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Author SHA1 Message Date
Dominic Zimmer
4d10148e49 Update scripts 2023-06-16 12:32:22 +02:00
Dominic Zimmer
6b99136661 Update ipynb 2023-06-16 12:31:43 +02:00
5 changed files with 281 additions and 143 deletions
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0
crawler/mk.py → crawler/markov.py
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6
hp/hp.py
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@ -45,6 +45,10 @@ while i < len(lines):
print("Parsing lines")
corpus = " ".join(truelines)
#with open("hp_parsed.txt", "w") as f:
# f.writelines(corpus)
tokens = corpus.split(" ")
words = set(tokens)
id_to_word = dict(enumerate(words))
@ -55,8 +59,10 @@ from numpy import matrix as M, array
#m = M( [ [ 0 for _ in range(len(words)) ] for _ in range(len(words)) ] )
print("allocating array")
# ich zähle alle folgeworte i→j
m = array([0])
m.resize(N, N)
# die wahrscheinlichkeiten
M = array([0.0])
M.resize(N, N)

1
hp/hp_parsed.txt Normal file
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190
jupyter/The Art of Memory Loss.html
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@ -15142,7 +15142,8 @@ body[data-format='mobile'] .jp-OutputArea-child .jp-OutputArea-output {
<img src="https://cdn-icons-png.flaticon.com/512/3997/3997691.png"/>
<img src="https://upload.wikimedia.org/wikipedia/commons/thumb/5/53/Google_%22G%22_Logo.svg/2008px-Google_%22G%22_Logo.svg.png" />
<img src="https://upload.wikimedia.org/wikipedia/commons/thumb/0/04/ChatGPT_logo.svg/1024px-ChatGPT_logo.svg.png" />
<img src="https://static.vecteezy.com/system/resources/previews/023/636/525/original/3d-rendering-radiation-icons-sign-caution-danger-symbol-free-png.png" />
<img src="https://www.artandstick.be/getsupercustomizedimage.php5?objid=289&colorid1=2&colorid2=4&colorid3=4&colorid4=4&colorid5=4&way=NORMAL&transparent=Y" />
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<img src="https://thegraphicsfairy.com/wp-content/uploads/2016/07/Frog-Drawing-Green-3-GraphicsFairy.jpg" />
</div>
@ -15156,7 +15157,7 @@ body[data-format='mobile'] .jp-OutputArea-child .jp-OutputArea-output {
</div>
<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput " data-mime-type="text/markdown">
<h1 id="Fr%C3%B6sche,-Wetten,-Wetter-und-Wetterfr%C3%B6sche">Fr&#246;sche, Wetten, Wetter und Wetterfr&#246;sche<a class="anchor-link" href="#Fr%C3%B6sche,-Wetten,-Wetter-und-Wetterfr%C3%B6sche">&#182;</a></h1>
<h1 id="Fr%C3%B6sche,-Wetter-und-Wetterfr%C3%B6sche">Fr&#246;sche, Wetter und Wetterfr&#246;sche<a class="anchor-link" href="#Fr%C3%B6sche,-Wetter-und-Wetterfr%C3%B6sche">&#182;</a></h1>
</div>
</div>
</div>
@ -15222,7 +15223,7 @@ body[data-format='mobile'] .jp-OutputArea-child .jp-OutputArea-output {
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
</div>
<div class="jp-InputArea jp-Cell-inputArea">
<div class="jp-InputPrompt jp-InputArea-prompt">In&nbsp;[1]:</div>
<div class="jp-InputPrompt jp-InputArea-prompt">In&nbsp;[7]:</div>
<div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
<div class="CodeMirror cm-s-jupyter">
<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
@ -15231,7 +15232,7 @@ body[data-format='mobile'] .jp-OutputArea-child .jp-OutputArea-output {
<span class="n">p</span> <span class="o">=</span> <span class="mf">0.6</span> <span class="c1"># von l nach r</span>
<span class="n">q</span> <span class="o">=</span> <span class="mf">0.2</span> <span class="c1"># von r nach l</span>
<span class="n">N</span> <span class="o">=</span> <span class="mi">100_000</span> <span class="c1"># Simulationen</span>
<span class="n">N</span> <span class="o">=</span> <span class="mi">1_000_000</span> <span class="c1"># Simulationen</span>
<span class="c1"># Los geht&#39;s!</span>
</pre></div>
@ -15246,7 +15247,7 @@ body[data-format='mobile'] .jp-OutputArea-child .jp-OutputArea-output {
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
</div>
<div class="jp-InputArea jp-Cell-inputArea">
<div class="jp-InputPrompt jp-InputArea-prompt">In&nbsp;[2]:</div>
<div class="jp-InputPrompt jp-InputArea-prompt">In&nbsp;[8]:</div>
<div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
<div class="CodeMirror cm-s-jupyter">
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">visits</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span>
@ -15287,9 +15288,9 @@ body[data-format='mobile'] .jp-OutputArea-child .jp-OutputArea-output {
<div class="jp-RenderedText jp-OutputArea-output" data-mime-type="text/plain">
<pre>100000/100000
0.2473 of the time at 0 (24728 total)
0.7527 of the time at 1 (75272 total)
<pre>1000000/1000000
0.2501 of the time at 0 (250098 total)
0.7499 of the time at 1 (749902 total)
</pre>
</div>
</div>
@ -15697,7 +15698,7 @@ $$
M = \frac{1}{10} \begin{pmatrix}6 &amp; 3 &amp; 1 \\ 4 &amp; 3 &amp; 3 \\ 1 &amp; 5 &amp; 4 \end{pmatrix}
= \begin{pmatrix}0.6 &amp; 0.3 &amp; 0.1 \\ 0.4 &amp; 0.3 &amp; 0.3 \\ 0.1 &amp; 0.5 &amp; 0.4 \end{pmatrix}
\end{align*}
$$<p>Wenn es heute regnet $X_0 = \begin{pmatrix}1 &amp; 0 &amp; 0 \end{pmatrix}$, ist die Wettervorschau für morgen $X_0 \cdot M$, bzw für in einer Woche $X_0 \cdot M \cdot \dots M = X_0 \cdot M^{14}$.</p>
$$<p>Wenn heute die Sonne scheint $X_0 = \begin{pmatrix}1 &amp; 0 &amp; 0 \end{pmatrix}$, ist die Wettervorschau für morgen $X_0 \cdot M$, bzw für in zwei Wochen $X_{14} = X_0 \cdot M \cdot \dots M = X_0 \cdot M^{14}$.</p>
</div>
</div>
@ -15807,15 +15808,19 @@ $$
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
</div>
<div class="jp-InputArea jp-Cell-inputArea">
<div class="jp-InputPrompt jp-InputArea-prompt">In&nbsp;[9]:</div>
<div class="jp-InputPrompt jp-InputArea-prompt">In&nbsp;[19]:</div>
<div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
<div class="CodeMirror cm-s-jupyter">
<div class=" highlight hl-ipython3"><pre><span></span><span class="c1">#from sympy import symbols as S, Matrix as Mat</span>
<span class="kn">from</span> <span class="nn">numpy</span> <span class="kn">import</span> <span class="n">array</span>
<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">numpy</span> <span class="kn">import</span> <span class="n">array</span>
<span class="n">M</span> <span class="o">=</span> <span class="n">array</span><span class="p">([</span>
<span class="p">[</span><span class="mf">0.6</span><span class="p">,</span> <span class="mf">0.3</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">],</span>
<span class="p">[</span><span class="mf">0.4</span><span class="p">,</span> <span class="mf">0.3</span><span class="p">,</span> <span class="mf">0.3</span><span class="p">],</span>
<span class="p">[</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">]]</span>
<span class="p">)</span>
<span class="n">M</span> <span class="o">=</span> <span class="n">array</span><span class="p">([[</span><span class="mf">0.6</span><span class="p">,</span> <span class="mf">0.3</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">],</span> <span class="p">[</span><span class="mf">0.4</span><span class="p">,</span> <span class="mf">0.3</span><span class="p">,</span> <span class="mf">0.3</span><span class="p">],</span> <span class="p">[</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">]])</span>
<span class="n">x0</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</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="n">x0</span> <span class="o">@</span> <span class="n">M</span> <span class="o">@</span> <span class="n">M</span> <span class="o">@</span> <span class="n">M</span> <span class="o">@</span> <span class="n">M</span> <span class="o">@</span> <span class="n">M</span> <span class="o">@</span> <span class="n">M</span> <span class="o">@</span> <span class="n">M</span> <span class="o">@</span> <span class="n">M</span> <span class="o">@</span> <span class="n">M</span> <span class="o">@</span> <span class="n">M</span> <span class="o">@</span> <span class="n">M</span> <span class="o">@</span> <span class="n">M</span> <span class="o">@</span> <span class="n">M</span> <span class="o">@</span> <span class="n">M</span>
<span class="n">x0</span>
</pre></div>
</div>
@ -15831,13 +15836,13 @@ $$
<div class="jp-OutputArea jp-Cell-outputArea">
<div class="jp-OutputArea-child jp-OutputArea-executeResult">
<div class="jp-OutputPrompt jp-OutputArea-prompt">Out[9]:</div>
<div class="jp-OutputPrompt jp-OutputArea-prompt">Out[19]:</div>
<div class="jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult" data-mime-type="text/plain">
<pre>array([0.40909225, 0.3484844 , 0.24242335])</pre>
<pre>[1, 0, 0]</pre>
</div>
</div>
@ -15846,16 +15851,17 @@ $$
</div>
</div><div id="cell-id=ae437f47" class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs ">
</div><div id="cell-id=ae437f47" class="jp-Cell jp-CodeCell jp-Notebook-cell ">
<div class="jp-Cell-inputWrapper">
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
</div>
<div class="jp-InputArea jp-Cell-inputArea">
<div class="jp-InputPrompt jp-InputArea-prompt">In&nbsp;[&nbsp;]:</div>
<div class="jp-InputPrompt jp-InputArea-prompt">In&nbsp;[21]:</div>
<div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
<div class="CodeMirror cm-s-jupyter">
<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">numpy</span> <span class="kn">import</span> <span class="n">linalg</span>
<span class="n">x0</span> <span class="o">@</span> <span class="n">linalg</span><span class="o">.</span><span class="n">matrix_power</span><span class="p">(</span><span class="n">M</span><span class="p">,</span> <span class="mi">14</span><span class="p">)</span>
<span class="n">x0</span> <span class="o">=</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">1</span><span class="p">]</span>
<span class="n">x0</span> <span class="o">@</span> <span class="n">linalg</span><span class="o">.</span><span class="n">matrix_power</span><span class="p">(</span><span class="n">M</span><span class="p">,</span> <span class="mi">14</span><span class="p">)</span> <span class="c1"># schnelles Exponenzieren</span>
</pre></div>
</div>
@ -15863,6 +15869,29 @@ $$
</div>
</div>
<div class="jp-Cell-outputWrapper">
<div class="jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser">
</div>
<div class="jp-OutputArea jp-Cell-outputArea">
<div class="jp-OutputArea-child jp-OutputArea-executeResult">
<div class="jp-OutputPrompt jp-OutputArea-prompt">Out[21]:</div>
<div class="jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult" data-mime-type="text/plain">
<pre>array([0.40908903, 0.34848547, 0.2424255 ])</pre>
</div>
</div>
</div>
</div>
</div>
<div id="cell-id=6efbd936" class="jp-Cell jp-MarkdownCell jp-Notebook-cell">
<div class="jp-Cell-inputWrapper">
@ -15887,12 +15916,12 @@ $$<p>aus. Hierbei ist $\lambda != 0$ eine Zahl, die man auch <em>Eigenwert</em>
</div>
</div>
</div>
</div><div id="cell-id=9b76997c" class="jp-Cell jp-CodeCell jp-Notebook-cell ">
</div><div id="cell-id=9b76997c" class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs ">
<div class="jp-Cell-inputWrapper">
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
</div>
<div class="jp-InputArea jp-Cell-inputArea">
<div class="jp-InputPrompt jp-InputArea-prompt">In&nbsp;[13]:</div>
<div class="jp-InputPrompt jp-InputArea-prompt">In&nbsp;[&nbsp;]:</div>
<div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
<div class="CodeMirror cm-s-jupyter">
<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># linalg.eig berechnet Rechts-Eigenvektoren von Matrizen, wir suchen allerdings Links-Eigenvektoren</span>
@ -15918,29 +15947,6 @@ $$<p>aus. Hierbei ist $\lambda != 0$ eine Zahl, die man auch <em>Eigenwert</em>
</div>
</div>
<div class="jp-Cell-outputWrapper">
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<pre>0.9999999999999989
[0.40909091 0.34848485 0.24242424]
[0.40909091 0.34848485 0.24242424]
</pre>
</div>
</div>
</div>
</div>
</div>
<div id="cell-id=b7f0b716" class="jp-Cell jp-MarkdownCell jp-Notebook-cell">
<div class="jp-Cell-inputWrapper">
@ -15949,7 +15955,7 @@ $$<p>aus. Hierbei ist $\lambda != 0$ eine Zahl, die man auch <em>Eigenwert</em>
<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput " data-mime-type="text/markdown">
<h1 id="Fr%C3%B6sche-brauchen-Zufall">Fr&#246;sche brauchen Zufall<a class="anchor-link" href="#Fr%C3%B6sche-brauchen-Zufall">&#182;</a></h1><div class="alert alert-info">
<p>Viele Leute werfen Münzen in den Teich der Frösche.
<p>Viele Leute werfen <strong>faire</strong> Münzen in den Teich der Frösche.
Wir sollen einen Frosch aussuchen, der der neue Schatzmeister werden soll.
Wie können wir aus den 7 Fröschen <strong>fair</strong> einen auswählen?</p>
</div>
@ -15990,7 +15996,7 @@ Wie können wir aus den 7 Fröschen <strong>fair</strong> einen auswählen?</p>
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
</div>
<div class="jp-InputArea jp-Cell-inputArea">
<div class="jp-InputPrompt jp-InputArea-prompt">In&nbsp;[32]:</div>
<div class="jp-InputPrompt jp-InputArea-prompt">In&nbsp;[28]:</div>
<div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
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<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">numpy</span> <span class="kn">import</span> <span class="n">array</span>
@ -16012,7 +16018,7 @@ Wie können wir aus den 7 Fröschen <strong>fair</strong> einen auswählen?</p>
<span class="p">[</span> <span class="mf">0.0</span> <span class="p">,</span> <span class="mf">0.0</span> <span class="p">,</span> <span class="mf">0.0</span> <span class="p">,</span> <span class="mf">0.0</span> <span class="p">,</span> <span class="mf">0.0</span> <span class="p">,</span> <span class="mf">0.0</span> <span class="p">,</span> <span class="mf">0.0</span> <span class="p">,</span> <span class="mf">0.0</span> <span class="p">,</span> <span class="mf">0.0</span> <span class="p">,</span> <span class="mf">0.0</span> <span class="p">,</span> <span class="mf">0.0</span> <span class="p">,</span> <span class="mf">0.0</span> <span class="p">,</span> <span class="mf">0.0</span> <span class="p">,</span> <span class="mf">1.0</span><span class="p">]</span>
<span class="p">])</span>
<span class="n">v</span> <span class="o">=</span> <span class="n">array</span><span class="p">([</span><span class="mi">1</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="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="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="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="p">,</span> <span class="mi">0</span> <span class="p">])</span>
<span class="n">v</span> <span class="o">@</span> <span class="n">M</span>
<span class="n">v</span> <span class="o">@</span> <span class="n">linalg</span><span class="o">.</span><span class="n">matrix_power</span><span class="p">(</span><span class="n">M</span><span class="p">,</span> <span class="mi">3</span><span class="o">*</span><span class="mi">100</span><span class="p">)</span>
</pre></div>
</div>
@ -16028,14 +16034,16 @@ Wie können wir aus den 7 Fröschen <strong>fair</strong> einen auswählen?</p>
<div class="jp-OutputArea jp-Cell-outputArea">
<div class="jp-OutputArea-child jp-OutputArea-executeResult">
<div class="jp-OutputPrompt jp-OutputArea-prompt">Out[32]:</div>
<div class="jp-OutputPrompt jp-OutputArea-prompt">Out[28]:</div>
<div class="jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult" data-mime-type="text/plain">
<pre>array([0. , 0.5, 0.5, 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. ,
0. ])</pre>
<pre>array([4.90909347e-91, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 1.42857143e-01,
1.42857143e-01, 1.42857143e-01, 1.42857143e-01, 1.42857143e-01,
1.42857143e-01, 1.42857143e-01])</pre>
</div>
</div>
@ -16053,8 +16061,9 @@ Wie können wir aus den 7 Fröschen <strong>fair</strong> einen auswählen?</p>
</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput " data-mime-type="text/markdown">
<h1 id="Markovketten">Markovketten<a class="anchor-link" href="#Markovketten">&#182;</a></h1><p>Die Prozesse, die wir bisher gesehen haben lassen sich als <em>Markovketten</em> verstehen. Die Ketten, die wir betrachten teilen die folgenden Eigenschaften:</p>
<ul>
<li>Zeit vergeht für unsere Prozesse $X_1, X_2, \dots$ <strong>diskret</strong></li>
<li>Zeit vergeht für unsere Prozesse $X_0, X_1, X_2, \dots$ <strong>diskret</strong></li>
<li>Wir können die Übergangswahrscheinlichkeiten in einer $n \times n$ Matrix $M$ auflisten</li>
<li>Markovketten sind gedächtnislos</li>
</ul>
<p>Außerdem ist $M$ eine <em>stochastische Matrix</em> und erfüllt</p>
<ul>
@ -16062,6 +16071,85 @@ Wie können wir aus den 7 Fröschen <strong>fair</strong> einen auswählen?</p>
<li>jede Zeile summiert sich zu $1$</li>
</ul>
</div>
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<h1 id="A:-A-simple-Language-Model">A: A simple Language Model<a class="anchor-link" href="#A:-A-simple-Language-Model">&#182;</a></h1>
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<p>Mit dem <code>hp.txt</code>, generiere Harry Potter fanfiction! Ein brandneues Universum an Unsinn erwartet dich!</p>
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<p><a href="https://dominic.leafbla.de/hp_parsed.txt">https://dominic.leafbla.de/hp_parsed.txt</a>
<a href="https://dominic.leafbla.de/forschungstage">https://dominic.leafbla.de/forschungstage</a></p>
<h3 id="Code-Beispiele">Code Beispiele<a class="anchor-link" href="#Code-Beispiele">&#182;</a></h3><p><a href="https://dominic.leafbla.de/crawler.py">https://dominic.leafbla.de/crawler.py</a> (Crawlt Wiki)
<a href="https://dominic.leafbla.de/markov.py">https://dominic.leafbla.de/markov.py</a> (Rechnet mit den Daten davon)</p>
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<h1 id="B:-Monopoly">B: Monopoly<a class="anchor-link" href="#B:-Monopoly">&#182;</a></h1>
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<p>Wo sollte ich in Monopoly versuchen meine Häuser zu bauen?</p>
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<h1 id="C:-Pagerank">C: Pagerank<a class="anchor-link" href="#C:-Pagerank">&#182;</a></h1>
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<p>Crawle eine kleine Wiki, analysiere ihre Links und finde die <em>relevantesten</em> Seiten!</p>
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