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<TITLE>9.3 Data Transformation and Visualization</TITLE>
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<H1><A NAME=SECTION03630000000000000000>9.3 Data Transformation and Visualization</A></H1>
<P>
Data transformation and visualization tools transform raw data
collected during program execution to yield data and images more
easily understood by the programmer. In this section, we provide a
general discussion of transformation and display techniques,
indicating which are useful for which purposes. In the next section,
we present examples of specific tools and describe specific
transformations and display formats.
<P>
<H2><A NAME=SECTION03631000000000000000>9.3.1 Profile and Counts</A></H2>
<P>
<A NAME=14382> </A>
A typical profile provides information about the time spent in
<A NAME=14383> </A>
each procedure on each processor, the number of times each procedure
is called, the number of messages generated on each processor, the
volume of these messages, and so forth. Data reduction techniques can
be used to reduce this multidimensional data to a smaller number of
dimensions, and various forms of display can be used to visualize both
the original and the reduced data.
<P>
Zero-dimensional (scalar) data are of course trivial to display,
consisting of a single number: total computation time, total number of
messages, mean message size, and so forth. However, numbers of this
sort provide relatively little insight into program behavior. For
example, we may notice that total communication volume is greater than
expected. This observation may stimulate us to ask several questions.
Is the additional communication concentrated in a subset of the
processors? Is it concentrated in a single procedure? In which phase
of the computation does it occur? More data are required if we are to
answer these questions.
<P>
The histogram is often a convenient display format for one-dimensional
<A NAME=14384> </A>
data. If the number of processors is large, the size of a histogram
can be reduced by binning, in which case histogram bars represent the
number of processors (or procedures or whatever) that have computation
time in a specified range. Two-dimensional data can be displayed
using color and a two-dimensional matrix. For example, in
<A HREF="#gauge">Plate 7</A> and <A HREF="#paragraph1">Plate 8</A>
<P>
color is used, respectively, to indicate execution time per procedure per processor,
and communication volume between pairs of processors.
<P>
<P>
<P><HR><P>
<EM>Plate 7 is not available in the online version.</EM>
<P><HR>
<P>
<P>
<P><HR><P>
<EM>Plate 8 is not available in the online version.</EM>
<P><HR>
<H2><A NAME=SECTION03632000000000000000>9.3.2 Traces</A></H2>
<P>
<A NAME=14394> </A>
Trace data can often be reduced to one, two, or three dimensions and
<A NAME=14395> </A>
then displayed using the histogram techniques described in
Section 9.3.1. For example, we can plot communication volume or
efficiency as a function of time, or plot histograms of trace values.
Other forms of display can provide more detailed views of temporal
dependencies between different processors and program components by
sacrificing scalability and abstraction for detail. We describe just
two displays of this sort; others are illustrated in later sections.
<P>
<A NAME=14396> </A>
The <em> Gantt chart
</em>
<A NAME=14398> </A>
is a horizontal bar chart in
<A NAME=14399> </A>
which each bar
<A NAME=14400> </A>
represents the status of each processor as a function of time
<A HREF="#paragraph1">(Plate 8</A> and <A HREF="#tilson">Plate
12).</A>
<P>
Bars can simply represent status (computing, communicating, or idling)
and/or indicate the program component or procedure that is executing
on each processor at a particular time. A Gantt chart can highlight
unexpected
<A NAME=14405> </A>
dependencies between program components. Note that dependencies
inferred from these sorts of displays are valid only if the computer
and performance tool that we are using ensure that times recorded for
events occurring on different processors are consistent. This will
generally be the case if we use the performance tools described in
this chapter, as these all incorporate appropriate clock
synchronization logic.
<A NAME=14406> </A>
<P>
If we augment a Gantt chart by drawing lines to connect corresponding
send and receive events on different processors, we obtain a <em>
space-time diagram
</em>, illustrated in the lower part of
<A HREF="#paragraph1">Plate 8</A>.
<P>
A space-time diagram can make it easier to infer temporal
dependencies, because it is often possible to identify the specific
communication event for which a processor is waiting and hence idle.
<P>
<H2><A NAME=SECTION03633000000000000000>9.3.3 Data-Parallel Languages</A></H2>
<P>
<A NAME=secpthpf> </A>
<P>
<A NAME=14414> </A>
In data-parallel languages such as HPF and pC++
,
performance analysis is simplified by the fact that each processor
<A NAME=14415> </A>
typically executes the same program. On the other hand, the semantic
gap between parallel program and executable code is particularly high.
Apparently innocuous assignment statements can cause large amounts of
communication if distributions do not match, while a compiler may
restructure code to eliminate other communication operations that the
programmer may assume will occur. Similarly, the mapping of
computation to processors may not be obvious to the programmer.
Therefore, low-level information about computation and
communication tends to have only limited value.
<P>
Performance tools for data-parallel languages both can take advantage
of the SPMD nature of data-parallel computation and overcome the
semantic gap by relating performance data to the program statements
concerned. For example, they can label the source code with
communication costs or can color data arrays to indicate the
computation costs and communication volumes associated with each
element. These forms of display can involve a considerable degree of
compiler assistance and/or postprocessing, since in many cases the
executed code has been transformed out of recognition. This approach
is illustrated in
<A HREF="#prism">Plate 9</A>,
<P>
which shows a communication summary produced by Thinking Machine's
<A NAME=14420> </A>
Prism performance tool. The program illustrated is the
<A NAME=14421> </A>
Gaussian elimination code used as a case study in
<A NAME=14422> </A>
Chapter <A HREF="node82.html#chaphpf" tppabs="http://www.dit.hcmut.edu.vn/books/system/par_anl/node82.html#chaphpf">7</A>. The plate indicates sources of communication
<A NAME=14424> </A>
in a data-parallel Fortran program and the relative cost of each
communication operation.
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<A NAME=prism HREF="prism3.gif" tppabs="http://www.dit.hcmut.edu.vn/books/system/par_anl/prism3.gif"> <img
ALIGN=MIDDLE src="prism3_small.gif" tppabs="http://www.dit.hcmut.edu.vn/books/system/par_anl/prism3_small.gif"></A>
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(GIF <A HREF="prism3.gif" tppabs="http://www.dit.hcmut.edu.vn/books/system/par_anl/prism3.gif">27721</A> bytes; RGB <A
HREF="javascript:if(confirm('http://www.dit.hcmut.edu.vn/books/system/par_anl/prism3.rgb \n\nThis file was not retrieved by Teleport Pro, because the server reports that this file cannot be found. \n\nDo you want to open it from the server?'))window.location='http://www.dit.hcmut.edu.vn/books/system/par_anl/prism3.rgb'" tppabs="http://www.dit.hcmut.edu.vn/books/system/par_anl/prism3.rgb">295002</A> bytes.)
Plate 9: Thinking Machine's PRISM performance
tool, here applied to a Gaussian elimination algorithm. Image
courtesy of D. Reed.
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<B> Next:</B> <A NAME=tex2html3285 HREF="node110.html" tppabs="http://www.dit.hcmut.edu.vn/books/system/par_anl/node110.html">9.4 Tools</A>
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<B> Previous:</B> <A NAME=tex2html3277 HREF="node108.html" tppabs="http://www.dit.hcmut.edu.vn/books/system/par_anl/node108.html">9.2 Data Collection</A>
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<I>© Copyright 1995 by <A href="msgs0.htm#6" tppabs="http://www.dit.hcmut.edu.vn/books/system/par_anl/tppmsgs/msgs0.htm#6">Ian Foster</a></I>
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