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<!DOCTYPE html>
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<title>ranges.py</title>
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<div class='docs'><h1> ranges.py</h1><p> This is ttv1 code (Timm tools, version 1).</p></div>
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<p><em>Ranges</em> implements discretization; i.e. transform quantitative
data into qualitative data. Even for algorithms that can directly
deal with quantitative data, dscretization can led to faster,
more effective learning.</p>
<p>It turns out that a generic recursive bi-clustering procedure
can implement all the following discretization processes:</p>
<ul>
<li>Divide a list of numbers into a small number of ranges;</li>
<li>Given rows of data...</li>
<li>Fayyad-Iranni discretization:
- ... find ranges in one column that
minimizes the expected value of the
entropy in another column of symbols.</li>
<li>CART-style discretization:
- ... find ranges in one column that
minimizes the expected value of the
standard deviation in another column of numbers.</li>
<li>Scott-Knott ranking of treatments (clustering together
treatments whose distributions are statistically
indistinguishable).</li>
</ul>
<h3>Examples</h3>
<h4><code>div</code>: Separate a List into Ranges</h4>
<pre><code> from ranges import div
#
for rng in div([ 10, 11, 13, 14, 15, 15, 16, 16, 17,
20, 21, 23, 24, 25, 25, 26, 26, 27,
30, 31, 33, 34, 35, 35, 36, 36, 37
]):
print("range,rng["id"],":",
dict(lo= rng["x"].lo,
hi= rng["x"].hi))
# Output
range 1: {'lo': 10, 'hi': 20} # nums 10 to 20
range 2: {'lo': 21, 'hi': 31} # nums 21 to 31
range 3: {'lo': 33, 'hi': 37} # nums 33 to 37
</code></pre>
<h4><code>ediv</code>: Separate pairs of Number,Symbols into Ranges</h4>
<pre><code> from ranges import div,ediv
#
a,b = "a","b"
for rng in ediv([
(10,a),(11,a),(13,a),(14,a),(15,a),
(20,b),(21,b),(23,b),(24,b),(25,b),
(30,b),(31,b),(33,b),(34,b),(35,b) ]):
print(dict(id= rng["id"],
lo= rng["x"].lo,
hi= rng["x"].hi))
# Output
range 0 : {'lo': 10, 'hi': 20}
range 1 : {'lo': 21, 'hi': 35}
</code></pre>
<h4><code>sdiv</code>: Separate pairs of Number,Numbers into Ranges</h4>
<pre><code> lst= [( 0.7, 2), ( 0.75, 2 ), ( 0.8, 2 ),
( 0,85 ,2), ( 0.9, 2), ( 0.8 , 2 ),
( 1 , 2 ), ( 1.05 , 2), ( 1,2),
( 0.7, 2), ( 0.75, 2 ), ( 0.8, 2 ),
( 0.85 , 2), ( 0.9, 2), (10 , 14 ),
(10.5, 13.5),(11 ,13), (11.5, 13),
(12 , 12.5),(12.5, 12 ),(13 ,11.5),
(13.5, 10.5),(14 , 10 ),(14.5, 9.5),
(15 , 9), (15.5, 8.5) ]
for rng in sdiv(lst):
print("range",rng["id"],":",
dict(lo= rng["x"].lo,
hi= rng["x"].hi))
# Output
range 0 : {'lo': 0, 'hi': 0.9}
range 1 : {'lo': 0.9, 'hi': 15.5}
</code></pre>
<h4><code>ddiv</code>: Separate lists of Treatment into Ranges</h4>
<pre><code> for rng in ddv(dict(x1= [0.34, 0.49, 0.51, 0.6],
x2= [0.6, 0.7, 0.8, 0.9],
x3= [0.15, 0.25, 0.4, 0.35],
x4= [0.6, 0.7, 0.8, 0.9],
x5= [0.1, 0.2, 0.3, 0.4])):
print("range", rng["id"],":",
[x[0].label for x in rng["has"]],
dict(lo= rng["x"].lo,
hi= rng["x"].hi))
# Output
range 0 : ['x5', 'x3'] {'lo': 0.1, 'hi': 0.4}
range 1 : ['x1'] {'lo': 0.34, 'hi': 0.6}
range 2 : ['x2', 'x4'] {'lo': 0.6, 'hi': 0.9}
</code></pre>
<h3>Internal Details</h3>
<p><code>Ranges</code> assumes that the input data contains a list of doubles <em>(x,y)</em>
pairs. The process assumes <em>x</em> is always numeric, but <em>y</em> may
be numeric or symbols. </p>
<ul>
<li>If <em>y</em> is <em>numeric</em>, we divide to minimize the expected
<em>variance</em> (after divisions).</li>
<li>If <em>y</em> is <em>symbolic</em>, we divide to minimize the expected
<em>entropy</em> (after divisions).</li>
</ul>
<p>To divide a list of numerics, this generates doubles <em>(x,x)</em>,
after which the same division process executes.</p>
<p>However it runs, this ranges returns a list of dictionaries:</p>
<pre><code> dict(label = label, score = score,
x = xoverall, # x.lo, x.hi defines the range
y = yoverall, # could be numerics or symbols
has = items,
id = aNumber)
</code></pre>
<hr />
<h2>Programmer's Guide</h2>
</div>
<div class='code'>
<div class="highlight"><pre><span class="kn">import</span> <span class="nn">sys</span><span class="o">,</span><span class="nn">math</span>
<span class="kn">from</span> <span class="nn">cliffsDelta</span> <span class="kn">import</span> <span class="n">cd</span>
<span class="kn">from</span> <span class="nn">bootstrap</span> <span class="kn">import</span> <span class="n">bootstrap</span></pre></div>
</div>
</div>
<div class='clearall'></div>
<div class='section' id='section-1'>
<div class='docs'>
<div class='octowrap'>
<a class='octothorpe' href='#section-1'>#</a>
</div>
<h3>Top-level drives</h3>
</div>
<div class='code'>
<div class="highlight"><pre></pre></div>
</div>
</div>
<div class='clearall'></div>
<div class='section' id='section-2'>
<div class='docs'>
<div class='octowrap'>
<a class='octothorpe' href='#section-2'>#</a>
</div>
<p>Short-cuts, defined for standard usages.</p>
</div>
<div class='code'>
<div class="highlight"><pre></pre></div>
</div>
</div>
<div class='clearall'></div>
<div class='section' id='section-3'>
<div class='docs'>
<div class='octowrap'>
<a class='octothorpe' href='#section-3'>#</a>
</div>
<p>Standard usage #1: divide a list of numbers.</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="k">def</span> <span class="nf">div</span><span class="p">(</span><span class="n">lst</span><span class="p">):</span>
<span class="k">return</span> <span class="n">ranges</span><span class="p">(</span><span class="n">lst</span><span class="p">)</span></pre></div>
</div>
</div>
<div class='clearall'></div>
<div class='section' id='section-4'>
<div class='docs'>
<div class='octowrap'>
<a class='octothorpe' href='#section-4'>#</a>
</div>
<p>Standard usage #2:</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="k">def</span> <span class="nf">sdiv</span><span class="p">(</span><span class="n">lst</span><span class="p">,</span>
<span class="n">x</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">z</span><span class="p">:</span><span class="n">z</span><span class="p">[</span> <span class="mi">0</span><span class="p">],</span>
<span class="n">y</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">z</span><span class="p">:</span><span class="n">z</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span>
<span class="n">key</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">z</span><span class="p">:</span><span class="n">z</span><span class="p">[</span> <span class="mi">0</span><span class="p">]):</span>
<span class="k">return</span> <span class="n">ranges</span><span class="p">(</span><span class="n">lst</span><span class="p">,</span> <span class="n">key</span><span class="o">=</span><span class="n">key</span><span class="p">,</span> <span class="n">x</span><span class="o">=</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="o">=</span><span class="n">y</span><span class="p">)</span></pre></div>
</div>
</div>
<div class='clearall'></div>
<div class='section' id='section-5'>
<div class='docs'>
<div class='octowrap'>
<a class='octothorpe' href='#section-5'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre><span class="k">def</span> <span class="nf">ediv</span><span class="p">(</span><span class="n">lst</span><span class="p">,</span>
<span class="n">x</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">z</span><span class="p">:</span><span class="n">z</span><span class="p">[</span> <span class="mi">0</span><span class="p">],</span>
<span class="n">y</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">z</span><span class="p">:</span><span class="n">z</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span>
<span class="n">key</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">z</span><span class="p">:</span><span class="n">z</span><span class="p">[</span> <span class="mi">0</span><span class="p">]):</span></pre></div>
</div>
</div>
<div class='clearall'></div>
<div class='section' id='section-6'>
<div class='docs'>
<div class='octowrap'>
<a class='octothorpe' href='#section-6'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre> <span class="k">def</span> <span class="nf">fayyadIranni</span><span class="p">(</span><span class="n">lhs</span><span class="p">,</span><span class="n">rhs</span><span class="p">,</span><span class="nb">all</span><span class="p">,</span><span class="n">score</span><span class="p">):</span>
<span class="n">gain</span> <span class="o">=</span> <span class="nb">all</span><span class="o">.</span><span class="n">ent</span><span class="p">()</span> <span class="o">-</span> <span class="n">score</span>
<span class="n">delta</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="mi">3</span><span class="o">**</span><span class="nb">all</span><span class="o">.</span><span class="n">k</span><span class="p">()</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span><span class="mi">2</span><span class="p">)</span> <span class="o">-</span> <span class="p">(</span><span class="nb">all</span><span class="o">.</span><span class="n">ke</span><span class="p">()</span> <span class="o">-</span> <span class="n">lhs</span><span class="o">.</span><span class="n">ke</span><span class="p">()</span> <span class="o">-</span> <span class="n">rhs</span><span class="o">.</span><span class="n">ke</span><span class="p">())</span>
<span class="k">return</span> <span class="n">gain</span> <span class="o">></span> <span class="p">(</span><span class="n">math</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="nb">all</span><span class="o">.</span><span class="n">n</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="n">delta</span><span class="p">)</span><span class="o">/</span><span class="nb">all</span><span class="o">.</span><span class="n">n</span>
<span class="k">return</span> <span class="n">ranges</span><span class="p">(</span><span class="n">lst</span><span class="p">,</span>
<span class="n">ynum</span><span class="o">=</span><span class="bp">False</span><span class="p">,</span>
<span class="n">goodysplit</span><span class="o">=</span><span class="n">fayyadIranni</span><span class="p">,</span><span class="n">key</span><span class="o">=</span><span class="n">key</span><span class="p">,</span> <span class="n">x</span><span class="o">=</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="o">=</span><span class="n">y</span><span class="p">)</span></pre></div>
</div>
</div>
<div class='clearall'></div>
<div class='section' id='section-7'>
<div class='docs'>
<div class='octowrap'>
<a class='octothorpe' href='#section-7'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre><span class="k">def</span> <span class="nf">scottknot</span><span class="p">(</span><span class="n">d</span><span class="p">):</span></pre></div>
</div>
</div>
<div class='clearall'></div>
<div class='section' id='section-8'>
<div class='docs'>
<div class='octowrap'>
<a class='octothorpe' href='#section-8'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre> <span class="k">def</span> <span class="nf">expectedMuChange</span><span class="p">(</span><span class="n">lhs</span><span class="p">,</span><span class="n">rhs</span><span class="p">,</span><span class="nb">all</span><span class="p">):</span>
<span class="k">return</span> <span class="n">lhs</span><span class="o">.</span><span class="n">n</span><span class="o">/</span><span class="nb">all</span><span class="o">.</span><span class="n">n</span> <span class="o">*</span> <span class="nb">abs</span><span class="p">(</span><span class="n">lhs</span><span class="o">.</span><span class="n">median</span><span class="p">()</span> <span class="o">-</span> <span class="nb">all</span><span class="o">.</span><span class="n">median</span><span class="p">())</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> \
<span class="n">rhs</span><span class="o">.</span><span class="n">n</span><span class="o">/</span><span class="nb">all</span><span class="o">.</span><span class="n">n</span> <span class="o">*</span> <span class="nb">abs</span><span class="p">(</span><span class="n">rhs</span><span class="o">.</span><span class="n">median</span><span class="p">()</span> <span class="o">-</span> <span class="nb">all</span><span class="o">.</span><span class="n">median</span><span class="p">())</span><span class="o">**</span><span class="mi">2</span></pre></div>
</div>
</div>
<div class='clearall'></div>
<div class='section' id='section-9'>
<div class='docs'>
<div class='octowrap'>
<a class='octothorpe' href='#section-9'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre> <span class="k">def</span> <span class="nf">stats</span><span class="p">(</span><span class="n">lhs</span><span class="p">,</span><span class="n">rhs</span><span class="p">,</span><span class="n">_</span><span class="p">):</span>
<span class="n">tmp</span> <span class="o">=</span> <span class="ow">not</span> <span class="n">cd</span><span class="p">(</span><span class="n">lhs</span><span class="o">.</span><span class="n">all</span><span class="p">,</span><span class="n">rhs</span><span class="o">.</span><span class="n">all</span><span class="p">)</span> <span class="ow">and</span> <span class="ow">not</span> <span class="n">bootstrap</span><span class="p">(</span><span class="n">lhs</span><span class="o">.</span><span class="n">all</span><span class="p">,</span><span class="n">rhs</span><span class="o">.</span><span class="n">all</span><span class="p">)</span></pre></div>
</div>
</div>
<div class='clearall'></div>
<div class='section' id='section-10'>
<div class='docs'>
<div class='octowrap'>
<a class='octothorpe' href='#section-10'>#</a>
</div>
<p>print(tmp, lhs.all, rhs.all)</p>
</div>
<div class='code'>
<div class="highlight"><pre> <span class="k">return</span> <span class="n">tmp</span>
<span class="n">lst</span><span class="o">=</span><span class="p">[]</span>
<span class="k">for</span> <span class="n">k</span><span class="p">,</span><span class="n">v</span> <span class="ow">in</span> <span class="n">d</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
<span class="n">tmp</span><span class="o">=</span><span class="n">num</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
<span class="n">tmp</span><span class="o">.</span><span class="n">label</span><span class="o">=</span> <span class="n">k</span>
<span class="n">lst</span> <span class="o">+=</span> <span class="p">[</span><span class="n">tmp</span><span class="p">]</span>
<span class="k">return</span> <span class="n">ranges</span><span class="p">(</span><span class="n">lst</span><span class="p">,</span>
<span class="n">flat</span><span class="o">=</span><span class="bp">False</span><span class="p">,</span>
<span class="n">d</span><span class="o">=</span><span class="mf">0.1</span><span class="p">,</span>
<span class="n">x</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">z</span><span class="p">:</span><span class="n">z</span><span class="o">.</span><span class="n">all</span><span class="p">,</span>
<span class="n">y</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">z</span><span class="p">:</span><span class="n">z</span><span class="o">.</span><span class="n">all</span><span class="p">,</span>
<span class="n">goodxsplit</span> <span class="o">=</span> <span class="n">stats</span><span class="p">,</span></pre></div>
</div>
</div>
<div class='clearall'></div>
<div class='section' id='section-11'>
<div class='docs'>
<div class='octowrap'>
<a class='octothorpe' href='#section-11'>#</a>
</div>
<p>evaly = expectedMuChange,</p>
</div>
<div class='code'>
<div class="highlight"><pre> <span class="n">key</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">z</span><span class="p">:</span><span class="n">z</span><span class="o">.</span><span class="n">median</span><span class="p">())</span></pre></div>
</div>
</div>
<div class='clearall'></div>
<div class='section' id='section-12'>
<div class='docs'>
<div class='octowrap'>
<a class='octothorpe' href='#section-12'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre><span class="k">def</span> <span class="nf">ddiv</span><span class="p">(</span><span class="n">d</span><span class="p">,</span><span class="n">f</span><span class="o">=</span><span class="bp">None</span><span class="p">):</span>
<span class="n">lst</span><span class="o">=</span><span class="p">[]</span>
<span class="k">for</span> <span class="n">k</span><span class="p">,</span><span class="n">v</span> <span class="ow">in</span> <span class="n">d</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
<span class="n">tmp</span><span class="o">=</span><span class="n">num</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
<span class="n">tmp</span><span class="o">.</span><span class="n">label</span><span class="o">=</span> <span class="n">k</span>
<span class="n">lst</span> <span class="o">+=</span> <span class="p">[</span><span class="n">tmp</span><span class="p">]</span>
<span class="k">return</span> <span class="n">ranges</span><span class="p">(</span><span class="n">lst</span><span class="p">,</span>
<span class="n">flat</span><span class="o">=</span><span class="bp">False</span><span class="p">,</span>
<span class="n">x</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">z</span><span class="p">:</span><span class="n">z</span><span class="o">.</span><span class="n">all</span><span class="p">,</span>
<span class="n">y</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">z</span><span class="p">:</span><span class="n">z</span><span class="o">.</span><span class="n">all</span><span class="p">,</span>
<span class="n">key</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">z</span><span class="p">:</span><span class="n">z</span><span class="o">.</span><span class="n">median</span><span class="p">())</span></pre></div>
</div>
</div>
<div class='clearall'></div>
<div class='section' id='section-13'>
<div class='docs'>
<div class='octowrap'>
<a class='octothorpe' href='#section-13'>#</a>
</div>
<hr />
</div>
<div class='code'>
<div class="highlight"><pre><span class="k">def</span> <span class="nf">ranges</span><span class="p">(</span><span class="n">lst</span><span class="p">,</span>
<span class="n">d</span> <span class="o">=</span> <span class="mf">0.3</span><span class="p">,</span>
<span class="n">cliffsDelta</span><span class="o">=</span> <span class="mf">0.147</span><span class="p">,</span>
<span class="n">enough</span> <span class="o">=</span> <span class="bp">None</span><span class="p">,</span>
<span class="n">enoughth</span> <span class="o">=</span> <span class="mf">0.71</span><span class="p">,</span>
<span class="n">epsilon</span> <span class="o">=</span> <span class="bp">None</span><span class="p">,</span>
<span class="n">evaly</span> <span class="o">=</span> <span class="bp">None</span><span class="p">,</span>
<span class="n">flat</span> <span class="o">=</span> <span class="bp">True</span><span class="p">,</span>
<span class="n">goodxsplit</span> <span class="o">=</span> <span class="bp">None</span><span class="p">,</span>
<span class="n">goodysplit</span> <span class="o">=</span> <span class="bp">None</span><span class="p">,</span>
<span class="n">greedy</span> <span class="o">=</span> <span class="bp">True</span><span class="p">,</span>
<span class="n">label</span> <span class="o">=</span> <span class="s">"ranges"</span><span class="p">,</span>
<span class="n">rnd</span> <span class="o">=</span> <span class="mi">3</span><span class="p">,</span>
<span class="n">trivial</span> <span class="o">=</span> <span class="mf">1.05</span><span class="p">,</span> <span class="c"># 1%</span>
<span class="n">key</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">z</span><span class="p">:</span><span class="n">z</span><span class="p">,</span>
<span class="n">verbose</span> <span class="o">=</span> <span class="bp">False</span><span class="p">,</span>
<span class="n">x</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">z</span><span class="p">:</span><span class="n">z</span><span class="p">,</span>
<span class="n">y</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">z</span><span class="p">:</span><span class="n">z</span><span class="p">,</span>
<span class="n">ynum</span> <span class="o">=</span> <span class="bp">True</span><span class="p">,</span>
<span class="p">):</span></pre></div>
</div>
</div>
<div class='clearall'></div>
<div class='section' id='section-14'>
<div class='docs'>
<div class='octowrap'>
<a class='octothorpe' href='#section-14'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre> <span class="k">def</span> <span class="nf">expectedWriggle</span><span class="p">(</span><span class="n">lhs</span><span class="p">,</span><span class="n">rhs</span><span class="p">,</span><span class="nb">all</span><span class="p">):</span>
<span class="k">return</span> <span class="n">lhs</span><span class="o">.</span><span class="n">n</span><span class="o">/</span><span class="nb">all</span><span class="o">.</span><span class="n">n</span> <span class="o">*</span> <span class="n">lhs</span><span class="o">.</span><span class="n">wriggle</span><span class="p">()</span> <span class="o">+</span> \
<span class="n">rhs</span><span class="o">.</span><span class="n">n</span><span class="o">/</span><span class="nb">all</span><span class="o">.</span><span class="n">n</span> <span class="o">*</span> <span class="n">rhs</span><span class="o">.</span><span class="n">wriggle</span><span class="p">()</span></pre></div>
</div>
</div>
<div class='clearall'></div>
<div class='section' id='section-15'>
<div class='docs'>
<div class='octowrap'>
<a class='octothorpe' href='#section-15'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre> <span class="k">def</span> <span class="nf">yes</span><span class="p">(</span><span class="o">*</span><span class="n">l</span><span class="p">,</span><span class="o">**</span><span class="n">d</span><span class="p">):</span> <span class="k">return</span> <span class="bp">True</span>
<span class="n">evaly</span><span class="o">=</span> <span class="n">evaly</span> <span class="ow">or</span> <span class="n">expectedWriggle</span>
<span class="n">goodxsplit</span> <span class="o">=</span> <span class="n">goodxsplit</span> <span class="ow">or</span> <span class="n">yes</span>
<span class="n">goodysplit</span> <span class="o">=</span> <span class="n">goodysplit</span> <span class="ow">or</span> <span class="n">yes</span></pre></div>
</div>
</div>
<div class='clearall'></div>
<div class='section' id='section-16'>
<div class='docs'>
<div class='octowrap'>
<a class='octothorpe' href='#section-16'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre> <span class="k">def</span> <span class="nf">stats</span><span class="p">(</span><span class="n">segment</span><span class="p">,</span> <span class="n">xall</span><span class="p">,</span> <span class="n">yall</span><span class="p">,</span><span class="n">flat</span><span class="p">):</span>
<span class="n">xs</span><span class="p">,</span><span class="n">ys</span> <span class="o">=</span> <span class="n">num</span><span class="p">(),</span><span class="n">yklass</span><span class="p">()</span>
<span class="k">if</span> <span class="n">flat</span><span class="p">:</span>
<span class="k">for</span> <span class="n">one</span> <span class="ow">in</span> <span class="n">segment</span><span class="p">:</span>
<span class="n">x1</span> <span class="o">=</span> <span class="n">x</span><span class="p">(</span><span class="n">one</span><span class="p">)</span>
<span class="n">y1</span> <span class="o">=</span> <span class="n">y</span><span class="p">(</span><span class="n">one</span><span class="p">)</span>
<span class="n">xs</span> <span class="o">+</span> <span class="n">x1</span>
<span class="n">xall</span> <span class="o">+</span> <span class="n">x1</span>
<span class="n">ys</span> <span class="o">+</span> <span class="n">y1</span>
<span class="n">yall</span> <span class="o">+</span> <span class="n">y1</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">for</span> <span class="n">x1</span> <span class="ow">in</span> <span class="n">segment</span><span class="o">.</span><span class="n">all</span><span class="p">:</span>
<span class="n">xs</span><span class="o">.</span><span class="n">label</span> <span class="o">=</span> <span class="n">segment</span><span class="o">.</span><span class="n">label</span>
<span class="n">ys</span><span class="o">.</span><span class="n">label</span> <span class="o">=</span> <span class="n">segment</span><span class="o">.</span><span class="n">label</span>
<span class="n">xs</span> <span class="o">+</span> <span class="n">x1</span>
<span class="n">xall</span> <span class="o">+</span> <span class="n">x1</span>
<span class="n">ys</span> <span class="o">+</span> <span class="n">x1</span>
<span class="n">yall</span> <span class="o">+</span> <span class="n">x1</span>
<span class="k">return</span> <span class="n">xs</span><span class="p">,</span><span class="n">ys</span></pre></div>
</div>
</div>
<div class='clearall'></div>
<div class='section' id='section-17'>
<div class='docs'>
<div class='octowrap'>
<a class='octothorpe' href='#section-17'>#</a>
</div>
<hr />
</div>
<div class='code'>
<div class="highlight"><pre> <span class="k">def</span> <span class="nf">summary</span><span class="p">(</span><span class="n">segments</span><span class="p">):</span>
<span class="n">xall</span><span class="p">,</span><span class="n">yall</span><span class="o">=</span><span class="p">[],[]</span>
<span class="n">xs</span><span class="p">,</span> <span class="n">ys</span> <span class="o">=</span> <span class="p">{},{}</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">)</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">segments</span><span class="p">[::</span><span class="o">-</span><span class="mi">1</span><span class="p">]):</span>
<span class="n">j</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">segments</span><span class="p">)</span> <span class="o">-</span> <span class="n">i</span> <span class="o">-</span> <span class="mi">1</span>
<span class="n">xall</span> <span class="o">+=</span> <span class="n">x</span><span class="o">.</span><span class="n">all</span>
<span class="n">yall</span> <span class="o">+=</span> <span class="n">y</span><span class="o">.</span><span class="n">all</span>
<span class="n">newx</span> <span class="o">=</span> <span class="n">num</span><span class="p">(</span><span class="n">xall</span><span class="p">)</span>
<span class="n">newy</span> <span class="o">=</span> <span class="n">yklass</span><span class="p">(</span><span class="n">yall</span><span class="p">)</span>
<span class="n">xs</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">newx</span>
<span class="n">ys</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">newy</span></pre></div>
</div>
</div>
<div class='clearall'></div>
<div class='section' id='section-18'>
<div class='docs'>
<div class='octowrap'>
<a class='octothorpe' href='#section-18'>#</a>
</div>
<p>print("!!!",j,newx,newy)</p>
</div>
<div class='code'>
<div class="highlight"><pre> <span class="k">return</span> <span class="n">xs</span><span class="p">,</span> <span class="n">ys</span><span class="p">,</span> <span class="n">num</span><span class="p">(</span><span class="n">xall</span><span class="p">),</span> <span class="n">yklass</span><span class="p">(</span><span class="n">yall</span><span class="p">)</span></pre></div>
</div>
</div>
<div class='clearall'></div>
<div class='section' id='section-19'>
<div class='docs'>
<div class='octowrap'>
<a class='octothorpe' href='#section-19'>#</a>
</div>
<hr />
</div>
<div class='code'>
<div class="highlight"><pre> <span class="k">def</span> <span class="nf">divide</span><span class="p">(</span><span class="n">segments</span><span class="p">,</span> <span class="n">out</span><span class="p">,</span><span class="n">lvl</span><span class="p">,</span> <span class="n">cut</span><span class="o">=</span><span class="bp">None</span><span class="p">):</span>
<span class="n">xrhsall</span><span class="p">,</span> <span class="n">yrhsall</span><span class="p">,</span> <span class="n">xoverall</span><span class="p">,</span> <span class="n">yoverall</span> <span class="o">=</span> <span class="n">summary</span><span class="p">(</span><span class="n">segments</span><span class="p">)</span>
<span class="n">score</span><span class="p">,</span> <span class="n">score1</span> <span class="o">=</span> <span class="n">yoverall</span><span class="o">.</span><span class="n">wriggle</span><span class="p">(),</span> <span class="bp">None</span>
<span class="n">xlhs</span><span class="p">,</span> <span class="n">ylhs</span> <span class="o">=</span> <span class="n">num</span><span class="p">(),</span> <span class="n">yklass</span><span class="p">()</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">)</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">segments</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">]):</span>
<span class="n">xrhs</span> <span class="o">=</span> <span class="n">xrhsall</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span>
<span class="n">yrhs</span> <span class="o">=</span> <span class="n">yrhsall</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span>
<span class="p">[</span><span class="n">xlhs</span><span class="o">+</span><span class="n">z</span> <span class="k">for</span> <span class="n">z</span> <span class="ow">in</span> <span class="n">x</span><span class="o">.</span><span class="n">all</span><span class="p">]</span>
<span class="p">[</span><span class="n">ylhs</span><span class="o">+</span><span class="n">z</span> <span class="k">for</span> <span class="n">z</span> <span class="ow">in</span> <span class="n">y</span><span class="o">.</span><span class="n">all</span><span class="p">]</span>
<span class="k">if</span> <span class="n">xlhs</span><span class="o">.</span><span class="n">median</span><span class="p">()</span> <span class="o">+</span> <span class="n">epsilon</span> <span class="o"><</span> <span class="n">xrhs</span><span class="o">.</span><span class="n">median</span><span class="p">():</span>
<span class="n">score1</span> <span class="o">=</span> <span class="n">evaly</span><span class="p">(</span><span class="n">ylhs</span><span class="p">,</span><span class="n">yrhs</span><span class="p">,</span><span class="n">yoverall</span><span class="p">)</span>
<span class="k">if</span> <span class="n">score1</span><span class="o">*</span><span class="n">trivial</span> <span class="o"><</span> <span class="n">score</span><span class="p">:</span>
<span class="k">if</span> <span class="n">yklass</span> <span class="o">==</span> <span class="n">num</span><span class="p">:</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">greedy</span> <span class="ow">or</span> <span class="n">ylhs</span><span class="o">.</span><span class="n">median</span><span class="p">()</span><span class="o">*</span><span class="n">trivial</span> <span class="o"><</span> <span class="n">yrhs</span><span class="o">.</span><span class="n">median</span><span class="p">():</span>
<span class="k">if</span> <span class="n">goodxsplit</span><span class="p">(</span><span class="n">xlhs</span><span class="p">,</span><span class="n">xrhs</span><span class="p">,</span><span class="n">xoverall</span><span class="p">):</span> <span class="c"># hook for stats</span>
<span class="n">cut</span><span class="p">,</span><span class="n">score</span> <span class="o">=</span> <span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span><span class="n">score1</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">greedy</span> <span class="ow">or</span> <span class="n">ylhs</span><span class="o">.</span><span class="n">mode</span> <span class="o">!=</span> <span class="n">yrhs</span><span class="o">.</span><span class="n">mode</span><span class="p">:</span>
<span class="k">if</span> <span class="n">goodysplit</span><span class="p">(</span><span class="n">ylhs</span><span class="p">,</span><span class="n">yrhs</span><span class="p">,</span><span class="n">yoverall</span><span class="p">,</span> <span class="n">score1</span><span class="p">):</span>
<span class="k">if</span> <span class="n">goodxsplit</span><span class="p">(</span><span class="n">xlhs</span><span class="p">,</span><span class="n">xrhs</span><span class="p">,</span><span class="n">xoverall</span><span class="p">):</span> <span class="c"># hook for stats</span>
<span class="n">cut</span><span class="p">,</span><span class="n">score</span> <span class="o">=</span> <span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span><span class="n">score1</span>
<span class="k">if</span> <span class="n">verbose</span><span class="p">:</span>
<span class="n">score1</span> <span class="o">=</span> <span class="nb">round</span><span class="p">(</span><span class="n">score1</span><span class="p">,</span><span class="n">rnd</span><span class="p">)</span> <span class="k">if</span> <span class="n">score1</span> <span class="k">else</span> <span class="s">'.'</span>
<span class="k">print</span><span class="p">(</span><span class="s">' ..'</span><span class="o">*</span><span class="n">lvl</span><span class="p">,</span><span class="n">xoverall</span><span class="o">.</span><span class="n">n</span><span class="p">,</span><span class="n">score1</span><span class="p">)</span>
<span class="k">if</span> <span class="n">cut</span><span class="p">:</span>
<span class="n">divide</span><span class="p">(</span><span class="n">segments</span><span class="p">[:</span><span class="n">cut</span><span class="p">],</span> <span class="n">out</span><span class="o">=</span> <span class="n">out</span><span class="p">,</span> <span class="n">lvl</span><span class="o">=</span> <span class="n">lvl</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
<span class="n">divide</span><span class="p">(</span><span class="n">segments</span><span class="p">[</span><span class="n">cut</span><span class="p">:],</span> <span class="n">out</span><span class="o">=</span> <span class="n">out</span><span class="p">,</span> <span class="n">lvl</span><span class="o">=</span> <span class="n">lvl</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">assert</span> <span class="n">xoverall</span><span class="o">.</span><span class="n">lo</span> <span class="o"><=</span> <span class="n">xoverall</span><span class="o">.</span><span class="n">hi</span>
<span class="n">out</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">dict</span><span class="p">(</span><span class="n">label</span> <span class="o">=</span> <span class="n">label</span><span class="p">,</span> <span class="n">score</span> <span class="o">=</span> <span class="n">score</span><span class="p">,</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">xoverall</span><span class="p">,</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">yoverall</span><span class="p">,</span>
<span class="n">has</span> <span class="o">=</span> <span class="n">segments</span><span class="p">,</span><span class="nb">id</span><span class="o">=</span><span class="nb">len</span><span class="p">(</span><span class="n">out</span><span class="p">)))</span>
<span class="k">return</span> <span class="n">out</span></pre></div>
</div>
</div>
<div class='clearall'></div>
<div class='section' id='section-20'>
<div class='docs'>
<div class='octowrap'>
<a class='octothorpe' href='#section-20'>#</a>
</div>
<hr />
</div>
<div class='code'>
<div class="highlight"><pre> <span class="k">def</span> <span class="nf">chunks</span><span class="p">(</span><span class="n">l</span><span class="p">,</span> <span class="n">n</span><span class="p">):</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">l</span><span class="p">),</span> <span class="n">n</span><span class="p">):</span> <span class="k">yield</span> <span class="n">l</span><span class="p">[</span><span class="n">i</span><span class="p">:</span><span class="n">i</span> <span class="o">+</span> <span class="n">n</span><span class="p">]</span></pre></div>
</div>
</div>
<div class='clearall'></div>
<div class='section' id='section-21'>
<div class='docs'>
<div class='octowrap'>
<a class='octothorpe' href='#section-21'>#</a>
</div>
<hr />
</div>
<div class='code'>
<div class="highlight"><pre> <span class="k">if</span> <span class="ow">not</span> <span class="n">lst</span><span class="p">:</span>
<span class="k">return</span> <span class="p">[]</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">lst</span> <span class="o">=</span> <span class="n">lst</span><span class="p">[:]</span>
<span class="n">yklass</span> <span class="o">=</span> <span class="n">num</span> <span class="k">if</span> <span class="n">ynum</span> <span class="k">else</span> <span class="n">sym</span>
<span class="n">xall</span><span class="p">,</span> <span class="n">yall</span> <span class="o">=</span> <span class="n">num</span><span class="p">(),</span> <span class="n">yklass</span><span class="p">()</span>
<span class="n">width</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">enough</span> <span class="ow">or</span> <span class="nb">len</span><span class="p">(</span><span class="n">lst</span><span class="p">)</span><span class="o">**</span><span class="n">enoughth</span><span class="p">)</span>
<span class="n">ordered</span> <span class="o">=</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">lst</span><span class="p">,</span><span class="n">key</span><span class="o">=</span><span class="n">key</span><span class="p">)</span>
<span class="n">segments</span> <span class="o">=</span> <span class="n">ordered</span> <span class="k">if</span> <span class="ow">not</span> <span class="n">flat</span> <span class="k">else</span> <span class="p">[</span><span class="n">z</span> <span class="k">for</span> <span class="n">z</span> <span class="ow">in</span> <span class="n">chunks</span><span class="p">(</span><span class="n">ordered</span><span class="p">,</span><span class="n">width</span><span class="p">)]</span>
<span class="n">parts</span> <span class="o">=</span> <span class="p">[</span><span class="n">stats</span><span class="p">(</span><span class="n">segment</span><span class="p">,</span> <span class="n">xall</span><span class="p">,</span> <span class="n">yall</span><span class="p">,</span><span class="n">flat</span><span class="p">)</span> <span class="k">for</span> <span class="n">segment</span> <span class="ow">in</span> <span class="n">segments</span><span class="p">]</span>
<span class="n">epsilon</span> <span class="o">=</span> <span class="n">epsilon</span> <span class="ow">or</span> <span class="n">d</span> <span class="o">*</span> <span class="n">xall</span><span class="o">.</span><span class="n">wriggle</span><span class="p">()</span>
<span class="k">return</span> <span class="n">divide</span><span class="p">(</span><span class="n">parts</span><span class="p">,</span><span class="n">out</span><span class="o">=</span><span class="p">[],</span> <span class="n">lvl</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span></pre></div>
</div>
</div>
<div class='clearall'></div>
<div class='section' id='section-22'>
<div class='docs'>
<div class='octowrap'>
<a class='octothorpe' href='#section-22'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre><span class="k">class</span> <span class="nc">ordered</span><span class="p">:</span></pre></div>
</div>
</div>
<div class='clearall'></div>
<div class='section' id='section-23'>
<div class='docs'>
<div class='octowrap'>
<a class='octothorpe' href='#section-23'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre> <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="n">lst</span><span class="p">):</span>
<span class="n">i</span><span class="o">.</span><span class="n">sorted</span><span class="o">=</span> <span class="bp">False</span>
<span class="n">i</span><span class="o">.</span><span class="n">_median</span> <span class="o">=</span> <span class="bp">None</span>
<span class="n">i</span><span class="o">.</span><span class="n">all</span> <span class="o">=</span> <span class="n">lst</span></pre></div>
</div>
</div>
<div class='clearall'></div>
<div class='section' id='section-24'>
<div class='docs'>
<div class='octowrap'>
<a class='octothorpe' href='#section-24'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre> <span class="k">def</span> <span class="nf">__add__</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="n">x</span><span class="p">):</span>
<span class="n">i</span><span class="o">.</span><span class="n">sorted</span><span class="o">=</span><span class="bp">False</span>
<span class="n">i</span><span class="o">.</span><span class="n">all</span> <span class="o">+=</span> <span class="p">[</span><span class="n">x</span><span class="p">]</span></pre></div>
</div>
</div>
<div class='clearall'></div>
<div class='section' id='section-25'>
<div class='docs'>
<div class='octowrap'>
<a class='octothorpe' href='#section-25'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre> <span class="k">def</span> <span class="nf">wriggle</span><span class="p">(</span><span class="n">i</span><span class="p">):</span>
<span class="k">return</span> <span class="n">i</span><span class="o">.</span><span class="n">median</span><span class="p">()</span></pre></div>
</div>
</div>
<div class='clearall'></div>
<div class='section' id='section-26'>
<div class='docs'>
<div class='octowrap'>
<a class='octothorpe' href='#section-26'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre> <span class="k">def</span> <span class="nf">median</span><span class="p">(</span><span class="n">i</span><span class="p">):</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">i</span><span class="o">.</span><span class="n">sorted</span> <span class="ow">or</span> <span class="ow">not</span> <span class="n">i</span><span class="o">.</span><span class="n">_median</span><span class="p">:</span>
<span class="n">i</span><span class="o">.</span><span class="n">sorted</span> <span class="o">=</span> <span class="bp">True</span>
<span class="n">i</span><span class="o">.</span><span class="n">all</span> <span class="o">=</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">i</span><span class="o">.</span><span class="n">all</span><span class="p">)</span>
<span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">i</span><span class="o">.</span><span class="n">all</span><span class="p">)</span>
<span class="n">p</span> <span class="o">=</span> <span class="n">q</span> <span class="o">=</span> <span class="n">n</span><span class="o">//</span><span class="mi">2</span>
<span class="k">if</span> <span class="n">n</span> <span class="o"><</span> <span class="mi">3</span><span class="p">:</span>
<span class="n">p</span><span class="p">,</span><span class="n">q</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span> <span class="n">n</span><span class="o">-</span><span class="mi">1</span>
<span class="k">elif</span> <span class="ow">not</span> <span class="n">n</span> <span class="o">%</span> <span class="mi">2</span><span class="p">:</span>
<span class="n">q</span> <span class="o">=</span> <span class="n">p</span> <span class="o">-</span><span class="mi">1</span>
<span class="n">i</span><span class="o">.</span><span class="n">_median</span> <span class="o">=</span> <span class="n">i</span><span class="o">.</span><span class="n">all</span><span class="p">[</span><span class="n">p</span><span class="p">]</span> <span class="k">if</span> <span class="n">p</span><span class="o">==</span><span class="n">q</span> <span class="k">else</span> <span class="p">(</span><span class="n">i</span><span class="o">.</span><span class="n">all</span><span class="p">[</span><span class="n">p</span><span class="p">]</span><span class="o">+</span><span class="n">i</span><span class="o">.</span><span class="n">all</span><span class="p">[</span><span class="n">q</span><span class="p">])</span><span class="o">/</span><span class="mi">2</span>
<span class="k">return</span> <span class="n">i</span><span class="o">.</span><span class="n">_median</span></pre></div>
</div>
</div>
<div class='clearall'></div>
<div class='section' id='section-27'>
<div class='docs'>
<div class='octowrap'>
<a class='octothorpe' href='#section-27'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre><span class="k">class</span> <span class="nc">num</span><span class="p">:</span></pre></div>
</div>
</div>
<div class='clearall'></div>
<div class='section' id='section-28'>
<div class='docs'>
<div class='octowrap'>
<a class='octothorpe' href='#section-28'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre> <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="n">inits</span><span class="o">=</span><span class="p">[]):</span>
<span class="n">i</span><span class="o">.</span><span class="n">lo</span><span class="p">,</span> <span class="n">i</span><span class="o">.</span><span class="n">hi</span><span class="p">,</span> <span class="n">i</span><span class="o">.</span><span class="n">n</span><span class="p">,</span> <span class="n">i</span><span class="o">.</span><span class="n">mu</span><span class="p">,</span> <span class="n">i</span><span class="o">.</span><span class="n">m2</span> <span class="o">=</span> <span class="mf">1e32</span><span class="p">,</span><span class="o">-</span><span class="mf">1e32</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span>
<span class="n">i</span><span class="o">.</span><span class="n">sd</span> <span class="o">=</span> <span class="bp">None</span>
<span class="n">i</span><span class="o">.</span><span class="n">all</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">i</span><span class="o">.</span><span class="n">ordered</span><span class="o">=</span><span class="n">ordered</span><span class="p">(</span><span class="n">i</span><span class="o">.</span><span class="n">all</span><span class="p">)</span>
<span class="p">[</span><span class="n">i</span> <span class="o">+</span> <span class="n">x</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">inits</span><span class="p">]</span></pre></div>
</div>
</div>
<div class='clearall'></div>
<div class='section' id='section-29'>
<div class='docs'>
<div class='octowrap'>
<a class='octothorpe' href='#section-29'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre> <span class="k">def</span> <span class="nf">__add__</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="n">x</span><span class="p">):</span>
<span class="n">i</span><span class="o">.</span><span class="n">ordered</span> <span class="o">+</span> <span class="n">x</span>
<span class="n">i</span><span class="o">.</span><span class="n">sorted</span><span class="o">=</span><span class="bp">False</span>
<span class="n">i</span><span class="o">.</span><span class="n">lo</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">i</span><span class="o">.</span><span class="n">lo</span><span class="p">)</span>
<span class="n">i</span><span class="o">.</span><span class="n">hi</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">i</span><span class="o">.</span><span class="n">hi</span><span class="p">)</span>
<span class="n">i</span><span class="o">.</span><span class="n">n</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="n">delta</span> <span class="o">=</span> <span class="n">x</span> <span class="o">-</span> <span class="n">i</span><span class="o">.</span><span class="n">mu</span>
<span class="n">i</span><span class="o">.</span><span class="n">mu</span> <span class="o">+=</span> <span class="n">delta</span><span class="o">/</span><span class="n">i</span><span class="o">.</span><span class="n">n</span>
<span class="n">i</span><span class="o">.</span><span class="n">m2</span> <span class="o">+=</span> <span class="n">delta</span><span class="o">*</span><span class="p">(</span><span class="n">x</span> <span class="o">-</span> <span class="n">i</span><span class="o">.</span><span class="n">mu</span><span class="p">)</span>
<span class="k">if</span> <span class="n">i</span><span class="o">.</span><span class="n">n</span> <span class="o">></span> <span class="mi">1</span><span class="p">:</span>
<span class="n">i</span><span class="o">.</span><span class="n">sd</span> <span class="o">=</span> <span class="p">(</span><span class="n">i</span><span class="o">.</span><span class="n">m2</span><span class="o">/</span><span class="p">(</span><span class="n">i</span><span class="o">.</span><span class="n">n</span><span class="o">-</span><span class="mi">1</span><span class="p">))</span><span class="o">**</span><span class="mf">0.5</span></pre></div>
</div>
</div>
<div class='clearall'></div>
<div class='section' id='section-30'>
<div class='docs'>
<div class='octowrap'>
<a class='octothorpe' href='#section-30'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre> <span class="k">def</span> <span class="nf">wriggle</span><span class="p">(</span><span class="n">i</span><span class="p">):</span>
<span class="k">return</span> <span class="n">i</span><span class="o">.</span><span class="n">sd</span></pre></div>
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<div class='section' id='section-31'>
<div class='docs'>
<div class='octowrap'>
<a class='octothorpe' href='#section-31'>#</a>
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</div>
<div class='code'>
<div class="highlight"><pre> <span class="k">def</span> <span class="nf">median</span><span class="p">(</span><span class="n">i</span><span class="p">):</span>
<span class="k">return</span> <span class="n">i</span><span class="o">.</span><span class="n">ordered</span><span class="o">.</span><span class="n">median</span><span class="p">()</span></pre></div>
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<div class='section' id='section-32'>
<div class='docs'>
<div class='octowrap'>
<a class='octothorpe' href='#section-32'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre> <span class="k">def</span> <span class="nf">__repr__</span><span class="p">(</span><span class="n">i</span><span class="p">):</span>
<span class="k">return</span> <span class="s">"(:lo </span><span class="si">%.4f</span><span class="s"> :hi </span><span class="si">%.4f</span><span class="s"> :n </span><span class="si">%.4f</span><span class="s"> :med </span><span class="si">%.4f</span><span class="s"> :sd </span><span class="si">%.4f</span><span class="s">)"</span> <span class="o">%</span> <span class="p">(</span><span class="n">i</span><span class="o">.</span><span class="n">lo</span><span class="p">,</span> <span class="n">i</span><span class="o">.</span><span class="n">hi</span><span class="p">,</span> <span class="n">i</span><span class="o">.</span><span class="n">n</span><span class="p">,</span><span class="n">i</span><span class="o">.</span><span class="n">median</span><span class="p">(),</span><span class="n">i</span><span class="o">.</span><span class="n">sd</span><span class="p">)</span></pre></div>
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<div class='clearall'></div>
<div class='section' id='section-33'>
<div class='docs'>
<div class='octowrap'>
<a class='octothorpe' href='#section-33'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre><span class="k">class</span> <span class="nc">sym</span><span class="p">:</span></pre></div>
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<div class='docs'>
<div class='octowrap'>
<a class='octothorpe' href='#section-34'>#</a>
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<div class='code'>
<div class="highlight"><pre> <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="n">inits</span><span class="o">=</span><span class="p">[]):</span>
<span class="n">i</span><span class="o">.</span><span class="n">n</span><span class="p">,</span> <span class="n">i</span><span class="o">.</span><span class="n">most</span><span class="p">,</span> <span class="n">i</span><span class="o">.</span><span class="n">mode</span><span class="p">,</span> <span class="n">i</span><span class="o">.</span><span class="n">counts</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="bp">None</span><span class="p">,{}</span>
<span class="n">i</span><span class="o">.</span><span class="n">all</span><span class="o">=</span><span class="p">[]</span>
<span class="n">i</span><span class="o">.</span><span class="n">_ent</span><span class="o">=</span><span class="bp">None</span>
<span class="p">[</span><span class="n">i</span> <span class="o">+</span> <span class="n">x</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">inits</span><span class="p">]</span></pre></div>
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<div class='section' id='section-35'>
<div class='docs'>
<div class='octowrap'>
<a class='octothorpe' href='#section-35'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre> <span class="k">def</span> <span class="nf">__add__</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="n">x</span><span class="p">):</span>
<span class="n">i</span><span class="o">.</span><span class="n">all</span> <span class="o">+=</span> <span class="p">[</span><span class="n">x</span><span class="p">]</span>
<span class="n">i</span><span class="o">.</span><span class="n">n</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="n">i</span><span class="o">.</span><span class="n">_ent</span><span class="o">=</span><span class="bp">None</span>
<span class="n">count</span><span class="o">=</span> <span class="n">i</span><span class="o">.</span><span class="n">counts</span><span class="p">[</span><span class="n">x</span><span class="p">]</span> <span class="o">=</span> <span class="n">i</span><span class="o">.</span><span class="n">counts</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="mi">0</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span>
<span class="k">if</span> <span class="n">count</span> <span class="o">></span> <span class="n">i</span><span class="o">.</span><span class="n">most</span><span class="p">:</span>
<span class="n">i</span><span class="o">.</span><span class="n">most</span><span class="p">,</span><span class="n">i</span><span class="o">.</span><span class="n">mode</span><span class="o">=</span><span class="n">count</span><span class="p">,</span><span class="n">x</span></pre></div>
</div>
</div>
<div class='clearall'></div>
<div class='section' id='section-36'>
<div class='docs'>
<div class='octowrap'>
<a class='octothorpe' href='#section-36'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre> <span class="k">def</span> <span class="nf">wriggle</span><span class="p">(</span><span class="n">i</span><span class="p">):</span> <span class="k">return</span> <span class="n">i</span><span class="o">.</span><span class="n">ent</span><span class="p">()</span></pre></div>
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<div class='clearall'></div>
<div class='section' id='section-37'>
<div class='docs'>
<div class='octowrap'>
<a class='octothorpe' href='#section-37'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre> <span class="k">def</span> <span class="nf">ent</span><span class="p">(</span><span class="n">i</span><span class="p">):</span>
<span class="k">if</span> <span class="n">i</span><span class="o">.</span><span class="n">_ent</span> <span class="ow">is</span> <span class="bp">None</span><span class="p">:</span>
<span class="n">i</span><span class="o">.</span><span class="n">_ent</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">i</span><span class="o">.</span><span class="n">counts</span><span class="p">:</span>
<span class="n">p</span> <span class="o">=</span> <span class="n">i</span><span class="o">.</span><span class="n">counts</span><span class="p">[</span><span class="n">k</span><span class="p">]</span><span class="o">/</span><span class="n">i</span><span class="o">.</span><span class="n">n</span>
<span class="n">i</span><span class="o">.</span><span class="n">_ent</span> <span class="o">-=</span> <span class="n">p</span><span class="o">*</span><span class="n">math</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">p</span><span class="p">,</span><span class="mi">2</span><span class="p">)</span>
<span class="k">return</span> <span class="n">i</span><span class="o">.</span><span class="n">_ent</span></pre></div>
</div>
</div>
<div class='clearall'></div>
<div class='section' id='section-38'>
<div class='docs'>
<div class='octowrap'>
<a class='octothorpe' href='#section-38'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre> <span class="k">def</span> <span class="nf">k</span><span class="p">(</span><span class="n">i</span><span class="p">):</span> <span class="k">return</span> <span class="nb">len</span><span class="p">(</span><span class="n">i</span><span class="o">.</span><span class="n">counts</span><span class="o">.</span><span class="n">keys</span><span class="p">())</span></pre></div>
</div>
</div>
<div class='clearall'></div>
<div class='section' id='section-39'>
<div class='docs'>
<div class='octowrap'>
<a class='octothorpe' href='#section-39'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre> <span class="k">def</span> <span class="nf">ke</span><span class="p">(</span><span class="n">i</span><span class="p">):</span> <span class="k">return</span> <span class="n">i</span><span class="o">.</span><span class="n">k</span><span class="p">()</span><span class="o">*</span><span class="n">i</span><span class="o">.</span><span class="n">ent</span><span class="p">()</span></pre></div>
</div>
</div>
<div class='clearall'></div>
<div class='section' id='section-40'>
<div class='docs'>
<div class='octowrap'>
<a class='octothorpe' href='#section-40'>#</a>
</div>
<hr />
<p><img align=right
src="https://raw.githubusercontent.com/timm/timm.github.io/master/timm.png"
width=170></p>
<h2>Copyleft</h2>
<p>Copyright © 2016,2017 Tim Menzies <a href="mailto:tim@menzies.us">tim@menzies.us</a>, MIT license v2.</p>
<p>Permission is hereby granted, free of charge, to any person obtaining
a copy of this software and associated documentation files (the
"Software"), to deal in the Software without restriction, including
without limitation the rights to use, copy, modify, merge, publish,
distribute, sublicense, and/or sell copies of the Software, and to
permit persons to whom the Software is furnished to do so, subject
to the following conditions:</p>
<p>The above copyright notice and this permission notice shall be
included in all copies or substantial portions of the Software.</p>
<p>THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR
ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF
CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.</p>
<p>Share and enjoy.</p>
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