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star_bashing.html
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star_bashing.html
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<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8" />
<title>star_bashing</title>
<script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.1.10/require.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/2.0.3/jquery.min.js"></script>
<style type="text/css">
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<h2 id="Star-Bashing">Star Bashing<a class="anchor-link" href="#Star-Bashing">¶</a></h2><p>Someone came by looking for help on a homework question that took my fancy.<br>
Now that the term is over it should be okay to post my solution.</p>
<p>Basically given a text list with three columns of numbers representing (x,y)=z<br>
which is said to be a telescopic image of some starfield.<br>
The goal is to:</p>
<ul>
<li>Say how many stars there are, </li>
<li>Say where the stars are in the image, </li>
<li>Give relative brightness of the stars. </li>
</ul>
<p>And that is all the information we have.</p>
<p>This is clearly an image processing problem and there are
astronomy specific packages and libraries available to solve it.<br>
But it is not worth the time and effort to specalize in those tools unless it is your day job.</p>
<p>A new version <strong>ipython</strong> (now jupyter) was just released. I see it has a <strong>bash</strong> kernel,<br>
and GitHub announced it would render notebooks natively. All good reasons to see how far<br>
we get treating this as a data munging problem that is shareable with a much broader audience than typically appreciate the shell.</p>
<p>Our data set is a field, a representation of intensity at locations in two dimensions.<br>
Some locations will be stars and others will be background. We should figure out how to tell them apart.</p>
<p>the original data is available at:</p>
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<div class=" highlight hl-bash"><pre><span class="c"># wget http://homework.uoregon.edu/pub/class/sciprog15/stars.txt</span>
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<li>Step one is always look at the file (viewed as markdown the first column is wonky).</li>
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<pre>1. 1. 1028.
2. 1. 1335.
3. 1. 1375.
4. 1. 1361.
5. 1. 1310.
6. 1. 1332.
7. 1. 1994.
8. 1. 2116.
9. 1. 1949.
10. 1. 1867.
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<h3 id="Clean">Clean<a class="anchor-link" href="#Clean">¶</a></h3><p>See if the decimal points are ever significant.</p>
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<div class=" highlight hl-bash"><pre>grep <span class="s2">"\.[0-9]"</span> stars.txt
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<p>Nope. Never significant.</p>
<p>remove cruft -- decimal point, extra spaces, convert spaces to tabs (tabs are a default field seperator in the shell)</p>
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<div class=" highlight hl-bash"><pre>tr -d <span class="se">\.</span> < stars.txt <span class="p">|</span> tr -s <span class="s1">' '</span> <span class="p">|</span> tr <span class="s1">' '</span> <span class="s1">'\t'</span> > stars.tab
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<p>Check that what remains are well formed non negative integers.</p>
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<div class=" highlight hl-bash"><pre>grep -v <span class="s2">"^[0-9]*.[0-9]*.[0-9]*</span><span class="nv">$"</span><span class="s2"> stars.tab</span>
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<p>Yep, all whole numbers.</p>
<h3 id="Explore">Explore<a class="anchor-link" href="#Explore">¶</a></h3><p>Get the width and height.
They will be the largest values (locations) in the first two columns.</p>
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<div class=" highlight hl-bash"><pre><span class="nv">X</span><span class="o">=</span><span class="k">$(</span>cut -f1 stars.tab <span class="p">|</span> sort -n <span class="p">|</span> tail -n1<span class="k">)</span>
<span class="nv">Y</span><span class="o">=</span><span class="k">$(</span>cut -f2 stars.tab <span class="p">|</span> sort -n <span class="p">|</span> tail -n1<span class="k">)</span>
<span class="nb">echo</span> <span class="nv">$X</span> <span class="nv">$Y</span>
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<pre>1124 1024
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<p>How many distinct intensity values are in the third column?</p>
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<div class=" highlight hl-bash"><pre>cut -f3 stars.tab <span class="p">|</span> sort -n <span class="p">|</span> uniq -c <span class="p">|</span> wc -l
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<pre>5146
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<p>What are the min and max intensity?</p>
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<div class=" highlight hl-bash"><pre><span class="nv">IMIN</span><span class="o">=</span><span class="k">$(</span>cut -f3 stars.tab <span class="p">|</span> sort -n <span class="p">|</span> head -n1<span class="k">)</span>
<span class="nb">echo</span> <span class="si">${</span><span class="nv">IMIN</span><span class="si">}</span>
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<pre>263
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<div class=" highlight hl-bash"><pre><span class="nv">IMAX</span><span class="o">=</span><span class="k">$(</span>cut -f3 stars.tab <span class="p">|</span> sort -nr <span class="p">|</span> head -n1<span class="k">)</span>
<span class="nb">echo</span> <span class="si">${</span><span class="nv">IMAX</span><span class="si">}</span>
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<pre>65535
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<div class=" highlight hl-bash"><pre><span class="nb">echo</span> <span class="s2">"2^16-1"</span> <span class="p">|</span> bc
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<pre>65535
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<p>That max intensity most probably represents a saturation of the sensor because<br>
the number of photons hitting a CCD well will not accidentally equal a power of two minus one very often.</p>
<p>The data for those pixels (and any it overflowed into) are suboptimal.</p>
<h3 id="Adjust">Adjust<a class="anchor-link" href="#Adjust">¶</a></h3><p>It will not change our relative measurements to reduce all intensities by 263<br>
and it will provide a bit of headroom below 2^16 with a base of zero.</p>
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<div class=" highlight hl-bash"><pre>awk -v <span class="nv">OFS</span><span class="o">=</span><span class="s2">"\t"</span> -v<span class="s2">"IMIN=</span><span class="si">${</span><span class="nv">IMIN</span><span class="si">}</span><span class="s2">"</span> <span class="s1">'{$3-=IMIN;print}'</span> stars.tab > stars_0.tab
<span class="nv">IMIN</span><span class="o">=</span><span class="k">$(</span>cut -f3 stars_0.tab <span class="p">|</span> sort -n <span class="p">|</span> head -n1<span class="k">)</span>
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<pre>0
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<div class=" highlight hl-bash"><pre><span class="nv">IMAX</span><span class="o">=</span><span class="k">$(</span>cut -f3 stars_0.tab <span class="p">|</span> sort -nr<span class="p">|</span> head -n1<span class="k">)</span>
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<pre>65272
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<h3 id="Measure-more">Measure more<a class="anchor-link" href="#Measure-more">¶</a></h3><p>What is the average intensity?</p>
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<div class=" highlight hl-bash"><pre>awk <span class="s1">'{a+=$3}END{print a/NR}'</span> stars_0.tab
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<pre>256.93
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<p>Note: Since background plus stars averages to about 257 the actual background must be below this value.</p>
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<div class=" highlight hl-bash"><pre><span class="nb">echo</span> <span class="s2">"scale=3;257/65272*100"</span> <span class="p">|</span> bc
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<pre>.300
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<p>Average intensity is less than a third of one percent of the brightest.<br>
Or the bright ones are around 300 times the average.</p>
<p>From a more CS big-O perspective 2^8 goes into 2^16<br>
2^8 times so the bright point(s) are the average intensity squared.</p>
<h3 id="Histogram">Histogram<a class="anchor-link" href="#Histogram">¶</a></h3><p>Generate a histogram. Remember there were 5,146 distinct intensities.<br>
This histogram is the the number of pixels of an intensity, ordered by intensity.</p>
<p>Expect to start with many shades of (dark) gray and a spike of bright towards the end.</p>
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<div class=" highlight hl-bash"><pre>cut -f3 stars_0.tab <span class="p">|</span> sort -n <span class="p">|</span> uniq -c <span class="p">|</span> <span class="se">\</span>
sed <span class="s1">'s| *\([0-9]*\) *\([0-9]*\)|\1\t\2|g'</span> > stars.hist
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<pre>1 0
1 2
1 3
3 4
1 6
1 7
1 8
3 9
2 10
1 11
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<div class=" highlight hl-bash"><pre>tail stars.hist
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<pre>1 64455
2 64621
1 64710
1 64935
1 64990
1 64996
1 65146
1 65156
1 65271
521 65272
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<p>Nothing too exciting at the extremes except
the hundreds of saturated pixels.<br>
What are the most common values (expect background)?</p>
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<div class=" highlight hl-bash"><pre>sort -nr stars.hist <span class="p">|</span> head
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<pre>41503 176
40999 181
38081 180
37711 179
37280 184
36519 182
36423 178
36216 183
33256 175
30890 177
sort: write failed: standard output: Broken pipe
sort: write error
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<p>(<em>The broken pipe message seems to be an artifact of the jupyter notebook</em>)</p>
<p>The most common intensities are below 200
which agrees well with the background needing to be below the average (256.9).</p>
<p>Histograms like to be seen.<br>
We could write a simple script to print something.<br>
But gnuplot is ancient, flexible, widely available and very good to be aware of.</p>
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<div class=" highlight hl-bash"><pre>gnuplot <span class="s"><< END</span>
<span class="s">set xrange [0:65272];</span>
<span class="s">set yrange[0:30890];</span>
<span class="s">set terminal dumb;</span>
<span class="s">plot 'stars.hist' using 2:1;</span>
<span class="s">END</span>
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A---------+----------+---------+---------+---------+----------+----+
30000 A+ + + + 'stars.hist' using 2:1 A ++
A |
A |
25000 A+ ++
A |
A |
20000 ++ ++
A |
A |
15000 A+ ++
A |
A |
10000 A+ ++
A |
A |
5000 A+ ++
A |
A + + + + + + |
0 AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA-AAAA
0 10000 20000 30000 40000 50000 60000
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<p>Effectvily no interesting structure at this resolution.
A spike near x=0 and y is close to zero elsewhere.</p>
<p>Try taking the log of the counts of intensities.</p>
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<div class=" highlight hl-bash"><pre>gnuplot <span class="s"><< END</span>
<span class="s">set xrange [0:65272];</span>
<span class="s">set yrange[0:12];</span>
<span class="s">set terminal dumb;</span>
<span class="s">plot "<awk '{print \$2,log(\$1)}' stars.hist" ;</span>
<span class="s">END</span>
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12 ++---------+---------+----------+----------+----------+---------+----++
+ + + "<awk '{print $2,log($1)}' stars.hist" +A |
A |
10 A+ ++
A |
A |
8 A+ ++
A |
A |
6 A+ +A
A |
A |
AA |
4 AA ++
AA |
AAA |
2 AAAA ++
AAAAAAA |
AAAAAAAAAAAAAAAAAAAA + A AAA A + + + A+ A|
0 AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
0 10000 20000 30000 40000 50000 60000
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