.<br>
<br>
For tracking, the off-diagonal elements arise naturally in the
process of fitting and some of the correlations are certainly
significant. So the values are both non-zero and meaningful; they
should be kept.<br>
<br>
-- Mark<br>
<br>
On 08/18/2011 06:19 PM, Richard Jones wrote:
<blockquote cite="mid:4E4D900C.6050702@uconn.edu" type="cite"> In
laying out the dst format for MC studies, I claimed in an earlier
message that the error matrix used to store the errors on neutral
hit parameters only needs to contain 3 (bcal) or 2 (fcal)
off-diagonal elements. Our argument follows below. The starting
point for this is a single cluster reconstructed in the bcal or
fcal. No vertex hypothesis has yet been applied to this hit, nor
has a momentum vector been assigned to it. It is just a neutral
cluster in a calorimeter.<br>
<br>
<ol>
<li><b>bcal</b> - the set of measured hit parameters which are
most loosely coupled in terms of the raw measurements are
(r,phi,z,E,t). A transformation can be used to convert into
any other preferred set of hit parameters. Correlations are
(r,z) , (r,E) , and (z,E).<br>
</li>
<ul>
<li>phi is decoupled from all of the others.<br>
</li>
<li>r is directly measured through the radial profile, but
couples to z and E implicitly.<br>
</li>
<li>z is independently measured using timing, but is
implicitly correlated with r through fluctuations in the
energy deposition for oblique showers, and with E through
the position of the shower maximum, and explicitly with E
through the attenuation correction.<br>
</li>
<li>E correlates implicitly to r,z through shower depth
variations, and explicitly to z through the attenuation
correction.<br>
</li>
<li>the t of the shower maximum correlates with r,z (and
through them with E). However this correlation is trivial,
and will be taken out when the time is projected back from
the shower maximum to a reference vertex. Since the speed
of light is independent of E, this correlation of t with r,z
is trivial and need not be carried along with the shower.<br>
</li>
</ul>
<li><b>fcal</b> - the set of measured hit parameters which are
most loosely coupled in terms of the raw measurements are
(x,y,E,t). Note that the depth z of the shower maximum is not
measured in the fcal, so it does not belong in the list, being
a pure function of E. Correlations are (x,y) , (x,E) , and
(y,E).<br>
</li>
<ol>
<li>x,y are implicitly correlated with each other by the shape
of shower deposition in the fcal, and with E through shower
depth.<br>
</li>
<li>as for the fcal, the t of the shower maximum is trivially
correlated with E,x,y. I argue that this correlation is
trivial and need not be carried along with the shower object
for the same reasons as given above under the bcal heading.</li>
</ol>
</ol>
Thus, for the bcal we must keep 3 off-diagonal error matrix
elements per shower. For the fcal there are also 3 non-trivial
off-diagonal elements, but two of them are related to each other
in a simple way:<br>
<br>
x * sigma(y,E) = y * sigma(x,E)<br>
<br>
So strictly speaking there are only 2 off-diagonal error matrix
elements per shower that must be kept in the fcal.<br>
<br>
-Richard J.<br>
<pre wrap="">
<fieldset class="mimeAttachmentHeader"></fieldset>
_______________________________________________
Halld-physics mailing list
<a class="moz-txt-link-abbreviated" href="mailto:Halld-physics@jlab.org">Halld-physics@jlab.org</a>
<a class="moz-txt-link-freetext" href="https://mailman.jlab.org/mailman/listinfo/halld-physics">https://mailman.jlab.org/mailman/listinfo/halld-physics</a></pre>
</blockquote>
<br>
</body>
</html>