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Overview
Comment: | aggiornate le slide delle lezioni 4 e 5 con i commenti |
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SHA1: | 6d9e084ded9f21cbf3e257853aeca63b6e53dd96 |
User & Date: | EnricoGiampieri 2017-03-16 15:36:18 |
Context
2017-03-16
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15:37 | inserito lo stub della seconda lezione extra su xarray check-in: 33ae3729a3 user: EnricoGiampieri tags: trunk | |
15:36 | aggiornate le slide delle lezioni 4 e 5 con i commenti check-in: 6d9e084ded user: EnricoGiampieri tags: trunk | |
15:28 | aggiunte le slide dell'esercitazione finale check-in: a5c76a0189 user: EnricoGiampieri tags: trunk | |
Changes
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<p>Provate a fare il parsing del file degli autori ed estrarre il numero di autori per paper, correlandolo con il successo del paper in questione!</p> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [1]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="o">%</span><span class="k">pwd</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> <div class="output"> <div class="output_area"> <div class="prompt output_prompt">Out[1]:</div> <div class="output_text output_subarea output_execute_result"> <pre>'/home/enrico/lavoro/DataProgrammingCourse'</pre> </div> </div> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [ ]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="o">%</span><span class="k">mkdir</span> esercitazione </pre></div> </div> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [41]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="o">%</span><span class="k">cd</span> esercitazione </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [ ]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="o">!</span>wget http://snap.stanford.edu/data/cit-HepTh-abstracts.tar.gz </pre></div> </div> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [48]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># questo comando creerà diverse cartelle con dentro i singoli file degli abstract</span> <span class="o">!</span>tar -xzf cit-HepTh-abstracts.tar.gz </pre></div> </div> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [ ]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span> </pre></div> </div> </div> </div> </div> </div> </div> </body> </html> |
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<p>Provate a fare il parsing del file degli autori ed estrarre il numero di autori per paper, correlandolo con il successo del paper in questione!</p> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [41]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="o">%</span><span class="k">mkdir</span> esercitazione <span class="o">%</span><span class="k">cd</span> esercitazione </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [ ]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="o">!</span>wget http://snap.stanford.edu/data/cit-HepTh-abstracts.tar.gz <span class="c1"># questo comando creerà diverse cartelle con dentro i singoli file degli abstract</span> <span class="o">!</span>tar -xzf cit-HepTh-abstracts.tar.gz </pre></div> </div> </div> </div> </div> </div> </div> </body> </html> |
Changes to Esercitazione finale.slides.html.
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<ul> <li>la coppia di paper citante-citato</li> <li>la data di pubblicazione di ciascun paper</li> </ul> </div> </div> </div> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> <div class="inner_cell"> <div class="text_cell_render border-box-sizing rendered_html"> <p>Passi dell'esercitazione:</p> <ol> ................................................................................ <li>fate una (o più) delle analisi possibili</li> <li>graficate i risultati e salvate la figura</li> <li>rendete la pipeline automatica con Snakemake</li> </ol> </div> </div> </div> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> <div class="inner_cell"> <div class="text_cell_render border-box-sizing rendered_html"> <p>domande possibili da rispondere:</p> <ul> ................................................................................ <li>qual è il numero di citazioni nel tempo di ciascun paper?</li> </ul> </li> </ul> </div> </div> </div> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> <div class="inner_cell"> <div class="text_cell_render border-box-sizing rendered_html"> <p>Per i più audaci: esiste la rete di citazioni dei paper teorici</p> <h2 id="http://snap.stanford.edu/data/cit-HepTh.html"><a href="http://snap.stanford.edu/data/cit-HepTh.html">http://snap.stanford.edu/data/cit-HepTh.html</a><a class="anchor-link" href="#http://snap.stanford.edu/data/cit-HepTh.html">¶</a></h2><p>che contiene anche i metadati sugli articoli, inclusi i nomi degli autori.</p> <p>Provate a fare il parsing del file degli autori ed estrarre il numero di autori per paper, correlandolo con il successo del paper in questione!</p> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [1]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="o">%</span><span class="k">pwd</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> <div class="output"> <div class="output_area"> <div class="prompt output_prompt">Out[1]:</div> <div class="output_text output_subarea output_execute_result"> <pre>'/home/enrico/lavoro/DataProgrammingCourse'</pre> </div> </div> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [ ]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="o">%</span><span class="k">mkdir</span> esercitazione </pre></div> </div> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [41]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="o">%</span><span class="k">cd</span> esercitazione </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ </pre> </div> </div> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [42]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="o">!</span>wget http://snap.stanford.edu/data/cit-HepPh.txt.gz <span class="o">!</span>gunzip -k cit-HepPh.txt.gz ................................................................................ </pre> </div> </div> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [43]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="o">!</span>wget http://snap.stanford.edu/data/cit-HepPh-dates.txt.gz <span class="o">!</span>gunzip -k cit-HepPh-dates.txt.gz ................................................................................ </pre> </div> </div> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [44]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="o">!</span>wget http://snap.stanford.edu/data/cit-HepTh-dates.txt.gz <span class="o">!</span>gunzip -k cit-HepTh-dates.txt.gz ................................................................................ </pre> </div> </div> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [45]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="o">!</span>wget http://snap.stanford.edu/data/cit-HepTh.txt.gz <span class="o">!</span>gunzip -k cit-HepTh.txt.gz ................................................................................ </pre> </div> </div> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [ ]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="o">!</span>wget http://snap.stanford.edu/data/cit-HepTh-abstracts.tar.gz </pre></div> </div> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [48]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># questo comando creerà diverse cartelle con dentro i singoli file degli abstract</span> <span class="o">!</span>tar -xzf cit-HepTh-abstracts.tar.gz </pre></div> </div> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [ ]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span> </pre></div> </div> </div> </div> </div></section></section> </div> </div> |
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<ul> <li>la coppia di paper citante-citato</li> <li>la data di pubblicazione di ciascun paper</li> </ul> </div> </div> </div></section></section><section><section> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> <div class="inner_cell"> <div class="text_cell_render border-box-sizing rendered_html"> <p>Passi dell'esercitazione:</p> <ol> ................................................................................ <li>fate una (o più) delle analisi possibili</li> <li>graficate i risultati e salvate la figura</li> <li>rendete la pipeline automatica con Snakemake</li> </ol> </div> </div> </div></section></section><section><section> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> <div class="inner_cell"> <div class="text_cell_render border-box-sizing rendered_html"> <p>domande possibili da rispondere:</p> <ul> ................................................................................ <li>qual è il numero di citazioni nel tempo di ciascun paper?</li> </ul> </li> </ul> </div> </div> </div></section></section><section><section> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> <div class="inner_cell"> <div class="text_cell_render border-box-sizing rendered_html"> <p>Per i più audaci: esiste la rete di citazioni dei paper teorici</p> <h2 id="http://snap.stanford.edu/data/cit-HepTh.html"><a href="http://snap.stanford.edu/data/cit-HepTh.html">http://snap.stanford.edu/data/cit-HepTh.html</a><a class="anchor-link" href="#http://snap.stanford.edu/data/cit-HepTh.html">¶</a></h2><p>che contiene anche i metadati sugli articoli, inclusi i nomi degli autori.</p> <p>Provate a fare il parsing del file degli autori ed estrarre il numero di autori per paper, correlandolo con il successo del paper in questione!</p> </div> </div> </div></section></section><section><section> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [41]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="o">%</span><span class="k">mkdir</span> esercitazione <span class="o">%</span><span class="k">cd</span> esercitazione </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ </pre> </div> </div> </div> </div> </div></section></section><section><section> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [42]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="o">!</span>wget http://snap.stanford.edu/data/cit-HepPh.txt.gz <span class="o">!</span>gunzip -k cit-HepPh.txt.gz ................................................................................ </pre> </div> </div> </div> </div> </div></section></section><section><section> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [43]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="o">!</span>wget http://snap.stanford.edu/data/cit-HepPh-dates.txt.gz <span class="o">!</span>gunzip -k cit-HepPh-dates.txt.gz ................................................................................ </pre> </div> </div> </div> </div> </div></section></section><section><section> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [44]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="o">!</span>wget http://snap.stanford.edu/data/cit-HepTh-dates.txt.gz <span class="o">!</span>gunzip -k cit-HepTh-dates.txt.gz ................................................................................ </pre> </div> </div> </div> </div> </div></section></section><section><section> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [45]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="o">!</span>wget http://snap.stanford.edu/data/cit-HepTh.txt.gz <span class="o">!</span>gunzip -k cit-HepTh.txt.gz ................................................................................ </pre> </div> </div> </div> </div> </div></section></section><section><section> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [ ]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="o">!</span>wget http://snap.stanford.edu/data/cit-HepTh-abstracts.tar.gz <span class="c1"># questo comando creerà diverse cartelle con dentro i singoli file degli abstract</span> <span class="o">!</span>tar -xzf cit-HepTh-abstracts.tar.gz </pre></div> </div> </div> </div> </div></section></section> </div> </div> |
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}); </script> <!-- End of mathjax configuration --></head> <body> <div tabindex="-1" id="notebook" class="border-box-sizing"> <div class="container" id="notebook-container"> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> <div class="inner_cell"> <div class="text_cell_render border-box-sizing rendered_html"> <h1 id="Precisione,-Accuratezza-e-Velocità">Precisione, Accuratezza e Velocità<a class="anchor-link" href="#Precisione,-Accuratezza-e-Velocità">¶</a></h1><h1 id="per-il-calcolo-scientifico">per il calcolo scientifico<a class="anchor-link" href="#per-il-calcolo-scientifico">¶</a></h1> </div> ................................................................................ <p>Ad esempio?</p> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [1]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="nb">print</span> <span class="p">(</span><span class="s2">"</span><span class="si">%f</span><span class="s2"> = </span><span class="si">%.32f</span><span class="s2">"</span><span class="o">%</span><span class="p">(</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">))</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"</span><span class="si">%.17f</span><span class="s2"> + </span><span class="si">%.17f</span><span class="s2"> = </span><span class="si">%.17f</span><span class="s2">"</span><span class="o">%</span><span class="p">(</span><span class="mf">0.1</span><span class="p">,</span><span class="mf">0.2</span><span class="p">,</span><span class="mf">0.1</span> <span class="o">+</span> <span class="mf">0.2</span><span class="p">))</span> <span class="nb">print</span> <span class="p">(</span><span class="mf">0.1</span><span class="p">)</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ </ul> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [2]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="mf">0.1</span> <span class="n">b</span> <span class="o">=</span> <span class="mf">0.2</span> <span class="n">c</span> <span class="o">=</span> <span class="mf">0.3</span> <span class="nb">print</span> <span class="p">((</span><span class="n">a</span> <span class="o">+</span> <span class="n">b</span><span class="p">)</span> <span class="o">+</span> <span class="n">c</span><span class="p">,</span> <span class="n">a</span> <span class="o">+</span> <span class="p">(</span><span class="n">b</span> <span class="o">+</span> <span class="n">c</span><span class="p">))</span> <span class="k">assert</span><span class="p">((</span><span class="n">a</span> <span class="o">+</span> <span class="n">b</span><span class="p">)</span> <span class="o">+</span> <span class="n">c</span> <span class="o">==</span> <span class="n">a</span> <span class="o">+</span> <span class="p">(</span><span class="n">b</span> <span class="o">+</span> <span class="n">c</span><span class="p">))</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <div class="output"> <div class="output_area"> <div class="prompt"></div> <div class="output_subarea output_stream output_stdout output_text"> <pre>0.6000000000000001 0.6 </pre> </div> </div> <div class="output_area"> <div class="prompt"></div> <div class="output_subarea output_text output_error"> <pre> <span class="ansi-red-fg">---------------------------------------------------------------------------</span> <span class="ansi-red-fg">AssertionError</span> Traceback (most recent call last) <span class="ansi-green-fg"><ipython-input-2-65fc2234e42f></span> in <span class="ansi-cyan-fg"><module></span><span class="ansi-blue-fg">()</span> <span class="ansi-green-intense-fg ansi-bold"> 3</span> c <span class="ansi-blue-fg">=</span> <span class="ansi-cyan-fg">0.3</span> <span class="ansi-green-intense-fg ansi-bold"> 4</span> print <span class="ansi-blue-fg">(</span><span class="ansi-blue-fg">(</span>a <span class="ansi-blue-fg">+</span> b<span class="ansi-blue-fg">)</span> <span class="ansi-blue-fg">+</span> c<span class="ansi-blue-fg">,</span> a <span class="ansi-blue-fg">+</span> <span class="ansi-blue-fg">(</span>b <span class="ansi-blue-fg">+</span> c<span class="ansi-blue-fg">)</span><span class="ansi-blue-fg">)</span> <span class="ansi-green-fg">----> 5</span><span class="ansi-red-fg"> </span><span class="ansi-green-fg">assert</span><span class="ansi-blue-fg">(</span><span class="ansi-blue-fg">(</span>a <span class="ansi-blue-fg">+</span> b<span class="ansi-blue-fg">)</span> <span class="ansi-blue-fg">+</span> c <span class="ansi-blue-fg">==</span> a <span class="ansi-blue-fg">+</span> <span class="ansi-blue-fg">(</span>b <span class="ansi-blue-fg">+</span> c<span class="ansi-blue-fg">)</span><span class="ansi-blue-fg">)</span> <span class="ansi-red-fg">AssertionError</span>: </pre> </div> </div> </div> </div> ................................................................................ <p>Chiunque (sfido il contrario!) utilizzerebbe la formula esattamente com'è scritta!</p> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [3]:</div> <div class="inner_cell"> <div class="input_area"> <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> <span class="nb">print</span> <span class="p">(</span><span class="mf">1.</span><span class="o">/</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">4</span><span class="p">))</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <h2 id="MA...">MA...<a class="anchor-link" href="#MA...">¶</a></h2><p>Qualcuno (non so davvero chi...decisamente me incluso) potrebbe pensare di calcolarla sviluppando il rapporto come:</p> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [4]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">isqrt</span><span class="p">(</span><span class="n">number</span><span class="p">):</span> <span class="k">assert</span> <span class="n">number</span> <span class="o">></span> <span class="mi">0</span> <span class="n">threehalfs</span> <span class="o">=</span> <span class="mf">1.5</span> <span class="n">x2</span> <span class="o">=</span> <span class="n">number</span> <span class="o">*</span> <span class="mf">0.5</span> <span class="n">y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">float32</span><span class="p">(</span><span class="n">number</span><span class="p">)</span> <span class="n">i</span> <span class="o">=</span> <span class="n">y</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">int32</span><span class="p">)</span> <span class="n">i</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">int32</span><span class="p">(</span><span class="mh">0x5f3759df</span><span class="p">)</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">int32</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">y</span> <span class="o">=</span> <span class="n">i</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span> <span class="n">y</span> <span class="o">=</span> <span class="n">y</span> <span class="o">*</span> <span class="p">(</span><span class="n">threehalfs</span> <span class="o">-</span> <span class="p">(</span><span class="n">x2</span> <span class="o">*</span> <span class="n">y</span> <span class="o">*</span> <span class="n">y</span><span class="p">))</span> <span class="k">return</span> <span class="nb">float</span><span class="p">(</span><span class="n">y</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="n">isqrt</span><span class="p">(</span><span class="mi">4</span><span class="p">))</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <div class="output"> <div class="output_area"> <div class="prompt"></div> <div class="output_subarea output_stream output_stdout output_text"> <pre>0.49915357479239103 </pre> </div> </div> </div> </div> ................................................................................ </div> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> <div class="inner_cell"> <div class="text_cell_render border-box-sizing rendered_html"> <h2 id="Un-esempio-più-comune">Un esempio più comune<a class="anchor-link" href="#Un-esempio-più-comune">¶</a></h2><p>Supponiamo di voler calcolare il valore medio di un vettore $x$. Saremo tutti d'accordo che questo sia calcolabile come:</p> <p>$E[x] = \sum_{i=0}^N \frac{x_i}{N}$</p> <p>che è certamente equivalente a</p> <p>$E[x] = \frac{1}{N}\sum_{i=0}^N x_i$</p> <p>Bene...proviamo allora</p> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [5]:</div> <div class="inner_cell"> <div class="input_area"> <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> <span class="n">N</span> <span class="o">=</span> <span class="mi">10000</span> <span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">N</span><span class="p">)</span> <span class="n">mean_1</span> <span class="o">=</span> <span class="mf">0.0</span> <span class="n">mean_2</span> <span class="o">=</span> <span class="mf">0.0</span> <span class="k">for</span> <span class="n">x_i</span> <span class="ow">in</span> <span class="n">x</span><span class="p">:</span> <span class="n">mean_1</span> <span class="o">+=</span> <span class="n">x_i</span> <span class="o">/</span> <span class="n">N</span> <span class="n">mean_2</span> <span class="o">+=</span> <span class="n">x_i</span> <span class="n">mean_2</span> <span class="o">/=</span> <span class="n">N</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"Media 1 = </span><span class="si">%.32f</span><span class="s2">"</span><span class="o">%</span><span class="p">(</span><span class="n">mean_1</span><span class="p">))</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"Media 2 = </span><span class="si">%.32f</span><span class="s2">"</span><span class="o">%</span><span class="p">(</span><span class="n">mean_2</span><span class="p">))</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> <div class="output"> <div class="output_area"> <div class="prompt"></div> <div class="output_subarea output_stream output_stdout output_text"> <pre>Media 1 = 0.50372520461176450989881914210855 Media 2 = 0.50372520461176406580960929204593 </pre> </div> </div> </div> </div> </div> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> <div class="inner_cell"> <div class="text_cell_render border-box-sizing rendered_html"> <h2 id="Cost-of-Operations">Cost of Operations<a class="anchor-link" href="#Cost-of-Operations">¶</a></h2><p><img src="./immagini/time.png" alt=""## Cost of Operations""></p> </div> </div> </div> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> <div class="inner_cell"> <div class="text_cell_render border-box-sizing rendered_html"> <h2 id="Cost-of-Functions">Cost of Functions<a class="anchor-link" href="#Cost-of-Functions">¶</a></h2><p><img src="./immagini/time2.png" alt=""## Cost of Operations""></p> </div> </div> </div> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> ................................................................................ </div> </div> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> <div class="inner_cell"> <div class="text_cell_render border-box-sizing rendered_html"> <h2 id="Ad-esempio">Ad esempio<a class="anchor-link" href="#Ad-esempio">¶</a></h2><p><img src="./immagini/vec.png" alt=""## Cost of Operations""></p> </div> </div> </div> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> ................................................................................ <p><strong>NOTA</strong>: la vettorizzazione di un loop è uno dei metodi più rapidi da implementare e con il miglior guadagno in tempi di calcolo...soprattutto nei linguaggi ad alto livello!</p> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [6]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="nb">print</span> <span class="p">(</span><span class="s1">'true'</span> <span class="k">if</span> <span class="kc">True</span> <span class="k">else</span> <span class="s1">'false'</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s1">'false'</span> <span class="k">if</span> <span class="kc">False</span> <span class="k">else</span> <span class="s1">'false'</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s1">'odd'</span> <span class="k">if</span> <span class="mi">5</span><span class="o">%</span><span class="k">2</span> else 'even') <span class="nb">print</span> <span class="p">(</span><span class="s1">'odd'</span> <span class="k">if</span> <span class="mi">4</span><span class="o">%</span><span class="k">2</span> else 'even') </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <h2 id="I-NumPy-array-e-ndarray">I NumPy array e ndarray<a class="anchor-link" href="#I-NumPy-array-e-ndarray">¶</a></h2><p>Proprio come gli std::vector<type> del C++, NumPy mette a disposizione i suoi contenitori per i vettori, chiamati np.ndarray (N-dimensional array object), contenitori <strong>veloci</strong>, <strong>flessibili</strong> per <strong>grandi data sets</strong>.</p> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [7]:</div> <div class="inner_cell"> <div class="input_area"> <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> <span class="n">a</span> <span class="o">=</span> <span class="n">np</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">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">])</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"a = "</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span> <span class="n">b</span> <span class="o">=</span> <span class="n">np</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">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">],[</span><span class="mi">5</span><span class="p">,</span><span class="mi">6</span><span class="p">,</span><span class="mi">7</span><span class="p">,</span><span class="mi">8</span><span class="p">]])</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"b = "</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ </ul> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [8]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">]</span> <span class="n">a_array</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="n">b_array</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">a</span><span class="p">))</span> <span class="nb">print</span> <span class="p">(</span><span class="n">a_array</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="n">b_array</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="n">a_array</span><span class="o">.</span><span class="n">dtype</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">a_array</span><span class="p">))</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> <div class="output"> <div class="output_area"> <div class="prompt"></div> <div class="output_subarea output_stream output_stdout output_text"> <pre>(4,) (4,) int64 4 </pre> </div> </div> </div> </div> ................................................................................ <h2 id="Creare-array">Creare array<a class="anchor-link" href="#Creare-array">¶</a></h2><p>Ci sono 3 funzioni importanti per la creazione di array e l'inizializzazione di array.</p> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [9]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="n">array_zeros</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"array_zeros = "</span><span class="p">,</span> <span class="n">array_zeros</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"array_zeros ha dimensioni : "</span><span class="p">,</span> <span class="n">array_zeros</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span> <span class="n">a_matzeros</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">2</span><span class="p">,</span><span class="mi">10</span><span class="p">))</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"a_matzeros ha dimensioni : "</span><span class="p">,</span> <span class="n">a_matzeros</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span> <span class="n">array_ones</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"aarray_ones = "</span><span class="p">,</span> <span class="n">array_ones</span><span class="p">)</span> <span class="n">a_empty</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">empty</span><span class="p">(</span><span class="mi">20</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"a_empty = "</span><span class="p">,</span> <span class="n">a_empty</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"a_empty contiene oggetti di tipo : "</span><span class="p">,</span> <span class="n">a_empty</span><span class="o">.</span><span class="n">dtype</span><span class="p">)</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <div class="output_area"> <div class="prompt"></div> <div class="output_subarea output_stream output_stdout output_text"> <pre>array_zeros = [ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.] array_zeros ha dimensioni : (10,) a_matzeros ha dimensioni : (2, 10) aarray_ones = [ 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.] a_empty = [ 6.91255410e-310 2.14713104e-316 6.91253074e-310 4.33854919e-274 6.91253076e-310 6.91253074e-310 -1.74801968e-218 6.91253076e-310 2.12335699e-316 -2.65620379e-021 6.91253076e-310 2.12340363e-316 -4.39613327e+118 6.91253076e-310 2.12345027e-316 2.02461812e+083 6.91253076e-310 2.12349691e-316 -9.23758036e-155 6.91253076e-310] a_empty contiene oggetti di tipo : float64 </pre> </div> </div> </div> </div> ................................................................................ <p>Le principali funzioni sono 2: np.arange e np.linspace</p> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [10]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">4</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="n">a</span><span class="p">)</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [11]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="n">np</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">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"a = "</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"a contiene elementi di tipo : "</span><span class="p">,</span> <span class="n">a</span><span class="o">.</span><span class="n">dtype</span><span class="p">)</span> <span class="n">a</span> <span class="o">=</span> <span class="n">np</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">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">uint32</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"a = "</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"a contiene elementi di tipo : "</span><span class="p">,</span> <span class="n">a</span><span class="o">.</span><span class="n">dtype</span><span class="p">)</span> <span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="s1">'1.21'</span><span class="p">,</span> <span class="s1">'.2'</span><span class="p">,</span> <span class="s1">'-.4'</span><span class="p">],</span> <span class="n">dtype</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">string_</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"a di stringhe = "</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"a cast 2 float = "</span><span class="p">,</span> <span class="n">a</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">))</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <div class="prompt"></div> <div class="output_subarea output_stream output_stdout output_text"> <pre>a = [ 1. 2. 3. 4.] a contiene elementi di tipo : float64 a = [1 2 3 4] a contiene elementi di tipo : uint32 a di stringhe = [b'1.21' b'.2' b'-.4'] a cast 2 float = [ 1.21 0.2 -0.4 ] </pre> </div> </div> </div> </div> ................................................................................ <p>...ma soprattutto hanno tutta una serie di operazioni <strong>già vettorizzate</strong>!!</p> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [12]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="n">np</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">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">])</span> <span class="n">b</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">5</span><span class="p">])</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"</span><span class="se">\n</span><span class="s2"> OPERAZIONI ARITMETICHE</span><span class="se">\n</span><span class="s2">"</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"a = "</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"b = "</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"a * 10 : "</span><span class="p">,</span> <span class="n">a</span> <span class="o">*</span> <span class="mi">10</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"a + 2 : "</span><span class="p">,</span> <span class="n">a</span> <span class="o">+</span> <span class="mi">2</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"a^2 : "</span><span class="p">,</span> <span class="n">a</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"</span><span class="se">\n</span><span class="s2"> OPERAZIONI TRA ARRAY</span><span class="se">\n</span><span class="s2">"</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"a * b : "</span><span class="p">,</span> <span class="n">a</span><span class="o">*</span><span class="n">b</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"a + b : "</span><span class="p">,</span> <span class="n">a</span><span class="o">+</span><span class="n">b</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"a - b : "</span><span class="p">,</span> <span class="n">a</span><span class="o">-</span><span class="n">b</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"1. / a : "</span><span class="p">,</span> <span class="mf">1.</span><span class="o">/</span><span class="n">a</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"1 / a : "</span><span class="p">,</span> <span class="mi">1</span><span class="o">/</span><span class="n">a</span><span class="p">)</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ OPERAZIONI TRA ARRAY a * b : [ 2 6 12 20] a + b : [3 5 7 9] a - b : [-1 -1 -1 -1] 1. / a : [ 1. 0.5 0.33333333 0.25 ] 1 / a : [ 1. 0.5 0.33333333 0.25 ] </pre> </div> </div> </div> </div> ................................................................................ <p>Posso anche prendere pezzi dei vettori e combinarli insieme.</p> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [13]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">20</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="n">a</span><span class="p">[</span><span class="mi">8</span><span class="p">])</span> <span class="nb">print</span> <span class="p">(</span><span class="n">a</span><span class="p">[:</span><span class="mi">8</span><span class="p">])</span> <span class="nb">print</span> <span class="p">(</span><span class="n">a</span><span class="p">[</span><span class="mi">8</span><span class="p">:</span><span class="mi">12</span><span class="p">])</span> <span class="nb">print</span> <span class="p">(</span><span class="n">a</span><span class="p">[</span><span class="mi">12</span><span class="p">:</span><span class="o">-</span><span class="mi">4</span><span class="p">])</span> <span class="nb">print</span> <span class="p">(</span><span class="n">a</span><span class="p">[</span><span class="o">-</span><span class="mi">4</span><span class="p">:])</span> <span class="k">assert</span><span class="p">(</span> <span class="n">np</span><span class="o">.</span><span class="n">all</span><span class="p">(</span><span class="n">a</span><span class="p">[</span><span class="o">-</span><span class="mi">15</span><span class="p">:</span><span class="o">-</span><span class="mi">10</span><span class="p">]</span> <span class="o">==</span> <span class="n">a</span><span class="p">[</span><span class="mi">5</span><span class="p">:</span><span class="mi">10</span><span class="p">]))</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <div class="text_cell_render border-box-sizing rendered_html"> <h2 id="ATTENZIONE!">ATTENZIONE!<a class="anchor-link" href="#ATTENZIONE!">¶</a></h2> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [14]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="n">arr_slice</span> <span class="o">=</span> <span class="n">a</span><span class="p">[</span><span class="mi">2</span><span class="p">:</span><span class="mi">5</span><span class="p">]</span> <span class="n">arr_slice</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="mi">10000</span> <span class="nb">print</span> <span class="p">(</span><span class="n">a</span><span class="p">)</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <pre><code> arr[2:5].copy()</code></pre> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [15]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="n">arr3d</span> <span class="o">=</span> <span class="n">np</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">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">]],</span> <span class="p">[[</span><span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">9</span><span class="p">],</span> <span class="p">[</span><span class="mi">10</span><span class="p">,</span> <span class="mi">11</span><span class="p">,</span> <span class="mi">12</span><span class="p">]]])</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">" a = "</span><span class="p">,</span> <span class="n">arr3d</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"primo elemento : "</span><span class="p">,</span> <span class="n">arr3d</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="nb">print</span> <span class="p">(</span><span class="s2">"prima riga : "</span><span class="p">,</span> <span class="n">arr3d</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="nb">print</span> <span class="p">(</span><span class="s2">"prima matrice : "</span><span class="p">,</span> <span class="n">arr3d</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"profondità : "</span><span class="p">,</span> <span class="n">arr3d</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <pre><code> np.mean(array)</code></pre> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [16]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="kn">import</span> <span class="nn">time</span> <span class="n">start_time</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span> <span class="n">N</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="mf">1e7</span><span class="p">)</span> <span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">N</span><span class="p">)</span> <span class="n">mean_for_1</span> <span class="o">=</span> <span class="mf">0.0</span> <span class="n">mean_for_2</span> <span class="o">=</span> <span class="mf">0.0</span> <span class="k">for</span> <span class="n">x_i</span> <span class="ow">in</span> <span class="n">x</span><span class="p">:</span> <span class="n">mean_for_1</span> <span class="o">+=</span> <span class="n">x_i</span><span class="o">/</span><span class="n">N</span> <span class="n">mean_for_2</span> <span class="o">+=</span> <span class="n">x_i</span> <span class="n">mean_for_2</span> <span class="o">/=</span> <span class="n">N</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"Mean 1 = </span><span class="si">%.32f</span><span class="s2">"</span><span class="o">%</span><span class="p">(</span><span class="n">mean_for_1</span><span class="p">))</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"Mean 2 = </span><span class="si">%.32f</span><span class="s2">"</span><span class="o">%</span><span class="p">(</span><span class="n">mean_for_2</span><span class="p">))</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"Calcolate in </span><span class="si">%.32f</span><span class="s2"> sec"</span><span class="o">%</span><span class="p">(</span><span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span><span class="o">-</span><span class="n">start_time</span><span class="p">))</span> <span class="n">start_time</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span> <span class="n">mean_vec</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"Mean vettorizzata = </span><span class="si">%.32f</span><span class="s2">"</span><span class="o">%</span><span class="p">(</span><span class="n">mean_vec</span><span class="p">))</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"Calcolata in </span><span class="si">%.32f</span><span class="s2"> sec"</span><span class="o">%</span><span class="p">(</span><span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span><span class="o">-</span><span class="n">start_time</span><span class="p">))</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <div class="output"> <div class="output_area"> <div class="prompt"></div> <div class="output_subarea output_stream output_stdout output_text"> <pre>Mean 1 = 0.50013625298338160174438371541328 Mean 2 = 0.50013625298346542358274291473208 Calcolate in 4.40506458282470703125000000000000 sec Mean vettorizzata = 0.50013625298339459135377182974480 Calcolata in 0.00512361526489257812500000000000 sec </pre> </div> </div> </div> </div> ................................................................................ <p>Numpy predispone già un'ampia gamma di generatori!</p> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [17]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">numpy</span> <span class="k">import</span> <span class="n">random</span> <span class="nb">print</span> <span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">())</span> <span class="c1"># uniform distribution</span> <span class="nb">print</span> <span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">())</span> <span class="c1"># normal distribution</span> <span class="nb">print</span> <span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">exponential</span><span class="p">())</span> <span class="c1"># exponential distribution</span> <span class="nb">print</span> <span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">))</span> <span class="c1"># random matrix</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <div class="output"> <div class="output_area"> <div class="prompt"></div> <div class="output_subarea output_stream output_stdout output_text"> <pre>0.8360009805434964 0.9891605650843475 4.412141950043221 [[ 0.84408589 0.07277303 0.57363996] [ 0.61573595 0.31707604 0.06528632]] </pre> </div> </div> </div> </div> ................................................................................ <h2 id="Una-carrellata-di-altre-funzioni-utili...">Una carrellata di altre funzioni utili...<a class="anchor-link" href="#Una-carrellata-di-altre-funzioni-utili...">¶</a></h2><p><strong>NOTA</strong> In Matlab la nomenclatura è <strong>quasi sempre</strong> la stessa, ovviamente senza l'np davanti!</p> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [19]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="n">np</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="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="mf">3.444</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="mf">4.29</span><span class="p">,</span> <span class="mf">6.98</span><span class="p">])</span> <span class="n">b</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">2</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="mf">3.44</span><span class="p">,</span> <span class="o">-</span><span class="mf">2.</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">7</span><span class="p">])</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"</span><span class="se">\n</span><span class="s2"> ALCUNE altre operazioni </span><span class="se">\n</span><span class="s2">"</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">a</span><span class="p">))</span> <span class="c1"># absolute value </span> <span class="nb">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">fabs</span><span class="p">(</span><span class="n">a</span><span class="p">))</span> <span class="c1"># absolute value </span> <span class="nb">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">a</span><span class="p">))</span> <span class="c1"># square root</span> <span class="nb">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">floor</span><span class="p">(</span><span class="n">a</span><span class="p">))</span> <span class="c1"># the largest integer value less than or equal to x</span> <span class="nb">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">ceil</span><span class="p">(</span><span class="n">a</span><span class="p">))</span> <span class="c1"># smallest integer value greater than or equal to x</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ </div> </div> <div class="output_area"> <div class="prompt"></div> <div class="output_subarea output_stream output_stderr output_text"> <pre>/usr/local/lib/python3.6/site-packages/ipykernel/__main__.py:8: RuntimeWarning: invalid value encountered in sqrt </pre> </div> </div> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [20]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="nb">print</span> <span class="p">(</span><span class="s2">"a = "</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"b = "</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"</span><span class="se">\n</span><span class="s2"> ALCUNE operazioni logiche </span><span class="se">\n</span><span class="s2">"</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">logical_and</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">))</span> <span class="c1"># AND</span> <span class="nb">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">logical_or</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">))</span> <span class="c1"># OR</span> <span class="nb">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">greater</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">))</span> <span class="c1"># ></span> <span class="nb">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">equal</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">))</span> <span class="c1"># ==</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [21]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="nb">print</span> <span class="p">(</span><span class="s2">"a = "</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"b = "</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"</span><span class="se">\n</span><span class="s2"> ALCUNE operazioni sul posizionamento </span><span class="se">\n</span><span class="s2">"</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sort</span><span class="p">(</span><span class="n">a</span><span class="p">))</span> <span class="c1"># SORTING ELEMENTS</span> <span class="nb">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">argsort</span><span class="p">(</span><span class="n">a</span><span class="p">))</span> <span class="c1"># SORTING INDICES</span> <span class="nb">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="n">a</span> <span class="o"><</span> <span class="mi">2</span><span class="p">)[</span><span class="mi">0</span><span class="p">])</span> <span class="c1"># INDICES WHERE CONDITION</span> <span class="nb">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="n">a</span> <span class="o">></span> <span class="mi">2</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="c1"># (CONDITION, IF(CONDITION), ELSE)</span> <span class="nb">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">median</span><span class="p">(</span><span class="n">a</span><span class="p">))</span> <span class="c1"># MEDIAN</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <h2 id="Basta-teoria!-E'-ora-di-sporcarsi-un-po'-le-mani-scrivendo-del-codice!">Basta teoria! E' ora di sporcarsi un po' le mani scrivendo del codice!<a class="anchor-link" href="#Basta-teoria!-E'-ora-di-sporcarsi-un-po'-le-mani-scrivendo-del-codice!">¶</a></h2><p>Da quello che abbiamo imparato dovreste essere in grado di vettorizzare facilmente il codice seguente per il calcolo del $\pi$. Controllate anche il tempo di esecuzione delle due versioni dell'algoritmo!</p> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [16]:</div> <div class="inner_cell"> <div class="input_area"> <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> <span class="kn">import</span> <span class="nn">time</span> <span class="n">N</span> <span class="o">=</span> <span class="mi">100000</span> <span class="c1"># number of MC events</span> <span class="n">N_run</span> <span class="o">=</span> <span class="mi">100</span> <span class="c1"># number of runs</span> <span class="n">Nhits</span> <span class="o">=</span> <span class="mf">0.0</span> <span class="c1"># number of points accepted</span> <span class="n">pi</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">N_run</span><span class="p">)</span> <span class="c1"># values of pi</span> <span class="n">start_time</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span> <span class="c1"># start clock </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="n">N_run</span><span class="p">):</span> <span class="n">Nhits</span> <span class="o">=</span> <span class="mf">0.0</span> ................................................................................ <span class="n">res</span> <span class="o">=</span> <span class="n">x</span><span class="o">*</span><span class="n">x</span> <span class="o">+</span> <span class="n">y</span><span class="o">*</span><span class="n">y</span> <span class="k">if</span> <span class="n">res</span> <span class="o"><</span> <span class="mi">1</span><span class="p">:</span> <span class="n">Nhits</span> <span class="o">+=</span> <span class="mf">1.0</span> <span class="n">pi</span><span class="p">[</span><span class="n">I</span><span class="p">]</span> <span class="o">+=</span> <span class="mf">4.</span> <span class="o">*</span> <span class="n">Nhits</span><span class="o">/</span><span class="n">N</span> <span class="n">run_time</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"pi with "</span><span class="p">,</span> <span class="n">N</span><span class="p">,</span> <span class="s2">" steps for "</span><span class="p">,</span> <span class="n">N_run</span><span class="p">,</span> <span class="s2">" runs is "</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">pi</span><span class="p">),</span> <span class="s2">" in "</span><span class="p">,</span> <span class="n">run_time</span><span class="o">-</span><span class="n">start_time</span><span class="p">,</span> <span class="s2">" sec"</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"Precision computation : "</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">pi</span><span class="p">)</span><span class="o">-</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">))</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> |
> > > > > > > > > > > > > | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > | | | |
11769 11770 11771 11772 11773 11774 11775 11776 11777 11778 11779 11780 11781 11782 11783 11784 11785 11786 11787 11788 11789 11790 11791 11792 11793 11794 11795 ..... 11944 11945 11946 11947 11948 11949 11950 11951 11952 11953 11954 11955 11956 11957 11958 11959 11960 11961 11962 11963 11964 ..... 12012 12013 12014 12015 12016 12017 12018 12019 12020 12021 12022 12023 12024 12025 12026 12027 12028 12029 12030 12031 12032 12033 ..... 12034 12035 12036 12037 12038 12039 12040 12041 12042 12043 12044 12045 12046 12047 12048 12049 12050 12051 12052 12053 12054 12055 12056 12057 12058 12059 12060 12061 12062 12063 ..... 12134 12135 12136 12137 12138 12139 12140 12141 12142 12143 12144 12145 12146 12147 12148 12149 12150 12151 12152 ..... 12174 12175 12176 12177 12178 12179 12180 12181 12182 12183 12184 12185 12186 12187 12188 12189 12190 12191 12192 12193 12194 12195 12196 12197 12198 12199 12200 12201 12202 12203 12204 ..... 12205 12206 12207 12208 12209 12210 12211 12212 12213 12214 12215 12216 12217 12218 12219 ..... 12231 12232 12233 12234 12235 12236 12237 12238 12239 12240 12241 12242 12243 12244 12245 12246 12247 12248 12249 12250 12251 12252 12253 12254 12255 12256 12257 12258 12259 12260 12261 12262 12263 12264 12265 12266 12267 12268 12269 12270 12271 12272 12273 12274 12275 12276 12277 12278 12279 12280 12281 12282 12283 12284 12285 12286 12287 12288 12289 12290 12291 12292 12293 12294 12295 12296 12297 12298 12299 12300 12301 12302 12303 12304 12305 12306 12307 12308 ..... 12360 12361 12362 12363 12364 12365 12366 12367 12368 12369 12370 12371 12372 12373 12374 ..... 12383 12384 12385 12386 12387 12388 12389 12390 12391 12392 12393 12394 12395 12396 12397 12398 12399 12400 12401 12402 12403 ..... 12440 12441 12442 12443 12444 12445 12446 12447 12448 12449 12450 12451 12452 12453 12454 12455 12456 12457 12458 12459 12460 12461 ..... 12491 12492 12493 12494 12495 12496 12497 12498 12499 12500 12501 12502 12503 12504 12505 12506 12507 12508 12509 12510 12511 12512 12513 12514 12515 12516 12517 12518 12519 12520 12521 12522 12523 12524 12525 12526 12527 12528 12529 12530 12531 ..... 12539 12540 12541 12542 12543 12544 12545 12546 12547 12548 12549 12550 12551 12552 12553 12554 12555 12556 12557 12558 12559 12560 12561 12562 12563 12564 12565 ..... 12567 12568 12569 12570 12571 12572 12573 12574 12575 12576 12577 12578 12579 12580 12581 12582 12583 12584 12585 12586 12587 12588 ..... 12608 12609 12610 12611 12612 12613 12614 12615 12616 12617 12618 12619 12620 12621 12622 12623 12624 12625 12626 12627 12628 12629 12630 ..... 12644 12645 12646 12647 12648 12649 12650 12651 12652 12653 12654 12655 12656 12657 12658 12659 12660 12661 12662 12663 12664 12665 12666 12667 12668 12669 ..... 12674 12675 12676 12677 12678 12679 12680 12681 12682 12683 12684 12685 12686 12687 12688 ..... 12697 12698 12699 12700 12701 12702 12703 12704 12705 12706 12707 12708 12709 12710 12711 12712 12713 12714 12715 12716 12717 12718 12719 12720 12721 12722 12723 12724 12725 12726 12727 ..... 12743 12744 12745 12746 12747 12748 12749 12750 12751 12752 12753 12754 12755 12756 12757 ..... 12764 12765 12766 12767 12768 12769 12770 12771 12772 12773 12774 12775 12776 12777 12778 12779 12780 12781 12782 12783 12784 12785 12786 12787 12788 ..... 12814 12815 12816 12817 12818 12819 12820 12821 12822 12823 12824 12825 12826 12827 12828 12829 12830 12831 12832 12833 12834 12835 ..... 12860 12861 12862 12863 12864 12865 12866 12867 12868 12869 12870 12871 12872 12873 12874 12875 12876 12877 12878 12879 12880 12881 12882 ..... 12916 12917 12918 12919 12920 12921 12922 12923 12924 12925 12926 12927 12928 12929 12930 12931 12932 12933 12934 12935 12936 12937 12938 12939 12940 12941 12942 12943 12944 12945 12946 12947 12948 12949 12950 ..... 12951 12952 12953 12954 12955 12956 12957 12958 12959 12960 12961 12962 12963 12964 12965 12966 12967 12968 12969 ..... 12977 12978 12979 12980 12981 12982 12983 12984 12985 12986 12987 12988 12989 12990 12991 12992 12993 12994 12995 12996 12997 12998 ..... 12999 13000 13001 13002 13003 13004 13005 13006 13007 13008 13009 13010 13011 13012 13013 13014 13015 13016 13017 ..... 13024 13025 13026 13027 13028 13029 13030 13031 13032 13033 13034 13035 13036 13037 13038 13039 13040 13041 13042 13043 13044 13045 13046 13047 13048 13049 13050 ..... 13067 13068 13069 13070 13071 13072 13073 13074 13075 13076 13077 13078 13079 13080 13081 13082 13083 13084 13085 13086 13087 13088 13089 13090 13091 13092 13093 13094 13095 13096 13097 13098 13099 13100 13101 13102 ..... 13122 13123 13124 13125 13126 13127 13128 13129 13130 13131 13132 13133 13134 13135 13136 13137 13138 13139 13140 13141 13142 13143 13144 13145 13146 13147 ..... 13195 13196 13197 13198 13199 13200 13201 13202 13203 13204 13205 13206 13207 13208 13209 13210 13211 13212 13213 13214 13215 13216 13217 13218 13219 13220 13221 13222 13223 13224 13225 13226 13227 13228 13229 13230 13231 13232 13233 13234 13235 13236 13237 13238 13239 13240 13241 13242 13243 13244 13245 13246 ..... 13250 13251 13252 13253 13254 13255 13256 13257 13258 13259 13260 13261 13262 13263 13264 13265 |
}); </script> <!-- End of mathjax configuration --></head> <body> <div tabindex="-1" id="notebook" class="border-box-sizing"> <div class="container" id="notebook-container"> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [12]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="kn">from</span> <span class="nn">__future__</span> <span class="kn">import</span> <span class="n">print_function</span> </pre></div> </div> </div> </div> </div> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> <div class="inner_cell"> <div class="text_cell_render border-box-sizing rendered_html"> <h1 id="Precisione,-Accuratezza-e-Velocità">Precisione, Accuratezza e Velocità<a class="anchor-link" href="#Precisione,-Accuratezza-e-Velocità">¶</a></h1><h1 id="per-il-calcolo-scientifico">per il calcolo scientifico<a class="anchor-link" href="#per-il-calcolo-scientifico">¶</a></h1> </div> ................................................................................ <p>Ad esempio?</p> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [13]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="k">print</span> <span class="p">(</span><span class="s2">"</span><span class="si">%f</span><span class="s2"> = </span><span class="si">%.32f</span><span class="s2">"</span><span class="o">%</span><span class="p">(</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">))</span> <span class="c1">#scrittura del numero 0.1 con 32 cifre decimali</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"</span><span class="si">%.17f</span><span class="s2"> + </span><span class="si">%.17f</span><span class="s2"> = </span><span class="si">%.17f</span><span class="s2">"</span><span class="o">%</span><span class="p">(</span><span class="mf">0.1</span><span class="p">,</span><span class="mf">0.2</span><span class="p">,</span><span class="mf">0.1</span> <span class="o">+</span> <span class="mf">0.2</span><span class="p">))</span> <span class="k">print</span> <span class="p">(</span><span class="mf">0.1</span><span class="p">)</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ </ul> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [14]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="mf">0.1</span> <span class="n">b</span> <span class="o">=</span> <span class="mf">0.2</span> <span class="n">c</span> <span class="o">=</span> <span class="mf">0.3</span> <span class="k">print</span> <span class="p">((</span><span class="n">a</span> <span class="o">+</span> <span class="n">b</span><span class="p">)</span> <span class="o">+</span> <span class="n">c</span><span class="p">,</span> <span class="n">a</span> <span class="o">+</span> <span class="p">(</span><span class="n">b</span> <span class="o">+</span> <span class="n">c</span><span class="p">))</span> <span class="k">assert</span><span class="p">((</span><span class="n">a</span> <span class="o">+</span> <span class="n">b</span><span class="p">)</span> <span class="o">+</span> <span class="n">c</span> <span class="o">==</span> <span class="n">a</span> <span class="o">+</span> <span class="p">(</span><span class="n">b</span> <span class="o">+</span> <span class="n">c</span><span class="p">))</span> <span class="c1">#verifica della proprietà associativa(+) considerando tutti i bit</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <div class="output"> <div class="output_area"> <div class="prompt"></div> <div class="output_subarea output_stream output_stdout output_text"> <pre>0.6 0.6 </pre> </div> </div> <div class="output_area"> <div class="prompt"></div> <div class="output_subarea output_text output_error"> <pre> <span class="ansi-red-fg">---------------------------------------------------------------------------</span> <span class="ansi-red-fg">AssertionError</span> Traceback (most recent call last) <span class="ansi-green-fg"><ipython-input-14-65fc2234e42f></span> in <span class="ansi-cyan-fg"><module></span><span class="ansi-blue-fg">()</span> <span class="ansi-green-intense-fg ansi-bold"> 3</span> c <span class="ansi-yellow-intense-fg ansi-bold">=</span> <span class="ansi-cyan-intense-fg ansi-bold">0.3</span> <span class="ansi-green-intense-fg ansi-bold"> 4</span> <span class="ansi-green-intense-fg ansi-bold">print</span> <span class="ansi-yellow-intense-fg ansi-bold">(</span><span class="ansi-yellow-intense-fg ansi-bold">(</span>a <span class="ansi-yellow-intense-fg ansi-bold">+</span> b<span class="ansi-yellow-intense-fg ansi-bold">)</span> <span class="ansi-yellow-intense-fg ansi-bold">+</span> c<span class="ansi-yellow-intense-fg ansi-bold">,</span> a <span class="ansi-yellow-intense-fg ansi-bold">+</span> <span class="ansi-yellow-intense-fg ansi-bold">(</span>b <span class="ansi-yellow-intense-fg ansi-bold">+</span> c<span class="ansi-yellow-intense-fg ansi-bold">)</span><span class="ansi-yellow-intense-fg ansi-bold">)</span> <span class="ansi-green-fg">----> 5</span><span class="ansi-red-fg"> </span><span class="ansi-green-intense-fg ansi-bold">assert</span><span class="ansi-yellow-intense-fg ansi-bold">(</span><span class="ansi-yellow-intense-fg ansi-bold">(</span>a <span class="ansi-yellow-intense-fg ansi-bold">+</span> b<span class="ansi-yellow-intense-fg ansi-bold">)</span> <span class="ansi-yellow-intense-fg ansi-bold">+</span> c <span class="ansi-yellow-intense-fg ansi-bold">==</span> a <span class="ansi-yellow-intense-fg ansi-bold">+</span> <span class="ansi-yellow-intense-fg ansi-bold">(</span>b <span class="ansi-yellow-intense-fg ansi-bold">+</span> c<span class="ansi-yellow-intense-fg ansi-bold">)</span><span class="ansi-yellow-intense-fg ansi-bold">)</span> <span class="ansi-red-fg">AssertionError</span>: </pre> </div> </div> </div> </div> ................................................................................ <p>Chiunque (sfido il contrario!) utilizzerebbe la formula esattamente com'è scritta!</p> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [15]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span> <span class="k">print</span> <span class="p">(</span><span class="mf">1.</span><span class="o">/</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">4</span><span class="p">))</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <h2 id="MA...">MA...<a class="anchor-link" href="#MA...">¶</a></h2><p>Qualcuno (non so davvero chi...decisamente me incluso) potrebbe pensare di calcolarla sviluppando il rapporto come:</p> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [16]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="k">def</span> <span class="nf">isqrt</span><span class="p">(</span><span class="n">number</span><span class="p">):</span> <span class="k">assert</span> <span class="n">number</span> <span class="o">></span> <span class="mi">0</span> <span class="n">threehalfs</span> <span class="o">=</span> <span class="mf">1.5</span> <span class="n">x2</span> <span class="o">=</span> <span class="n">number</span> <span class="o">*</span> <span class="mf">0.5</span> <span class="n">y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">float32</span><span class="p">(</span><span class="n">number</span><span class="p">)</span> <span class="c1">#conversione a float32 del numero</span> <span class="n">i</span> <span class="o">=</span> <span class="n">y</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">int32</span><span class="p">)</span> <span class="c1">#"vedi" y come una variabile int32</span> <span class="n">i</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">int32</span><span class="p">(</span><span class="mh">0x5f3759df</span><span class="p">)</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">int32</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="c1">#differenza tra numeri in bit-format</span> <span class="n">y</span> <span class="o">=</span> <span class="n">i</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span> <span class="n">y</span> <span class="o">=</span> <span class="n">y</span> <span class="o">*</span> <span class="p">(</span><span class="n">threehalfs</span> <span class="o">-</span> <span class="p">(</span><span class="n">x2</span> <span class="o">*</span> <span class="n">y</span> <span class="o">*</span> <span class="n">y</span><span class="p">))</span> <span class="k">return</span> <span class="nb">float</span><span class="p">(</span><span class="n">y</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="n">isqrt</span><span class="p">(</span><span class="mi">4</span><span class="p">))</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <div class="output"> <div class="output_area"> <div class="prompt"></div> <div class="output_subarea output_stream output_stdout output_text"> <pre>0.499153574792 </pre> </div> </div> </div> </div> ................................................................................ </div> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> <div class="inner_cell"> <div class="text_cell_render border-box-sizing rendered_html"> <h2 id="Un-esempio-più-comune">Un esempio più comune<a class="anchor-link" href="#Un-esempio-più-comune">¶</a></h2><p>Supponiamo di voler calcolare il valore medio di un vettore $x$. Saremo tutti d'accordo che questo sia calcolabile come:</p> <p>$E[x] = \sum_{i=1}^N \frac{x_i}{N}$</p> <p>che è certamente equivalente a</p> <p>$E[x] = \frac{1}{N}\sum_{i=1}^N x_i$</p> <p>Bene...proviamo allora</p> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [17]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span> <span class="n">N</span> <span class="o">=</span> <span class="mi">10000</span> <span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">N</span><span class="p">)</span> <span class="c1">#vettore contenente N numeri random estratti uniformemente in [0,1]</span> <span class="n">mean_1</span> <span class="o">=</span> <span class="mf">0.0</span> <span class="n">mean_2</span> <span class="o">=</span> <span class="mf">0.0</span> <span class="k">for</span> <span class="n">x_i</span> <span class="ow">in</span> <span class="n">x</span><span class="p">:</span> <span class="n">mean_1</span> <span class="o">+=</span> <span class="n">x_i</span> <span class="o">/</span> <span class="n">N</span> <span class="n">mean_2</span> <span class="o">+=</span> <span class="n">x_i</span> <span class="n">mean_2</span> <span class="o">/=</span> <span class="n">N</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"Media 1 = </span><span class="si">%.32f</span><span class="s2">"</span><span class="o">%</span><span class="p">(</span><span class="n">mean_1</span><span class="p">))</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"Media 2 = </span><span class="si">%.32f</span><span class="s2">"</span><span class="o">%</span><span class="p">(</span><span class="n">mean_2</span><span class="p">))</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> <div class="output"> <div class="output_area"> <div class="prompt"></div> <div class="output_subarea output_stream output_stdout output_text"> <pre>Media 1 = 0.49977160834157097202279373959755 Media 2 = 0.49977160834156963975516418940970 </pre> </div> </div> </div> </div> </div> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> <div class="inner_cell"> <div class="text_cell_render border-box-sizing rendered_html"> <h2 id="Cost-of-Operations">Cost of Operations<a class="anchor-link" href="#Cost-of-Operations">¶</a></h2><p><img src="./immagini/time.png" alt="alt text" title="## Cost of Operations"></p> </div> </div> </div> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> <div class="inner_cell"> <div class="text_cell_render border-box-sizing rendered_html"> <h2 id="Cost-of-Functions">Cost of Functions<a class="anchor-link" href="#Cost-of-Functions">¶</a></h2><p><img src="./immagini/time2.png" alt="alt text" title="## Cost of Operations"></p> </div> </div> </div> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> ................................................................................ </div> </div> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> <div class="inner_cell"> <div class="text_cell_render border-box-sizing rendered_html"> <h2 id="Ad-esempio">Ad esempio<a class="anchor-link" href="#Ad-esempio">¶</a></h2><p><img src="./immagini/vec.png" alt="alt text" title="## Cost of Operations"></p> </div> </div> </div> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> ................................................................................ <p><strong>NOTA</strong>: la vettorizzazione di un loop è uno dei metodi più rapidi da implementare e con il miglior guadagno in tempi di calcolo...soprattutto nei linguaggi ad alto livello!</p> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [18]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="k">print</span> <span class="p">(</span><span class="s1">'true'</span> <span class="k">if</span> <span class="bp">True</span> <span class="k">else</span> <span class="s1">'false'</span><span class="p">)</span> <span class="c1"># operatore ternario del C++ in Python: la sintassi è "output1 se condizione, altrimenti output2</span> <span class="k">print</span> <span class="p">(</span><span class="s1">'false'</span> <span class="k">if</span> <span class="bp">False</span> <span class="k">else</span> <span class="s1">'false'</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s1">'odd'</span> <span class="k">if</span> <span class="mi">5</span><span class="o">%</span><span class="k">2</span> else 'even') <span class="k">print</span> <span class="p">(</span><span class="s1">'odd'</span> <span class="k">if</span> <span class="mi">4</span><span class="o">%</span><span class="k">2</span> else 'even') </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <h2 id="I-NumPy-array-e-ndarray">I NumPy array e ndarray<a class="anchor-link" href="#I-NumPy-array-e-ndarray">¶</a></h2><p>Proprio come gli std::vector<type> del C++, NumPy mette a disposizione i suoi contenitori per i vettori, chiamati np.ndarray (N-dimensional array object), contenitori <strong>veloci</strong>, <strong>flessibili</strong> per <strong>grandi data sets</strong>.</p> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [19]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span> <span class="n">a</span> <span class="o">=</span> <span class="n">np</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">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">])</span> <span class="c1"># vettore 1x4</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"a = "</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span> <span class="n">b</span> <span class="o">=</span> <span class="n">np</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">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">],[</span><span class="mi">5</span><span class="p">,</span><span class="mi">6</span><span class="p">,</span><span class="mi">7</span><span class="p">,</span><span class="mi">8</span><span class="p">]])</span> <span class="c1"># matrice 2x4</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"b = "</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ </ul> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [20]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">]</span> <span class="n">a_array</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="n">b_array</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">a</span><span class="p">))</span> <span class="k">print</span> <span class="p">(</span><span class="n">a_array</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="n">b_array</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="n">a_array</span><span class="o">.</span><span class="n">dtype</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">a_array</span><span class="p">))</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> <div class="output"> <div class="output_area"> <div class="prompt"></div> <div class="output_subarea output_stream output_stdout output_text"> <pre>(4L,) (4L,) int32 4 </pre> </div> </div> </div> </div> ................................................................................ <h2 id="Creare-array">Creare array<a class="anchor-link" href="#Creare-array">¶</a></h2><p>Ci sono 3 funzioni importanti per la creazione di array e l'inizializzazione di array.</p> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [21]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="n">array_zeros</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span> <span class="c1"># vettore 1x10 di zeri</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"array_zeros = "</span><span class="p">,</span> <span class="n">array_zeros</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"array_zeros ha dimensioni : "</span><span class="p">,</span> <span class="n">array_zeros</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span> <span class="n">a_matzeros</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">2</span><span class="p">,</span><span class="mi">10</span><span class="p">))</span> <span class="c1"># matrice 2x10 di zeri</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"a_matzeros ha dimensioni : "</span><span class="p">,</span> <span class="n">a_matzeros</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span> <span class="n">array_ones</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span> <span class="c1"># vettore 1x10 di uno</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"aarray_ones = "</span><span class="p">,</span> <span class="n">array_ones</span><span class="p">)</span> <span class="n">a_empty</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">empty</span><span class="p">(</span><span class="mi">20</span><span class="p">)</span> <span class="c1"># vettore 1x20 di valori "vuoti"=locazioni di memoria libere</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"a_empty = "</span><span class="p">,</span> <span class="n">a_empty</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"a_empty contiene oggetti di tipo : "</span><span class="p">,</span> <span class="n">a_empty</span><span class="o">.</span><span class="n">dtype</span><span class="p">)</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <div class="output_area"> <div class="prompt"></div> <div class="output_subarea output_stream output_stdout output_text"> <pre>array_zeros = [ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.] array_zeros ha dimensioni : (10L,) a_matzeros ha dimensioni : (2L, 10L) aarray_ones = [ 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.] a_empty = [ 2.85808557e-316 6.22522714e-322 0.00000000e+000 0.00000000e+000 1.90979621e-313 5.30276956e+180 7.70748458e-043 2.99877042e-066 3.65961324e-086 4.25757156e-096 2.64936654e+180 3.80884741e+180 8.03704417e-095 9.97328607e-143 1.47278628e+179 8.37170573e-144 6.53456787e-042 3.21430743e-057 4.46920458e-090 1.72171244e+184] a_empty contiene oggetti di tipo : float64 </pre> </div> </div> </div> </div> ................................................................................ <p>Le principali funzioni sono 2: np.arange e np.linspace</p> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [22]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span> <span class="c1"># vettore di 10 elementi con numeri crescenti da 0(default) e 10</span> <span class="k">print</span> <span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span> <span class="c1"># (valore iniziale, valore finale, step)</span> <span class="k">print</span> <span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">4</span><span class="p">)</span> <span class="c1"># (valore iniziale, valore finale, numero di punti)</span> <span class="k">print</span> <span class="p">(</span><span class="n">a</span><span class="p">)</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [23]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="n">np</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">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"a = "</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"a contiene elementi di tipo : "</span><span class="p">,</span> <span class="n">a</span><span class="o">.</span><span class="n">dtype</span><span class="p">)</span> <span class="n">a</span> <span class="o">=</span> <span class="n">np</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">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">uint32</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"a = "</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"a contiene elementi di tipo : "</span><span class="p">,</span> <span class="n">a</span><span class="o">.</span><span class="n">dtype</span><span class="p">)</span> <span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="s1">'1.21'</span><span class="p">,</span> <span class="s1">'.2'</span><span class="p">,</span> <span class="s1">'-.4'</span><span class="p">],</span> <span class="n">dtype</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">string_</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"a di stringhe = "</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"a cast 2 float = "</span><span class="p">,</span> <span class="n">a</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">))</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <div class="prompt"></div> <div class="output_subarea output_stream output_stdout output_text"> <pre>a = [ 1. 2. 3. 4.] a contiene elementi di tipo : float64 a = [1 2 3 4] a contiene elementi di tipo : uint32 a di stringhe = ['1.21' '.2' '-.4'] a cast 2 float = [ 1.21 0.2 -0.4 ] </pre> </div> </div> </div> </div> ................................................................................ <p>...ma soprattutto hanno tutta una serie di operazioni <strong>già vettorizzate</strong>!!</p> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [24]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="n">np</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">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">])</span> <span class="n">b</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">5</span><span class="p">])</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"</span><span class="se">\n</span><span class="s2"> OPERAZIONI ARITMETICHE</span><span class="se">\n</span><span class="s2">"</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"a = "</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"b = "</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"a * 10 : "</span><span class="p">,</span> <span class="n">a</span> <span class="o">*</span> <span class="mi">10</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"a + 2 : "</span><span class="p">,</span> <span class="n">a</span> <span class="o">+</span> <span class="mi">2</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"a^2 : "</span><span class="p">,</span> <span class="n">a</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"</span><span class="se">\n</span><span class="s2"> OPERAZIONI TRA ARRAY</span><span class="se">\n</span><span class="s2">"</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"a * b : "</span><span class="p">,</span> <span class="n">a</span><span class="o">*</span><span class="n">b</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"a + b : "</span><span class="p">,</span> <span class="n">a</span><span class="o">+</span><span class="n">b</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"a - b : "</span><span class="p">,</span> <span class="n">a</span><span class="o">-</span><span class="n">b</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"1. / a : "</span><span class="p">,</span> <span class="mf">1.</span><span class="o">/</span><span class="n">a</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"1 / a : "</span><span class="p">,</span> <span class="mi">1</span><span class="o">/</span><span class="n">a</span><span class="p">)</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ OPERAZIONI TRA ARRAY a * b : [ 2 6 12 20] a + b : [3 5 7 9] a - b : [-1 -1 -1 -1] 1. / a : [ 1. 0.5 0.33333333 0.25 ] 1 / a : [1 0 0 0] </pre> </div> </div> </div> </div> ................................................................................ <p>Posso anche prendere pezzi dei vettori e combinarli insieme.</p> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [162]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">20</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="n">a</span><span class="p">[</span><span class="mi">8</span><span class="p">])</span> <span class="c1"># ottavo elemento del vettore</span> <span class="k">print</span> <span class="p">(</span><span class="n">a</span><span class="p">[:</span><span class="mi">8</span><span class="p">])</span> <span class="c1"># primi 8 elementi</span> <span class="k">print</span> <span class="p">(</span><span class="n">a</span><span class="p">[</span><span class="mi">8</span><span class="p">:</span><span class="mi">12</span><span class="p">])</span> <span class="c1"># elementi compresi tra l'ottavo e il dodicesimo</span> <span class="k">print</span> <span class="p">(</span><span class="n">a</span><span class="p">[</span><span class="mi">12</span><span class="p">:</span><span class="o">-</span><span class="mi">4</span><span class="p">])</span> <span class="c1"># elementi compresi tra il 12esimo e il quart'ultimo</span> <span class="k">print</span> <span class="p">(</span><span class="n">a</span><span class="p">[</span><span class="o">-</span><span class="mi">4</span><span class="p">:])</span> <span class="c1"># elementi dal quart'ultimo e la fine</span> <span class="k">assert</span><span class="p">(</span> <span class="n">np</span><span class="o">.</span><span class="n">all</span><span class="p">(</span><span class="n">a</span><span class="p">[</span><span class="o">-</span><span class="mi">15</span><span class="p">:</span><span class="o">-</span><span class="mi">10</span><span class="p">]</span> <span class="o">==</span> <span class="n">a</span><span class="p">[</span><span class="mi">5</span><span class="p">:</span><span class="mi">10</span><span class="p">]))</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <div class="text_cell_render border-box-sizing rendered_html"> <h2 id="ATTENZIONE!">ATTENZIONE!<a class="anchor-link" href="#ATTENZIONE!">¶</a></h2> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [165]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="n">arr_slice</span> <span class="o">=</span> <span class="n">a</span><span class="p">[</span><span class="mi">2</span><span class="p">:</span><span class="mi">5</span><span class="p">]</span> <span class="c1"># pezzo del vettore a</span> <span class="n">arr_slice</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="mi">10000</span> <span class="c1"># modifica del secondo elemento del pezzo di a</span> <span class="k">print</span> <span class="p">(</span><span class="n">a</span><span class="p">)</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <pre><code> arr[2:5].copy()</code></pre> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [176]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="n">arr3d</span> <span class="o">=</span> <span class="n">np</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">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">]],</span> <span class="p">[[</span><span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">9</span><span class="p">],</span> <span class="p">[</span><span class="mi">10</span><span class="p">,</span> <span class="mi">11</span><span class="p">,</span> <span class="mi">12</span><span class="p">]]])</span> <span class="k">print</span> <span class="p">(</span><span class="s2">" a = "</span><span class="p">,</span> <span class="n">arr3d</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"primo elemento : "</span><span class="p">,</span> <span class="n">arr3d</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="k">print</span> <span class="p">(</span><span class="s2">"prima riga : "</span><span class="p">,</span> <span class="n">arr3d</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="k">print</span> <span class="p">(</span><span class="s2">"prima matrice : "</span><span class="p">,</span> <span class="n">arr3d</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"profondità : "</span><span class="p">,</span> <span class="n">arr3d</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <pre><code> np.mean(array)</code></pre> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [15]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="kn">import</span> <span class="nn">time</span> <span class="n">start_time</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span> <span class="c1"># inizia a contare il tempo</span> <span class="n">N</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="mf">1e7</span><span class="p">)</span> <span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">N</span><span class="p">)</span> <span class="n">mean_for_1</span> <span class="o">=</span> <span class="mf">0.0</span> <span class="n">mean_for_2</span> <span class="o">=</span> <span class="mf">0.0</span> <span class="k">for</span> <span class="n">x_i</span> <span class="ow">in</span> <span class="n">x</span><span class="p">:</span> <span class="n">mean_for_1</span> <span class="o">+=</span> <span class="n">x_i</span><span class="o">/</span><span class="n">N</span> <span class="n">mean_for_2</span> <span class="o">+=</span> <span class="n">x_i</span> <span class="n">mean_for_2</span> <span class="o">/=</span> <span class="n">N</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"Mean 1 = </span><span class="si">%.32f</span><span class="s2">"</span><span class="o">%</span><span class="p">(</span><span class="n">mean_for_1</span><span class="p">))</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"Mean 2 = </span><span class="si">%.32f</span><span class="s2">"</span><span class="o">%</span><span class="p">(</span><span class="n">mean_for_2</span><span class="p">))</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"Calcolate in </span><span class="si">%.32f</span><span class="s2"> sec"</span><span class="o">%</span><span class="p">(</span><span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span><span class="o">-</span><span class="n">start_time</span><span class="p">))</span> <span class="n">start_time</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span> <span class="n">mean_vec</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"Mean vettorizzata = </span><span class="si">%.32f</span><span class="s2">"</span><span class="o">%</span><span class="p">(</span><span class="n">mean_vec</span><span class="p">))</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"Calcolata in </span><span class="si">%.32f</span><span class="s2"> sec"</span><span class="o">%</span><span class="p">(</span><span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span><span class="o">-</span><span class="n">start_time</span><span class="p">))</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <div class="output"> <div class="output_area"> <div class="prompt"></div> <div class="output_subarea output_stream output_stdout output_text"> <pre>Mean 1 = 0.50003546594170067418616554277833 Mean 2 = 0.50003546594162207039602208169526 Calcolate in 33.26500010490417480468750000000000 sec Mean vettorizzata = 0.50003546594165892980043963689241 Calcolata in 0.04699993133544921875000000000000 sec </pre> </div> </div> </div> </div> ................................................................................ <p>Numpy predispone già un'ampia gamma di generatori!</p> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [193]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="kn">from</span> <span class="nn">numpy</span> <span class="kn">import</span> <span class="n">random</span> <span class="k">print</span> <span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">())</span> <span class="c1"># uniform distribution</span> <span class="k">print</span> <span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">())</span> <span class="c1"># normal distribution</span> <span class="k">print</span> <span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">exponential</span><span class="p">())</span> <span class="c1"># exponential distribution</span> <span class="k">print</span> <span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">))</span> <span class="c1"># random matrix</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <div class="output"> <div class="output_area"> <div class="prompt"></div> <div class="output_subarea output_stream output_stdout output_text"> <pre>0.0803586638819 -1.11673488584 0.466184685074 [[ 0.73152502 0.59559674 0.73434003] [ 0.18037221 0.05359538 0.28565275]] </pre> </div> </div> </div> </div> ................................................................................ <h2 id="Una-carrellata-di-altre-funzioni-utili...">Una carrellata di altre funzioni utili...<a class="anchor-link" href="#Una-carrellata-di-altre-funzioni-utili...">¶</a></h2><p><strong>NOTA</strong> In Matlab la nomenclatura è <strong>quasi sempre</strong> la stessa, ovviamente senza l'np davanti!</p> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [30]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="n">np</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="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="mf">3.444</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="mf">4.29</span><span class="p">,</span> <span class="mf">6.98</span><span class="p">])</span> <span class="n">b</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">2</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="mf">3.44</span><span class="p">,</span> <span class="o">-</span><span class="mf">2.</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">7</span><span class="p">])</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"</span><span class="se">\n</span><span class="s2"> ALCUNE altre operazioni </span><span class="se">\n</span><span class="s2">"</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">a</span><span class="p">))</span> <span class="c1"># absolute value </span> <span class="k">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">fabs</span><span class="p">(</span><span class="n">a</span><span class="p">))</span> <span class="c1"># absolute value </span> <span class="k">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">a</span><span class="p">))</span> <span class="c1"># square root</span> <span class="k">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">floor</span><span class="p">(</span><span class="n">a</span><span class="p">))</span> <span class="c1"># the largest integer value less than or equal to x</span> <span class="k">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">ceil</span><span class="p">(</span><span class="n">a</span><span class="p">))</span> <span class="c1"># smallest integer value greater than or equal to x</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ </div> </div> <div class="output_area"> <div class="prompt"></div> <div class="output_subarea output_stream output_stderr output_text"> <pre>C:\Users\NICO\Anaconda2\lib\site-packages\ipykernel\__main__.py:8: RuntimeWarning: invalid value encountered in sqrt </pre> </div> </div> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [27]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="k">print</span> <span class="p">(</span><span class="s2">"a = "</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"b = "</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"</span><span class="se">\n</span><span class="s2"> ALCUNE operazioni logiche </span><span class="se">\n</span><span class="s2">"</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">logical_and</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">))</span> <span class="c1"># AND</span> <span class="k">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">logical_or</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">))</span> <span class="c1"># OR</span> <span class="k">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">greater</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">))</span> <span class="c1"># ></span> <span class="k">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">equal</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">))</span> <span class="c1"># ==</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [29]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="k">print</span> <span class="p">(</span><span class="s2">"a = "</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"b = "</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"</span><span class="se">\n</span><span class="s2"> ALCUNE operazioni sul posizionamento </span><span class="se">\n</span><span class="s2">"</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sort</span><span class="p">(</span><span class="n">a</span><span class="p">))</span> <span class="c1"># SORTING ELEMENTS</span> <span class="k">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">argsort</span><span class="p">(</span><span class="n">a</span><span class="p">))</span> <span class="c1"># SORTING INDICES</span> <span class="k">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="n">a</span> <span class="o"><</span> <span class="mi">2</span><span class="p">)[</span><span class="mi">0</span><span class="p">])</span> <span class="c1"># INDICES WHERE CONDITION</span> <span class="k">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="n">a</span> <span class="o">></span> <span class="mi">2</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="c1"># (CONDITION, IF(CONDITION), ELSE)</span> <span class="k">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">median</span><span class="p">(</span><span class="n">a</span><span class="p">))</span> <span class="c1"># MEDIAN</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <h2 id="Basta-teoria!-E'-ora-di-sporcarsi-un-po'-le-mani-scrivendo-del-codice!">Basta teoria! E' ora di sporcarsi un po' le mani scrivendo del codice!<a class="anchor-link" href="#Basta-teoria!-E'-ora-di-sporcarsi-un-po'-le-mani-scrivendo-del-codice!">¶</a></h2><p>Da quello che abbiamo imparato dovreste essere in grado di vettorizzare facilmente il codice seguente per il calcolo del $\pi$. Controllate anche il tempo di esecuzione delle due versioni dell'algoritmo!</p> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [ ]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span> <span class="kn">import</span> <span class="nn">time</span> <span class="sd">"""</span> <span class="sd">Metropolis Algorithm</span> <span class="sd">Algoritmo per il calcolo dell'integrale di una funzione attraverso un campionamento Monte Carlo. </span> <span class="sd">In questo esempio viene utilizzato per il calcolo del valore del pi-greco. Si consideri al proposito un cerchio di</span> <span class="sd">raggio unitario (r = 1) centrato nell'origine, inscritto in un quadrato. In questo modo il quadrato avrà lato pari a 2</span> <span class="sd">e la sua area sarà uguale a 4. Andando ad estrarre in modo uniforme nell'intervallo [-1,1] una coppia di numeri (x, y),</span> <span class="sd">qualora le coordinate risultino appartenenti al cerchio verrà conteggiato un Hit. La condizione da imporre sarà quindi:</span> <span class="sd"> x^2 + y^2 < 1</span> <span class="sd"> </span> <span class="sd">Secondo la teoria dei metodi Monte Carlo, il numero di Hit rispetto al totale sarà equivalente (per un numero tendente</span> <span class="sd">all'infinito di estrazioni) al rapporto tra le aree. In questo caso quindi</span> <span class="sd"> Hit/Tot = pi/4</span> <span class="sd"> </span> <span class="sd">Volendo estrarre un risultato più robusto si consiglia di campionare il valore di pi un numero N_runs di volte, in modo</span> <span class="sd">che il corretto valore di pi sia dato dalla media della distribuzione di più campionamenti Monte Carlo.</span> <span class="sd">"""</span> </pre></div> </div> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [16]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="n">N</span> <span class="o">=</span> <span class="mi">100000</span> <span class="c1"># number of MC events</span> <span class="n">N_run</span> <span class="o">=</span> <span class="mi">100</span> <span class="c1"># number of runs</span> <span class="n">Nhits</span> <span class="o">=</span> <span class="mf">0.0</span> <span class="c1"># number of points accepted</span> <span class="n">pi</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">N_run</span><span class="p">)</span> <span class="c1"># values of pi</span> <span class="n">start_time</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span> <span class="c1"># start clock </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="n">N_run</span><span class="p">):</span> <span class="n">Nhits</span> <span class="o">=</span> <span class="mf">0.0</span> ................................................................................ <span class="n">res</span> <span class="o">=</span> <span class="n">x</span><span class="o">*</span><span class="n">x</span> <span class="o">+</span> <span class="n">y</span><span class="o">*</span><span class="n">y</span> <span class="k">if</span> <span class="n">res</span> <span class="o"><</span> <span class="mi">1</span><span class="p">:</span> <span class="n">Nhits</span> <span class="o">+=</span> <span class="mf">1.0</span> <span class="n">pi</span><span class="p">[</span><span class="n">I</span><span class="p">]</span> <span class="o">+=</span> <span class="mf">4.</span> <span class="o">*</span> <span class="n">Nhits</span><span class="o">/</span><span class="n">N</span> <span class="n">run_time</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"pi with "</span><span class="p">,</span> <span class="n">N</span><span class="p">,</span> <span class="s2">" steps for "</span><span class="p">,</span> <span class="n">N_run</span><span class="p">,</span> <span class="s2">" runs is "</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">pi</span><span class="p">),</span> <span class="s2">" in "</span><span class="p">,</span> <span class="n">run_time</span><span class="o">-</span><span class="n">start_time</span><span class="p">,</span> <span class="s2">" sec"</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"Precision computation : "</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">pi</span><span class="p">)</span><span class="o">-</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">))</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> |
Changes to Lezione 4 - Vettorizzazione.ipynb.
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{ "cells": [ { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true, "nbpresent": { "id": "dfcf1b08-a43b-482c-9bff-ef4e3352bef7" ................................................................................ "Si va bene ma cosa vuol dire?\n", "\n", "Ad esempio?" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false, "deletable": true, "editable": true, "nbpresent": { "id": "6ab53abb-7acd-4f5b-9d45-0e25d37d7f33" }, ................................................................................ "0.100000 = 0.10000000000000000555111512312578\n", "0.10000000000000001 + 0.20000000000000001 = 0.30000000000000004\n", "0.1\n" ] } ], "source": [ "print (\"%f = %.32f\"%(0.1, 0.1))\n", "print (\"%.17f + %.17f = %.17f\"%(0.1,0.2,0.1 + 0.2))\n", "\n", "print (0.1)" ] }, { "cell_type": "markdown", ................................................................................ "* division : $a/b \\neq a \\times (1/b)$\n", "* algorithms : $(a+b) \\times (a-b) \\neq a^2-b^2$\n", "* ecc." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false, "deletable": true, "editable": true, "nbpresent": { "id": "e92059d4-9755-4743-92da-155a3caaec9d" }, ................................................................................ } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.6000000000000001 0.6\n" ] }, { "ename": "AssertionError", "evalue": "", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mAssertionError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m<ipython-input-2-65fc2234e42f>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0mc\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m0.3\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0mprint\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ma\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mb\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m \u001b[0;32massert\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mc\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0ma\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mb\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;31mAssertionError\u001b[0m: " ] } ], "source": [ "a = 0.1\n", "b = 0.2\n", "c = 0.3\n", "print ((a + b) + c, a + (b + c))\n", "assert((a + b) + c == a + (b + c))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true, ................................................................................ }, "source": [ "Chiunque (sfido il contrario!) utilizzerebbe la formula esattamente com'è scritta!" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false, "deletable": true, "editable": true, "nbpresent": { "id": "d6e6e52e-4bac-492e-89f3-98221a86b91c" }, ................................................................................ "## MA...\n", "\n", "Qualcuno (non so davvero chi...decisamente me incluso) potrebbe pensare di calcolarla sviluppando il rapporto come:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false, "deletable": true, "editable": true, "nbpresent": { "id": "2f57d0cf-dbb0-433c-833a-7db5f70cebac" }, ................................................................................ } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.49915357479239103\n" ] } ], "source": [ "def isqrt(number):\n", " assert number > 0\n", " threehalfs = 1.5\n", " x2 = number * 0.5\n", " y = np.float32(number)\n", "\n", " i = y.view(np.int32)\n", " i = np.int32(0x5f3759df) - np.int32(i >> 1)\n", " y = i.view(np.float32)\n", "\n", " y = y * (threehalfs - (x2 * y * y))\n", " return float(y)\n", "\n", "print (isqrt(4))" ] ................................................................................ } }, "source": [ "## Un esempio più comune\n", "\n", "Supponiamo di voler calcolare il valore medio di un vettore $x$. Saremo tutti d'accordo che questo sia calcolabile come:\n", "\n", "$E[x] = \\sum_{i=0}^N \\frac{x_i}{N}$\n", "\n", "che è certamente equivalente a \n", "\n", "$E[x] = \\frac{1}{N}\\sum_{i=0}^N x_i$\n", "\n", "Bene...proviamo allora" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "deletable": true, "editable": true, "nbpresent": { "id": "635b05e7-dbb3-4249-adf2-e650fc01baa7" }, ................................................................................ } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Media 1 = 0.50372520461176450989881914210855\n", "Media 2 = 0.50372520461176406580960929204593\n" ] } ], "source": [ "import numpy as np\n", "N = 10000\n", "x = np.random.rand(N)\n", "mean_1 = 0.0\n", "mean_2 = 0.0\n", "for x_i in x:\n", " mean_1 += x_i / N\n", " mean_2 += x_i\n", "mean_2 /= N\n", "print (\"Media 1 = %.32f\"%(mean_1))\n", ................................................................................ "slideshow": { "slide_type": "slide" } }, "source": [ "## Cost of Operations\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true, ................................................................................ "slideshow": { "slide_type": "slide" } }, "source": [ "## Cost of Functions\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true, ................................................................................ }, "slideshow": { "slide_type": "slide" } }, "source": [ "## Ad esempio\n", "" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true, ................................................................................ "* Ogni iterazione del loop deve essere eseguita!!(*)\n", "\n", "**NOTA**: la vettorizzazione di un loop è uno dei metodi più rapidi da implementare e con il miglior guadagno in tempi di calcolo...soprattutto nei linguaggi ad alto livello!" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "deletable": true, "editable": true, "nbpresent": { "id": "ac1da7a6-1d51-4350-b103-869c18e77204" }, ................................................................................ "false\n", "odd\n", "even\n" ] } ], "source": [ "print ('true' if True else 'false')\n", "print ('false' if False else 'false')\n", "print ('odd' if 5%2 else 'even')\n", "print ('odd' if 4%2 else 'even')" ] }, { "cell_type": "markdown", ................................................................................ "## I NumPy array e ndarray\n", "\n", "Proprio come gli std::vector<type> del C++, NumPy mette a disposizione i suoi contenitori per i vettori, chiamati np.ndarray (N-dimensional array object), contenitori **veloci**, **flessibili** per **grandi data sets**." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "deletable": true, "editable": true, "nbpresent": { "id": "6cbf22b1-059c-46ed-a42c-d4f758c0e953" }, ................................................................................ "b = [[1 2 3 4]\n", " [5 6 7 8]]\n" ] } ], "source": [ "import numpy as np\n", "a = np.array([1,2,3,4])\n", "print (\"a = \", a)\n", "b = np.array([[1,2,3,4],[5,6,7,8]])\n", "print (\"b = \", b)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, ................................................................................ "* array.dtype : ritorna il tipo di dato contenuto\n", "* len(array) : ritorna la dimensione delle **righe** di una matrice o più in generale la **prima** dimensione dell'ndarray.\n", "* np.array(lista) o np.array(tupla) : converte in un numpy array l'oggetto." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false, "deletable": true, "editable": true, "nbpresent": { "id": "68f36037-aebc-447f-9ed6-6756ae3175c0" }, ................................................................................ } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(4,)\n", "(4,)\n", "int64\n", "4\n" ] } ], "source": [ "a = [1,2,3,4]\n", "a_array = np.array(a)\n", ................................................................................ "## Creare array\n", "\n", "Ci sono 3 funzioni importanti per la creazione di array e l'inizializzazione di array." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false, "deletable": true, "editable": true, "nbpresent": { "id": "575117fd-1d32-4d36-b62b-610f5ed99ef1" }, ................................................................................ }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "array_zeros = [ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", "array_zeros ha dimensioni : (10,)\n", "a_matzeros ha dimensioni : (2, 10)\n", "aarray_ones = [ 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n", "a_empty = [ 6.91255410e-310 2.14713104e-316 6.91253074e-310 4.33854919e-274\n", " 6.91253076e-310 6.91253074e-310 -1.74801968e-218 6.91253076e-310\n", " 2.12335699e-316 -2.65620379e-021 6.91253076e-310 2.12340363e-316\n", " -4.39613327e+118 6.91253076e-310 2.12345027e-316 2.02461812e+083\n", " 6.91253076e-310 2.12349691e-316 -9.23758036e-155 6.91253076e-310]\n", "a_empty contiene oggetti di tipo : float64\n" ] } ], "source": [ "array_zeros = np.zeros(10)\n", "print (\"array_zeros = \", array_zeros)\n", "print (\"array_zeros ha dimensioni : \", array_zeros.shape)\n", "a_matzeros = np.zeros((2,10))\n", "print (\"a_matzeros ha dimensioni : \", a_matzeros.shape)\n", "array_ones = np.ones(10)\n", "print (\"aarray_ones = \", array_ones)\n", "a_empty = np.empty(20)\n", "print (\"a_empty = \", a_empty)\n", "print (\"a_empty contiene oggetti di tipo : \", a_empty.dtype)" ] }, { "cell_type": "markdown", "metadata": { ................................................................................ "Posso anche creare array che contengano numeri appartenenti ad un range numerico crescente o decrescente.\n", "\n", "Le principali funzioni sono 2: np.arange e np.linspace" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false, "deletable": true, "editable": true, "nbpresent": { "id": "7238ab2b-ae7b-4dea-bb79-df6b613f330d" }, ................................................................................ "[0 1 2 3 4 5 6 7 8 9]\n", "[1 3 5 7 9]\n", "[ 0. 0.66666667 1.33333333 2. ]\n" ] } ], "source": [ "a = np.arange(10)\n", "print (a)\n", "a = np.arange(1, 10, 2)\n", "print (a)\n", "a = np.linspace(0, 2, 4)\n", "print (a)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false, "deletable": true, "editable": true, "nbpresent": { "id": "8996df45-220a-4a74-8254-4a6e9082e7b4" }, ................................................................................ "name": "stdout", "output_type": "stream", "text": [ "a = [ 1. 2. 3. 4.]\n", "a contiene elementi di tipo : float64\n", "a = [1 2 3 4]\n", "a contiene elementi di tipo : uint32\n", "a di stringhe = [b'1.21' b'.2' b'-.4']\n", "a cast 2 float = [ 1.21 0.2 -0.4 ]\n" ] } ], "source": [ "a = np.array([1,2,3,4], dtype=np.float64)\n", "print (\"a = \", a)\n", ................................................................................ "I NumPy array non sono solo belli da vedersi ma ci tolgono anche tanti pensieri sul calcolo numerico e algebrico...\n", "\n", "...ma soprattutto hanno tutta una serie di operazioni **già vettorizzate**!!" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false, "deletable": true, "editable": true, "nbpresent": { "id": "177728b4-06e1-4d59-9ad4-058a334e9775" }, ................................................................................ "\n", " OPERAZIONI TRA ARRAY\n", "\n", "a * b : [ 2 6 12 20]\n", "a + b : [3 5 7 9]\n", "a - b : [-1 -1 -1 -1]\n", "1. / a : [ 1. 0.5 0.33333333 0.25 ]\n", "1 / a : [ 1. 0.5 0.33333333 0.25 ]\n" ] } ], "source": [ "a = np.array([1,2,3,4])\n", "b = np.array([2,3,4,5])\n", "print (\"\\n OPERAZIONI ARITMETICHE\\n\")\n", ................................................................................ }, "source": [ "Posso anche prendere pezzi dei vettori e combinarli insieme." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false, "deletable": true, "editable": true, "nbpresent": { "id": "183db7a5-f898-4085-a130-2ac7465a1bf0" }, ................................................................................ "[16 17 18 19]\n" ] } ], "source": [ "a = np.arange(20)\n", "print (a)\n", "print (a[8])\n", "print (a[:8])\n", "print (a[8:12])\n", "print (a[12:-4])\n", "print (a[-4:])\n", "assert( np.all(a[-15:-10] == a[5:10]))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true, ................................................................................ }, "source": [ "## ATTENZIONE!" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false, "deletable": true, "editable": true, "nbpresent": { "id": "e004ef40-362e-4b6d-9f3c-2826e6b41675" }, ................................................................................ "[ 0 1 2 10000 4 5 6 7 8 9]\n" ] } ], "source": [ "a = np.arange(10)\n", "print (a)\n", "arr_slice = a[2:5]\n", "arr_slice[1] = 10000\n", "print (a)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, ................................................................................ "Quando volete **copiare** una porzione di un array senza che le modifiche si ripercuotano sull'array originale dovete usare il comando appropriato...che con grande fantasia sarà\n", "\n", " arr[2:5].copy()" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false, "deletable": true, "editable": true, "nbpresent": { "id": "d50d09f6-0c49-4de9-9a81-25834375c865" }, ................................................................................ "NumPy mette a disposizione una sua versione vettorizzata del calcolo della media di un vettore\n", "\n", " np.mean(array)\n" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false, "deletable": true, "editable": true, "nbpresent": { "id": "73422ad3-02b5-4013-947f-326eae035105" }, ................................................................................ } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Mean 1 = 0.50013625298338160174438371541328\n", "Mean 2 = 0.50013625298346542358274291473208\n", "Calcolate in 4.40506458282470703125000000000000 sec\n", "Mean vettorizzata = 0.50013625298339459135377182974480\n", "Calcolata in 0.00512361526489257812500000000000 sec\n" ] } ], "source": [ "import time\n", "start_time = time.time()\n", "N = int(1e7)\n", "x = np.random.rand(N)\n", "mean_for_1 = 0.0\n", "mean_for_2 = 0.0\n", "for x_i in x:\n", " mean_for_1 += x_i/N\n", " mean_for_2 += x_i\n", ................................................................................ "Una classe di funzioni molto importante per la programmazione è la generazione di numeri random.\n", "\n", "Numpy predispone già un'ampia gamma di generatori!" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false, "deletable": true, "editable": true, "nbpresent": { "id": "c47b0755-85fb-4121-b2cd-d616f8d97fd5" }, ................................................................................ } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.8360009805434964\n", "0.9891605650843475\n", "4.412141950043221\n", "[[ 0.84408589 0.07277303 0.57363996]\n", " [ 0.61573595 0.31707604 0.06528632]]\n" ] } ], "source": [ "from numpy import random\n", "print (random.rand()) # uniform distribution\n", "print (random.randn()) # normal distribution\n", ................................................................................ "## Una carrellata di altre funzioni utili...\n", "\n", "**NOTA** In Matlab la nomenclatura è **quasi sempre** la stessa, ovviamente senza l'np davanti!" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false, "deletable": true, "editable": true, "nbpresent": { "id": "a0cd31f2-223a-4514-bbce-6259d0229faf" }, ................................................................................ "[ 1. -2. 4. -2. 5. 7.]\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/usr/local/lib/python3.6/site-packages/ipykernel/__main__.py:8: RuntimeWarning: invalid value encountered in sqrt\n" ] } ], "source": [ "a = np.array([1, -2, 3.444, -2, 4.29, 6.98])\n", "b = np.array([2, -2, 3.44, -2., 5, 7])\n", "\n", ................................................................................ "print (np.sqrt(a)) # square root\n", "print (np.floor(a)) # the largest integer value less than or equal to x\n", "print (np.ceil(a)) # smallest integer value greater than or equal to x" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false, "deletable": true, "editable": true, "slideshow": { "slide_type": "slide" } ................................................................................ "print (np.logical_or(a, b)) # OR\n", "print (np.greater(a, b)) # >\n", "print (np.equal(a, b)) # ==" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false, "deletable": true, "editable": true, "slideshow": { "slide_type": "slide" } ................................................................................ }, "source": [ "## Basta teoria! E' ora di sporcarsi un po' le mani scrivendo del codice!\n", "\n", "Da quello che abbiamo imparato dovreste essere in grado di vettorizzare facilmente il codice seguente per il calcolo del $\\pi$. Controllate anche il tempo di esecuzione delle due versioni dell'algoritmo!" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false, "deletable": true, "editable": true, ................................................................................ "text": [ "pi with 100000 steps for 100 runs is 3.1418768 in 48.2949998379 sec\n", "Precision computation : 0.000284146410207\n" ] } ], "source": [ "import numpy as np\n", "import time\n", "\n", "N = 100000 # number of MC events\n", "N_run = 100 # number of runs\n", "Nhits = 0.0 # number of points accepted\n", "pi = np.zeros(N_run) # values of pi\n", "\n", "start_time = time.time() # start clock \n", "for I in range(N_run):\n", ................................................................................ ] } ], "metadata": { "anaconda-cloud": {}, "celltoolbar": "Slideshow", "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.0" }, "nbpresent": { "slides": { "0003d80d-8617-4f6c-a1ba-5ed01cb56f2b": { "id": "0003d80d-8617-4f6c-a1ba-5ed01cb56f2b", "prev": "93eeb58b-fd7f-4329-823e-9c33af7a0c24", "regions": { |
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{ "cells": [ { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false, "deletable": true, "editable": true, "slideshow": { "slide_type": "skip" } }, "outputs": [], "source": [ "from __future__ import print_function" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true, "nbpresent": { "id": "dfcf1b08-a43b-482c-9bff-ef4e3352bef7" ................................................................................ "Si va bene ma cosa vuol dire?\n", "\n", "Ad esempio?" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false, "deletable": true, "editable": true, "nbpresent": { "id": "6ab53abb-7acd-4f5b-9d45-0e25d37d7f33" }, ................................................................................ "0.100000 = 0.10000000000000000555111512312578\n", "0.10000000000000001 + 0.20000000000000001 = 0.30000000000000004\n", "0.1\n" ] } ], "source": [ "print (\"%f = %.32f\"%(0.1, 0.1)) #scrittura del numero 0.1 con 32 cifre decimali\n", "print (\"%.17f + %.17f = %.17f\"%(0.1,0.2,0.1 + 0.2))\n", "\n", "print (0.1)" ] }, { "cell_type": "markdown", ................................................................................ "* division : $a/b \\neq a \\times (1/b)$\n", "* algorithms : $(a+b) \\times (a-b) \\neq a^2-b^2$\n", "* ecc." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false, "deletable": true, "editable": true, "nbpresent": { "id": "e92059d4-9755-4743-92da-155a3caaec9d" }, ................................................................................ } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.6 0.6\n" ] }, { "ename": "AssertionError", "evalue": "", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mAssertionError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m<ipython-input-14-65fc2234e42f>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0mc\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m0.3\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[1;32mprint\u001b[0m \u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ma\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0mb\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0mc\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0ma\u001b[0m \u001b[1;33m+\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mb\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0mc\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m \u001b[1;32massert\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ma\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0mb\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0mc\u001b[0m \u001b[1;33m==\u001b[0m \u001b[0ma\u001b[0m \u001b[1;33m+\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mb\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0mc\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;31mAssertionError\u001b[0m: " ] } ], "source": [ "a = 0.1\n", "b = 0.2\n", "c = 0.3\n", "print ((a + b) + c, a + (b + c))\n", "assert((a + b) + c == a + (b + c)) #verifica della proprietà associativa(+) considerando tutti i bit" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true, ................................................................................ }, "source": [ "Chiunque (sfido il contrario!) utilizzerebbe la formula esattamente com'è scritta!" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false, "deletable": true, "editable": true, "nbpresent": { "id": "d6e6e52e-4bac-492e-89f3-98221a86b91c" }, ................................................................................ "## MA...\n", "\n", "Qualcuno (non so davvero chi...decisamente me incluso) potrebbe pensare di calcolarla sviluppando il rapporto come:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false, "deletable": true, "editable": true, "nbpresent": { "id": "2f57d0cf-dbb0-433c-833a-7db5f70cebac" }, ................................................................................ } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.499153574792\n" ] } ], "source": [ "def isqrt(number):\n", " assert number > 0\n", " threehalfs = 1.5\n", " x2 = number * 0.5\n", " y = np.float32(number) #conversione a float32 del numero\n", "\n", " i = y.view(np.int32) #\"vedi\" y come una variabile int32\n", " i = np.int32(0x5f3759df) - np.int32(i >> 1) #differenza tra numeri in bit-format\n", " y = i.view(np.float32)\n", "\n", " y = y * (threehalfs - (x2 * y * y))\n", " return float(y)\n", "\n", "print (isqrt(4))" ] ................................................................................ } }, "source": [ "## Un esempio più comune\n", "\n", "Supponiamo di voler calcolare il valore medio di un vettore $x$. Saremo tutti d'accordo che questo sia calcolabile come:\n", "\n", "$E[x] = \\sum_{i=1}^N \\frac{x_i}{N}$\n", "\n", "che è certamente equivalente a \n", "\n", "$E[x] = \\frac{1}{N}\\sum_{i=1}^N x_i$\n", "\n", "Bene...proviamo allora" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false, "deletable": true, "editable": true, "nbpresent": { "id": "635b05e7-dbb3-4249-adf2-e650fc01baa7" }, ................................................................................ } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Media 1 = 0.49977160834157097202279373959755\n", "Media 2 = 0.49977160834156963975516418940970\n" ] } ], "source": [ "import numpy as np\n", "N = 10000\n", "x = np.random.rand(N) #vettore contenente N numeri random estratti uniformemente in [0,1]\n", "mean_1 = 0.0\n", "mean_2 = 0.0\n", "for x_i in x:\n", " mean_1 += x_i / N\n", " mean_2 += x_i\n", "mean_2 /= N\n", "print (\"Media 1 = %.32f\"%(mean_1))\n", ................................................................................ "slideshow": { "slide_type": "slide" } }, "source": [ "## Cost of Operations\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true, ................................................................................ "slideshow": { "slide_type": "slide" } }, "source": [ "## Cost of Functions\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true, ................................................................................ }, "slideshow": { "slide_type": "slide" } }, "source": [ "## Ad esempio\n", "" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true, ................................................................................ "* Ogni iterazione del loop deve essere eseguita!!(*)\n", "\n", "**NOTA**: la vettorizzazione di un loop è uno dei metodi più rapidi da implementare e con il miglior guadagno in tempi di calcolo...soprattutto nei linguaggi ad alto livello!" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false, "deletable": true, "editable": true, "nbpresent": { "id": "ac1da7a6-1d51-4350-b103-869c18e77204" }, ................................................................................ "false\n", "odd\n", "even\n" ] } ], "source": [ "print ('true' if True else 'false') # operatore ternario del C++ in Python: la sintassi è \"output1 se condizione, altrimenti output2\n", "print ('false' if False else 'false')\n", "print ('odd' if 5%2 else 'even')\n", "print ('odd' if 4%2 else 'even')" ] }, { "cell_type": "markdown", ................................................................................ "## I NumPy array e ndarray\n", "\n", "Proprio come gli std::vector<type> del C++, NumPy mette a disposizione i suoi contenitori per i vettori, chiamati np.ndarray (N-dimensional array object), contenitori **veloci**, **flessibili** per **grandi data sets**." ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false, "deletable": true, "editable": true, "nbpresent": { "id": "6cbf22b1-059c-46ed-a42c-d4f758c0e953" }, ................................................................................ "b = [[1 2 3 4]\n", " [5 6 7 8]]\n" ] } ], "source": [ "import numpy as np\n", "a = np.array([1,2,3,4]) # vettore 1x4\n", "print (\"a = \", a)\n", "b = np.array([[1,2,3,4],[5,6,7,8]]) # matrice 2x4\n", "print (\"b = \", b)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, ................................................................................ "* array.dtype : ritorna il tipo di dato contenuto\n", "* len(array) : ritorna la dimensione delle **righe** di una matrice o più in generale la **prima** dimensione dell'ndarray.\n", "* np.array(lista) o np.array(tupla) : converte in un numpy array l'oggetto." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false, "deletable": true, "editable": true, "nbpresent": { "id": "68f36037-aebc-447f-9ed6-6756ae3175c0" }, ................................................................................ } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(4L,)\n", "(4L,)\n", "int32\n", "4\n" ] } ], "source": [ "a = [1,2,3,4]\n", "a_array = np.array(a)\n", ................................................................................ "## Creare array\n", "\n", "Ci sono 3 funzioni importanti per la creazione di array e l'inizializzazione di array." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false, "deletable": true, "editable": true, "nbpresent": { "id": "575117fd-1d32-4d36-b62b-610f5ed99ef1" }, ................................................................................ }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "array_zeros = [ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", "array_zeros ha dimensioni : (10L,)\n", "a_matzeros ha dimensioni : (2L, 10L)\n", "aarray_ones = [ 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n", "a_empty = [ 2.85808557e-316 6.22522714e-322 0.00000000e+000 0.00000000e+000\n", " 1.90979621e-313 5.30276956e+180 7.70748458e-043 2.99877042e-066\n", " 3.65961324e-086 4.25757156e-096 2.64936654e+180 3.80884741e+180\n", " 8.03704417e-095 9.97328607e-143 1.47278628e+179 8.37170573e-144\n", " 6.53456787e-042 3.21430743e-057 4.46920458e-090 1.72171244e+184]\n", "a_empty contiene oggetti di tipo : float64\n" ] } ], "source": [ "array_zeros = np.zeros(10) # vettore 1x10 di zeri\n", "print (\"array_zeros = \", array_zeros)\n", "print (\"array_zeros ha dimensioni : \", array_zeros.shape)\n", "a_matzeros = np.zeros((2,10)) # matrice 2x10 di zeri\n", "print (\"a_matzeros ha dimensioni : \", a_matzeros.shape)\n", "array_ones = np.ones(10) # vettore 1x10 di uno\n", "print (\"aarray_ones = \", array_ones)\n", "a_empty = np.empty(20) # vettore 1x20 di valori \"vuoti\"=locazioni di memoria libere\n", "print (\"a_empty = \", a_empty)\n", "print (\"a_empty contiene oggetti di tipo : \", a_empty.dtype)" ] }, { "cell_type": "markdown", "metadata": { ................................................................................ "Posso anche creare array che contengano numeri appartenenti ad un range numerico crescente o decrescente.\n", "\n", "Le principali funzioni sono 2: np.arange e np.linspace" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false, "deletable": true, "editable": true, "nbpresent": { "id": "7238ab2b-ae7b-4dea-bb79-df6b613f330d" }, ................................................................................ "[0 1 2 3 4 5 6 7 8 9]\n", "[1 3 5 7 9]\n", "[ 0. 0.66666667 1.33333333 2. ]\n" ] } ], "source": [ "a = np.arange(10) # vettore di 10 elementi con numeri crescenti da 0(default) e 10\n", "print (a)\n", "a = np.arange(1, 10, 2) # (valore iniziale, valore finale, step)\n", "print (a)\n", "a = np.linspace(0, 2, 4) # (valore iniziale, valore finale, numero di punti)\n", "print (a)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false, "deletable": true, "editable": true, "nbpresent": { "id": "8996df45-220a-4a74-8254-4a6e9082e7b4" }, ................................................................................ "name": "stdout", "output_type": "stream", "text": [ "a = [ 1. 2. 3. 4.]\n", "a contiene elementi di tipo : float64\n", "a = [1 2 3 4]\n", "a contiene elementi di tipo : uint32\n", "a di stringhe = ['1.21' '.2' '-.4']\n", "a cast 2 float = [ 1.21 0.2 -0.4 ]\n" ] } ], "source": [ "a = np.array([1,2,3,4], dtype=np.float64)\n", "print (\"a = \", a)\n", ................................................................................ "I NumPy array non sono solo belli da vedersi ma ci tolgono anche tanti pensieri sul calcolo numerico e algebrico...\n", "\n", "...ma soprattutto hanno tutta una serie di operazioni **già vettorizzate**!!" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false, "deletable": true, "editable": true, "nbpresent": { "id": "177728b4-06e1-4d59-9ad4-058a334e9775" }, ................................................................................ "\n", " OPERAZIONI TRA ARRAY\n", "\n", "a * b : [ 2 6 12 20]\n", "a + b : [3 5 7 9]\n", "a - b : [-1 -1 -1 -1]\n", "1. / a : [ 1. 0.5 0.33333333 0.25 ]\n", "1 / a : [1 0 0 0]\n" ] } ], "source": [ "a = np.array([1,2,3,4])\n", "b = np.array([2,3,4,5])\n", "print (\"\\n OPERAZIONI ARITMETICHE\\n\")\n", ................................................................................ }, "source": [ "Posso anche prendere pezzi dei vettori e combinarli insieme." ] }, { "cell_type": "code", "execution_count": 162, "metadata": { "collapsed": false, "deletable": true, "editable": true, "nbpresent": { "id": "183db7a5-f898-4085-a130-2ac7465a1bf0" }, ................................................................................ "[16 17 18 19]\n" ] } ], "source": [ "a = np.arange(20)\n", "print (a)\n", "print (a[8]) # ottavo elemento del vettore\n", "print (a[:8]) # primi 8 elementi\n", "print (a[8:12]) # elementi compresi tra l'ottavo e il dodicesimo\n", "print (a[12:-4]) # elementi compresi tra il 12esimo e il quart'ultimo\n", "print (a[-4:]) # elementi dal quart'ultimo e la fine\n", "assert( np.all(a[-15:-10] == a[5:10])) " ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true, ................................................................................ }, "source": [ "## ATTENZIONE!" ] }, { "cell_type": "code", "execution_count": 165, "metadata": { "collapsed": false, "deletable": true, "editable": true, "nbpresent": { "id": "e004ef40-362e-4b6d-9f3c-2826e6b41675" }, ................................................................................ "[ 0 1 2 10000 4 5 6 7 8 9]\n" ] } ], "source": [ "a = np.arange(10)\n", "print (a)\n", "arr_slice = a[2:5] # pezzo del vettore a\n", "arr_slice[1] = 10000 # modifica del secondo elemento del pezzo di a\n", "print (a)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, ................................................................................ "Quando volete **copiare** una porzione di un array senza che le modifiche si ripercuotano sull'array originale dovete usare il comando appropriato...che con grande fantasia sarà\n", "\n", " arr[2:5].copy()" ] }, { "cell_type": "code", "execution_count": 176, "metadata": { "collapsed": false, "deletable": true, "editable": true, "nbpresent": { "id": "d50d09f6-0c49-4de9-9a81-25834375c865" }, ................................................................................ "NumPy mette a disposizione una sua versione vettorizzata del calcolo della media di un vettore\n", "\n", " np.mean(array)\n" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false, "deletable": true, "editable": true, "nbpresent": { "id": "73422ad3-02b5-4013-947f-326eae035105" }, ................................................................................ } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Mean 1 = 0.50003546594170067418616554277833\n", "Mean 2 = 0.50003546594162207039602208169526\n", "Calcolate in 33.26500010490417480468750000000000 sec\n", "Mean vettorizzata = 0.50003546594165892980043963689241\n", "Calcolata in 0.04699993133544921875000000000000 sec\n" ] } ], "source": [ "import time\n", "start_time = time.time() # inizia a contare il tempo\n", "N = int(1e7)\n", "x = np.random.rand(N)\n", "mean_for_1 = 0.0\n", "mean_for_2 = 0.0\n", "for x_i in x:\n", " mean_for_1 += x_i/N\n", " mean_for_2 += x_i\n", ................................................................................ "Una classe di funzioni molto importante per la programmazione è la generazione di numeri random.\n", "\n", "Numpy predispone già un'ampia gamma di generatori!" ] }, { "cell_type": "code", "execution_count": 193, "metadata": { "collapsed": false, "deletable": true, "editable": true, "nbpresent": { "id": "c47b0755-85fb-4121-b2cd-d616f8d97fd5" }, ................................................................................ } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.0803586638819\n", "-1.11673488584\n", "0.466184685074\n", "[[ 0.73152502 0.59559674 0.73434003]\n", " [ 0.18037221 0.05359538 0.28565275]]\n" ] } ], "source": [ "from numpy import random\n", "print (random.rand()) # uniform distribution\n", "print (random.randn()) # normal distribution\n", ................................................................................ "## Una carrellata di altre funzioni utili...\n", "\n", "**NOTA** In Matlab la nomenclatura è **quasi sempre** la stessa, ovviamente senza l'np davanti!" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false, "deletable": true, "editable": true, "nbpresent": { "id": "a0cd31f2-223a-4514-bbce-6259d0229faf" }, ................................................................................ "[ 1. -2. 4. -2. 5. 7.]\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "C:\\Users\\NICO\\Anaconda2\\lib\\site-packages\\ipykernel\\__main__.py:8: RuntimeWarning: invalid value encountered in sqrt\n" ] } ], "source": [ "a = np.array([1, -2, 3.444, -2, 4.29, 6.98])\n", "b = np.array([2, -2, 3.44, -2., 5, 7])\n", "\n", ................................................................................ "print (np.sqrt(a)) # square root\n", "print (np.floor(a)) # the largest integer value less than or equal to x\n", "print (np.ceil(a)) # smallest integer value greater than or equal to x" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false, "deletable": true, "editable": true, "slideshow": { "slide_type": "slide" } ................................................................................ "print (np.logical_or(a, b)) # OR\n", "print (np.greater(a, b)) # >\n", "print (np.equal(a, b)) # ==" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false, "deletable": true, "editable": true, "slideshow": { "slide_type": "slide" } ................................................................................ }, "source": [ "## Basta teoria! E' ora di sporcarsi un po' le mani scrivendo del codice!\n", "\n", "Da quello che abbiamo imparato dovreste essere in grado di vettorizzare facilmente il codice seguente per il calcolo del $\\pi$. Controllate anche il tempo di esecuzione delle due versioni dell'algoritmo!" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true, "deletable": true, "editable": true, "slideshow": { "slide_type": "slide" } }, "outputs": [], "source": [ "import numpy as np\n", "import time\n", "\n", "\"\"\"\n", "Metropolis Algorithm\n", "\n", "Algoritmo per il calcolo dell'integrale di una funzione attraverso un campionamento Monte Carlo. \n", "In questo esempio viene utilizzato per il calcolo del valore del pi-greco. Si consideri al proposito un cerchio di\n", "raggio unitario (r = 1) centrato nell'origine, inscritto in un quadrato. In questo modo il quadrato avrà lato pari a 2\n", "e la sua area sarà uguale a 4. Andando ad estrarre in modo uniforme nell'intervallo [-1,1] una coppia di numeri (x, y),\n", "qualora le coordinate risultino appartenenti al cerchio verrà conteggiato un Hit. La condizione da imporre sarà quindi:\n", "\n", " x^2 + y^2 < 1\n", " \n", "Secondo la teoria dei metodi Monte Carlo, il numero di Hit rispetto al totale sarà equivalente (per un numero tendente\n", "all'infinito di estrazioni) al rapporto tra le aree. In questo caso quindi\n", "\n", " Hit/Tot = pi/4\n", " \n", "Volendo estrarre un risultato più robusto si consiglia di campionare il valore di pi un numero N_runs di volte, in modo\n", "che il corretto valore di pi sia dato dalla media della distribuzione di più campionamenti Monte Carlo.\n", "\"\"\"" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false, "deletable": true, "editable": true, ................................................................................ "text": [ "pi with 100000 steps for 100 runs is 3.1418768 in 48.2949998379 sec\n", "Precision computation : 0.000284146410207\n" ] } ], "source": [ "N = 100000 # number of MC events\n", "N_run = 100 # number of runs\n", "Nhits = 0.0 # number of points accepted\n", "pi = np.zeros(N_run) # values of pi\n", "\n", "start_time = time.time() # start clock \n", "for I in range(N_run):\n", ................................................................................ ] } ], "metadata": { "anaconda-cloud": {}, "celltoolbar": "Slideshow", "kernelspec": { "display_name": "Python [default]", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.13" }, "nbpresent": { "slides": { "0003d80d-8617-4f6c-a1ba-5ed01cb56f2b": { "id": "0003d80d-8617-4f6c-a1ba-5ed01cb56f2b", "prev": "93eeb58b-fd7f-4329-823e-9c33af7a0c24", "regions": { |
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<p>Ad esempio?</p> </div> </div> </div></div></section></section><section><section> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [1]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="nb">print</span> <span class="p">(</span><span class="s2">"</span><span class="si">%f</span><span class="s2"> = </span><span class="si">%.32f</span><span class="s2">"</span><span class="o">%</span><span class="p">(</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">))</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"</span><span class="si">%.17f</span><span class="s2"> + </span><span class="si">%.17f</span><span class="s2"> = </span><span class="si">%.17f</span><span class="s2">"</span><span class="o">%</span><span class="p">(</span><span class="mf">0.1</span><span class="p">,</span><span class="mf">0.2</span><span class="p">,</span><span class="mf">0.1</span> <span class="o">+</span> <span class="mf">0.2</span><span class="p">))</span> <span class="nb">print</span> <span class="p">(</span><span class="mf">0.1</span><span class="p">)</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ </ul> </div> </div> </div></section></section><section><section> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [2]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="mf">0.1</span> <span class="n">b</span> <span class="o">=</span> <span class="mf">0.2</span> <span class="n">c</span> <span class="o">=</span> <span class="mf">0.3</span> <span class="nb">print</span> <span class="p">((</span><span class="n">a</span> <span class="o">+</span> <span class="n">b</span><span class="p">)</span> <span class="o">+</span> <span class="n">c</span><span class="p">,</span> <span class="n">a</span> <span class="o">+</span> <span class="p">(</span><span class="n">b</span> <span class="o">+</span> <span class="n">c</span><span class="p">))</span> <span class="k">assert</span><span class="p">((</span><span class="n">a</span> <span class="o">+</span> <span class="n">b</span><span class="p">)</span> <span class="o">+</span> <span class="n">c</span> <span class="o">==</span> <span class="n">a</span> <span class="o">+</span> <span class="p">(</span><span class="n">b</span> <span class="o">+</span> <span class="n">c</span><span class="p">))</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <div class="output"> <div class="output_area"> <div class="prompt"></div> <div class="output_subarea output_stream output_stdout output_text"> <pre>0.6000000000000001 0.6 </pre> </div> </div> <div class="output_area"> <div class="prompt"></div> <div class="output_subarea output_text output_error"> <pre> <span class="ansi-red-fg">---------------------------------------------------------------------------</span> <span class="ansi-red-fg">AssertionError</span> Traceback (most recent call last) <span class="ansi-green-fg"><ipython-input-2-65fc2234e42f></span> in <span class="ansi-cyan-fg"><module></span><span class="ansi-blue-fg">()</span> <span class="ansi-green-intense-fg ansi-bold"> 3</span> c <span class="ansi-blue-fg">=</span> <span class="ansi-cyan-fg">0.3</span> <span class="ansi-green-intense-fg ansi-bold"> 4</span> print <span class="ansi-blue-fg">(</span><span class="ansi-blue-fg">(</span>a <span class="ansi-blue-fg">+</span> b<span class="ansi-blue-fg">)</span> <span class="ansi-blue-fg">+</span> c<span class="ansi-blue-fg">,</span> a <span class="ansi-blue-fg">+</span> <span class="ansi-blue-fg">(</span>b <span class="ansi-blue-fg">+</span> c<span class="ansi-blue-fg">)</span><span class="ansi-blue-fg">)</span> <span class="ansi-green-fg">----> 5</span><span class="ansi-red-fg"> </span><span class="ansi-green-fg">assert</span><span class="ansi-blue-fg">(</span><span class="ansi-blue-fg">(</span>a <span class="ansi-blue-fg">+</span> b<span class="ansi-blue-fg">)</span> <span class="ansi-blue-fg">+</span> c <span class="ansi-blue-fg">==</span> a <span class="ansi-blue-fg">+</span> <span class="ansi-blue-fg">(</span>b <span class="ansi-blue-fg">+</span> c<span class="ansi-blue-fg">)</span><span class="ansi-blue-fg">)</span> <span class="ansi-red-fg">AssertionError</span>: </pre> </div> </div> </div> </div> ................................................................................ <p>Chiunque (sfido il contrario!) utilizzerebbe la formula esattamente com'è scritta!</p> </div> </div> </div></div></section></section><section><section> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [3]:</div> <div class="inner_cell"> <div class="input_area"> <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> <span class="nb">print</span> <span class="p">(</span><span class="mf">1.</span><span class="o">/</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">4</span><span class="p">))</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <h2 id="MA...">MA...<a class="anchor-link" href="#MA...">¶</a></h2><p>Qualcuno (non so davvero chi...decisamente me incluso) potrebbe pensare di calcolarla sviluppando il rapporto come:</p> </div> </div> </div></div></section></section><section><section> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [4]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">isqrt</span><span class="p">(</span><span class="n">number</span><span class="p">):</span> <span class="k">assert</span> <span class="n">number</span> <span class="o">></span> <span class="mi">0</span> <span class="n">threehalfs</span> <span class="o">=</span> <span class="mf">1.5</span> <span class="n">x2</span> <span class="o">=</span> <span class="n">number</span> <span class="o">*</span> <span class="mf">0.5</span> <span class="n">y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">float32</span><span class="p">(</span><span class="n">number</span><span class="p">)</span> <span class="n">i</span> <span class="o">=</span> <span class="n">y</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">int32</span><span class="p">)</span> <span class="n">i</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">int32</span><span class="p">(</span><span class="mh">0x5f3759df</span><span class="p">)</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">int32</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">y</span> <span class="o">=</span> <span class="n">i</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span> <span class="n">y</span> <span class="o">=</span> <span class="n">y</span> <span class="o">*</span> <span class="p">(</span><span class="n">threehalfs</span> <span class="o">-</span> <span class="p">(</span><span class="n">x2</span> <span class="o">*</span> <span class="n">y</span> <span class="o">*</span> <span class="n">y</span><span class="p">))</span> <span class="k">return</span> <span class="nb">float</span><span class="p">(</span><span class="n">y</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="n">isqrt</span><span class="p">(</span><span class="mi">4</span><span class="p">))</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <div class="output"> <div class="output_area"> <div class="prompt"></div> <div class="output_subarea output_stream output_stdout output_text"> <pre>0.49915357479239103 </pre> </div> </div> </div> </div> ................................................................................ </div></section></section><section><section> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> <div class="inner_cell"> <div class="text_cell_render border-box-sizing rendered_html"> <h2 id="Un-esempio-più-comune">Un esempio più comune<a class="anchor-link" href="#Un-esempio-più-comune">¶</a></h2><p>Supponiamo di voler calcolare il valore medio di un vettore $x$. Saremo tutti d'accordo che questo sia calcolabile come:</p> <p>$E[x] = \sum_{i=0}^N \frac{x_i}{N}$</p> <p>che è certamente equivalente a</p> <p>$E[x] = \frac{1}{N}\sum_{i=0}^N x_i$</p> <p>Bene...proviamo allora</p> </div> </div> </div></section></section><section><section> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [5]:</div> <div class="inner_cell"> <div class="input_area"> <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> <span class="n">N</span> <span class="o">=</span> <span class="mi">10000</span> <span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">N</span><span class="p">)</span> <span class="n">mean_1</span> <span class="o">=</span> <span class="mf">0.0</span> <span class="n">mean_2</span> <span class="o">=</span> <span class="mf">0.0</span> <span class="k">for</span> <span class="n">x_i</span> <span class="ow">in</span> <span class="n">x</span><span class="p">:</span> <span class="n">mean_1</span> <span class="o">+=</span> <span class="n">x_i</span> <span class="o">/</span> <span class="n">N</span> <span class="n">mean_2</span> <span class="o">+=</span> <span class="n">x_i</span> <span class="n">mean_2</span> <span class="o">/=</span> <span class="n">N</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"Media 1 = </span><span class="si">%.32f</span><span class="s2">"</span><span class="o">%</span><span class="p">(</span><span class="n">mean_1</span><span class="p">))</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"Media 2 = </span><span class="si">%.32f</span><span class="s2">"</span><span class="o">%</span><span class="p">(</span><span class="n">mean_2</span><span class="p">))</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> <div class="output"> <div class="output_area"> <div class="prompt"></div> <div class="output_subarea output_stream output_stdout output_text"> <pre>Media 1 = 0.50372520461176450989881914210855 Media 2 = 0.50372520461176406580960929204593 </pre> </div> </div> </div> </div> </div></section></section><section><section> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> <div class="inner_cell"> <div class="text_cell_render border-box-sizing rendered_html"> <h2 id="Cost-of-Operations">Cost of Operations<a class="anchor-link" href="#Cost-of-Operations">¶</a></h2><p><img src="./immagini/time.png" alt=""## Cost of Operations""></p> </div> </div> </div></section></section><section><section> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> <div class="inner_cell"> <div class="text_cell_render border-box-sizing rendered_html"> <h2 id="Cost-of-Functions">Cost of Functions<a class="anchor-link" href="#Cost-of-Functions">¶</a></h2><p><img src="./immagini/time2.png" alt=""## Cost of Operations""></p> </div> </div> </div></section></section><section><section> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> ................................................................................ </div> </div></div></section></section><section><section> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> <div class="inner_cell"> <div class="text_cell_render border-box-sizing rendered_html"> <h2 id="Ad-esempio">Ad esempio<a class="anchor-link" href="#Ad-esempio">¶</a></h2><p><img src="./immagini/vec.png" alt=""## Cost of Operations""></p> </div> </div> </div></section></section><section><section> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> ................................................................................ <p><strong>NOTA</strong>: la vettorizzazione di un loop è uno dei metodi più rapidi da implementare e con il miglior guadagno in tempi di calcolo...soprattutto nei linguaggi ad alto livello!</p> </div> </div> </div><div class="fragment"> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [6]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="nb">print</span> <span class="p">(</span><span class="s1">'true'</span> <span class="k">if</span> <span class="kc">True</span> <span class="k">else</span> <span class="s1">'false'</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s1">'false'</span> <span class="k">if</span> <span class="kc">False</span> <span class="k">else</span> <span class="s1">'false'</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s1">'odd'</span> <span class="k">if</span> <span class="mi">5</span><span class="o">%</span><span class="k">2</span> else 'even') <span class="nb">print</span> <span class="p">(</span><span class="s1">'odd'</span> <span class="k">if</span> <span class="mi">4</span><span class="o">%</span><span class="k">2</span> else 'even') </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <h2 id="I-NumPy-array-e-ndarray">I NumPy array e ndarray<a class="anchor-link" href="#I-NumPy-array-e-ndarray">¶</a></h2><p>Proprio come gli std::vector<type> del C++, NumPy mette a disposizione i suoi contenitori per i vettori, chiamati np.ndarray (N-dimensional array object), contenitori <strong>veloci</strong>, <strong>flessibili</strong> per <strong>grandi data sets</strong>.</p> </div> </div> </div><div class="fragment"> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [7]:</div> <div class="inner_cell"> <div class="input_area"> <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> <span class="n">a</span> <span class="o">=</span> <span class="n">np</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">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">])</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"a = "</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span> <span class="n">b</span> <span class="o">=</span> <span class="n">np</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">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">],[</span><span class="mi">5</span><span class="p">,</span><span class="mi">6</span><span class="p">,</span><span class="mi">7</span><span class="p">,</span><span class="mi">8</span><span class="p">]])</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"b = "</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ </ul> </div> </div> </div></section></section><section><section> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [8]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">]</span> <span class="n">a_array</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="n">b_array</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">a</span><span class="p">))</span> <span class="nb">print</span> <span class="p">(</span><span class="n">a_array</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="n">b_array</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="n">a_array</span><span class="o">.</span><span class="n">dtype</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">a_array</span><span class="p">))</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> <div class="output"> <div class="output_area"> <div class="prompt"></div> <div class="output_subarea output_stream output_stdout output_text"> <pre>(4,) (4,) int64 4 </pre> </div> </div> </div> </div> ................................................................................ <h2 id="Creare-array">Creare array<a class="anchor-link" href="#Creare-array">¶</a></h2><p>Ci sono 3 funzioni importanti per la creazione di array e l'inizializzazione di array.</p> </div> </div> </div><div class="fragment"> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [9]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="n">array_zeros</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"array_zeros = "</span><span class="p">,</span> <span class="n">array_zeros</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"array_zeros ha dimensioni : "</span><span class="p">,</span> <span class="n">array_zeros</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span> <span class="n">a_matzeros</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">2</span><span class="p">,</span><span class="mi">10</span><span class="p">))</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"a_matzeros ha dimensioni : "</span><span class="p">,</span> <span class="n">a_matzeros</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span> <span class="n">array_ones</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"aarray_ones = "</span><span class="p">,</span> <span class="n">array_ones</span><span class="p">)</span> <span class="n">a_empty</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">empty</span><span class="p">(</span><span class="mi">20</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"a_empty = "</span><span class="p">,</span> <span class="n">a_empty</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"a_empty contiene oggetti di tipo : "</span><span class="p">,</span> <span class="n">a_empty</span><span class="o">.</span><span class="n">dtype</span><span class="p">)</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <div class="output_area"> <div class="prompt"></div> <div class="output_subarea output_stream output_stdout output_text"> <pre>array_zeros = [ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.] array_zeros ha dimensioni : (10,) a_matzeros ha dimensioni : (2, 10) aarray_ones = [ 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.] a_empty = [ 6.91255410e-310 2.14713104e-316 6.91253074e-310 4.33854919e-274 6.91253076e-310 6.91253074e-310 -1.74801968e-218 6.91253076e-310 2.12335699e-316 -2.65620379e-021 6.91253076e-310 2.12340363e-316 -4.39613327e+118 6.91253076e-310 2.12345027e-316 2.02461812e+083 6.91253076e-310 2.12349691e-316 -9.23758036e-155 6.91253076e-310] a_empty contiene oggetti di tipo : float64 </pre> </div> </div> </div> </div> ................................................................................ <p>Le principali funzioni sono 2: np.arange e np.linspace</p> </div> </div> </div></section></section><section><section> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [10]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">4</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="n">a</span><span class="p">)</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ </div> </div> </div></section></section><section><section> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [11]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="n">np</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">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"a = "</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"a contiene elementi di tipo : "</span><span class="p">,</span> <span class="n">a</span><span class="o">.</span><span class="n">dtype</span><span class="p">)</span> <span class="n">a</span> <span class="o">=</span> <span class="n">np</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">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">uint32</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"a = "</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"a contiene elementi di tipo : "</span><span class="p">,</span> <span class="n">a</span><span class="o">.</span><span class="n">dtype</span><span class="p">)</span> <span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="s1">'1.21'</span><span class="p">,</span> <span class="s1">'.2'</span><span class="p">,</span> <span class="s1">'-.4'</span><span class="p">],</span> <span class="n">dtype</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">string_</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"a di stringhe = "</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"a cast 2 float = "</span><span class="p">,</span> <span class="n">a</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">))</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <div class="prompt"></div> <div class="output_subarea output_stream output_stdout output_text"> <pre>a = [ 1. 2. 3. 4.] a contiene elementi di tipo : float64 a = [1 2 3 4] a contiene elementi di tipo : uint32 a di stringhe = [b'1.21' b'.2' b'-.4'] a cast 2 float = [ 1.21 0.2 -0.4 ] </pre> </div> </div> </div> </div> ................................................................................ <p>...ma soprattutto hanno tutta una serie di operazioni <strong>già vettorizzate</strong>!!</p> </div> </div> </div></section></section><section><section> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [12]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="n">np</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">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">])</span> <span class="n">b</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">5</span><span class="p">])</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"</span><span class="se">\n</span><span class="s2"> OPERAZIONI ARITMETICHE</span><span class="se">\n</span><span class="s2">"</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"a = "</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"b = "</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"a * 10 : "</span><span class="p">,</span> <span class="n">a</span> <span class="o">*</span> <span class="mi">10</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"a + 2 : "</span><span class="p">,</span> <span class="n">a</span> <span class="o">+</span> <span class="mi">2</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"a^2 : "</span><span class="p">,</span> <span class="n">a</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"</span><span class="se">\n</span><span class="s2"> OPERAZIONI TRA ARRAY</span><span class="se">\n</span><span class="s2">"</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"a * b : "</span><span class="p">,</span> <span class="n">a</span><span class="o">*</span><span class="n">b</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"a + b : "</span><span class="p">,</span> <span class="n">a</span><span class="o">+</span><span class="n">b</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"a - b : "</span><span class="p">,</span> <span class="n">a</span><span class="o">-</span><span class="n">b</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"1. / a : "</span><span class="p">,</span> <span class="mf">1.</span><span class="o">/</span><span class="n">a</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"1 / a : "</span><span class="p">,</span> <span class="mi">1</span><span class="o">/</span><span class="n">a</span><span class="p">)</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ OPERAZIONI TRA ARRAY a * b : [ 2 6 12 20] a + b : [3 5 7 9] a - b : [-1 -1 -1 -1] 1. / a : [ 1. 0.5 0.33333333 0.25 ] 1 / a : [ 1. 0.5 0.33333333 0.25 ] </pre> </div> </div> </div> </div> ................................................................................ <p>Posso anche prendere pezzi dei vettori e combinarli insieme.</p> </div> </div> </div><div class="fragment"> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [13]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">20</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="n">a</span><span class="p">[</span><span class="mi">8</span><span class="p">])</span> <span class="nb">print</span> <span class="p">(</span><span class="n">a</span><span class="p">[:</span><span class="mi">8</span><span class="p">])</span> <span class="nb">print</span> <span class="p">(</span><span class="n">a</span><span class="p">[</span><span class="mi">8</span><span class="p">:</span><span class="mi">12</span><span class="p">])</span> <span class="nb">print</span> <span class="p">(</span><span class="n">a</span><span class="p">[</span><span class="mi">12</span><span class="p">:</span><span class="o">-</span><span class="mi">4</span><span class="p">])</span> <span class="nb">print</span> <span class="p">(</span><span class="n">a</span><span class="p">[</span><span class="o">-</span><span class="mi">4</span><span class="p">:])</span> <span class="k">assert</span><span class="p">(</span> <span class="n">np</span><span class="o">.</span><span class="n">all</span><span class="p">(</span><span class="n">a</span><span class="p">[</span><span class="o">-</span><span class="mi">15</span><span class="p">:</span><span class="o">-</span><span class="mi">10</span><span class="p">]</span> <span class="o">==</span> <span class="n">a</span><span class="p">[</span><span class="mi">5</span><span class="p">:</span><span class="mi">10</span><span class="p">]))</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <div class="text_cell_render border-box-sizing rendered_html"> <h2 id="ATTENZIONE!">ATTENZIONE!<a class="anchor-link" href="#ATTENZIONE!">¶</a></h2> </div> </div> </div><div class="fragment"> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [14]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="n">arr_slice</span> <span class="o">=</span> <span class="n">a</span><span class="p">[</span><span class="mi">2</span><span class="p">:</span><span class="mi">5</span><span class="p">]</span> <span class="n">arr_slice</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="mi">10000</span> <span class="nb">print</span> <span class="p">(</span><span class="n">a</span><span class="p">)</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <pre><code> arr[2:5].copy()</code></pre> </div> </div> </div></div></section></section><section><section> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [15]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="n">arr3d</span> <span class="o">=</span> <span class="n">np</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">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">]],</span> <span class="p">[[</span><span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">9</span><span class="p">],</span> <span class="p">[</span><span class="mi">10</span><span class="p">,</span> <span class="mi">11</span><span class="p">,</span> <span class="mi">12</span><span class="p">]]])</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">" a = "</span><span class="p">,</span> <span class="n">arr3d</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"primo elemento : "</span><span class="p">,</span> <span class="n">arr3d</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="nb">print</span> <span class="p">(</span><span class="s2">"prima riga : "</span><span class="p">,</span> <span class="n">arr3d</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="nb">print</span> <span class="p">(</span><span class="s2">"prima matrice : "</span><span class="p">,</span> <span class="n">arr3d</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"profondità : "</span><span class="p">,</span> <span class="n">arr3d</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <pre><code> np.mean(array)</code></pre> </div> </div> </div></section></section><section><section> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [16]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="kn">import</span> <span class="nn">time</span> <span class="n">start_time</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span> <span class="n">N</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="mf">1e7</span><span class="p">)</span> <span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">N</span><span class="p">)</span> <span class="n">mean_for_1</span> <span class="o">=</span> <span class="mf">0.0</span> <span class="n">mean_for_2</span> <span class="o">=</span> <span class="mf">0.0</span> <span class="k">for</span> <span class="n">x_i</span> <span class="ow">in</span> <span class="n">x</span><span class="p">:</span> <span class="n">mean_for_1</span> <span class="o">+=</span> <span class="n">x_i</span><span class="o">/</span><span class="n">N</span> <span class="n">mean_for_2</span> <span class="o">+=</span> <span class="n">x_i</span> <span class="n">mean_for_2</span> <span class="o">/=</span> <span class="n">N</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"Mean 1 = </span><span class="si">%.32f</span><span class="s2">"</span><span class="o">%</span><span class="p">(</span><span class="n">mean_for_1</span><span class="p">))</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"Mean 2 = </span><span class="si">%.32f</span><span class="s2">"</span><span class="o">%</span><span class="p">(</span><span class="n">mean_for_2</span><span class="p">))</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"Calcolate in </span><span class="si">%.32f</span><span class="s2"> sec"</span><span class="o">%</span><span class="p">(</span><span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span><span class="o">-</span><span class="n">start_time</span><span class="p">))</span> <span class="n">start_time</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span> <span class="n">mean_vec</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"Mean vettorizzata = </span><span class="si">%.32f</span><span class="s2">"</span><span class="o">%</span><span class="p">(</span><span class="n">mean_vec</span><span class="p">))</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"Calcolata in </span><span class="si">%.32f</span><span class="s2"> sec"</span><span class="o">%</span><span class="p">(</span><span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span><span class="o">-</span><span class="n">start_time</span><span class="p">))</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <div class="output"> <div class="output_area"> <div class="prompt"></div> <div class="output_subarea output_stream output_stdout output_text"> <pre>Mean 1 = 0.50013625298338160174438371541328 Mean 2 = 0.50013625298346542358274291473208 Calcolate in 4.40506458282470703125000000000000 sec Mean vettorizzata = 0.50013625298339459135377182974480 Calcolata in 0.00512361526489257812500000000000 sec </pre> </div> </div> </div> </div> ................................................................................ <p>Numpy predispone già un'ampia gamma di generatori!</p> </div> </div> </div><div class="fragment"> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [17]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">numpy</span> <span class="k">import</span> <span class="n">random</span> <span class="nb">print</span> <span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">())</span> <span class="c1"># uniform distribution</span> <span class="nb">print</span> <span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">())</span> <span class="c1"># normal distribution</span> <span class="nb">print</span> <span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">exponential</span><span class="p">())</span> <span class="c1"># exponential distribution</span> <span class="nb">print</span> <span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">))</span> <span class="c1"># random matrix</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <div class="output"> <div class="output_area"> <div class="prompt"></div> <div class="output_subarea output_stream output_stdout output_text"> <pre>0.8360009805434964 0.9891605650843475 4.412141950043221 [[ 0.84408589 0.07277303 0.57363996] [ 0.61573595 0.31707604 0.06528632]] </pre> </div> </div> </div> </div> ................................................................................ <h2 id="Una-carrellata-di-altre-funzioni-utili...">Una carrellata di altre funzioni utili...<a class="anchor-link" href="#Una-carrellata-di-altre-funzioni-utili...">¶</a></h2><p><strong>NOTA</strong> In Matlab la nomenclatura è <strong>quasi sempre</strong> la stessa, ovviamente senza l'np davanti!</p> </div> </div> </div><div class="fragment"> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [19]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="n">np</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="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="mf">3.444</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="mf">4.29</span><span class="p">,</span> <span class="mf">6.98</span><span class="p">])</span> <span class="n">b</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">2</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="mf">3.44</span><span class="p">,</span> <span class="o">-</span><span class="mf">2.</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">7</span><span class="p">])</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"</span><span class="se">\n</span><span class="s2"> ALCUNE altre operazioni </span><span class="se">\n</span><span class="s2">"</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">a</span><span class="p">))</span> <span class="c1"># absolute value </span> <span class="nb">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">fabs</span><span class="p">(</span><span class="n">a</span><span class="p">))</span> <span class="c1"># absolute value </span> <span class="nb">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">a</span><span class="p">))</span> <span class="c1"># square root</span> <span class="nb">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">floor</span><span class="p">(</span><span class="n">a</span><span class="p">))</span> <span class="c1"># the largest integer value less than or equal to x</span> <span class="nb">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">ceil</span><span class="p">(</span><span class="n">a</span><span class="p">))</span> <span class="c1"># smallest integer value greater than or equal to x</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ </div> </div> <div class="output_area"> <div class="prompt"></div> <div class="output_subarea output_stream output_stderr output_text"> <pre>/usr/local/lib/python3.6/site-packages/ipykernel/__main__.py:8: RuntimeWarning: invalid value encountered in sqrt </pre> </div> </div> </div> </div> </div></div></section></section><section><section> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [20]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="nb">print</span> <span class="p">(</span><span class="s2">"a = "</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"b = "</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"</span><span class="se">\n</span><span class="s2"> ALCUNE operazioni logiche </span><span class="se">\n</span><span class="s2">"</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">logical_and</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">))</span> <span class="c1"># AND</span> <span class="nb">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">logical_or</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">))</span> <span class="c1"># OR</span> <span class="nb">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">greater</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">))</span> <span class="c1"># ></span> <span class="nb">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">equal</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">))</span> <span class="c1"># ==</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ </div> </div> </div></section></section><section><section> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [21]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span></span><span class="nb">print</span> <span class="p">(</span><span class="s2">"a = "</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"b = "</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"</span><span class="se">\n</span><span class="s2"> ALCUNE operazioni sul posizionamento </span><span class="se">\n</span><span class="s2">"</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sort</span><span class="p">(</span><span class="n">a</span><span class="p">))</span> <span class="c1"># SORTING ELEMENTS</span> <span class="nb">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">argsort</span><span class="p">(</span><span class="n">a</span><span class="p">))</span> <span class="c1"># SORTING INDICES</span> <span class="nb">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="n">a</span> <span class="o"><</span> <span class="mi">2</span><span class="p">)[</span><span class="mi">0</span><span class="p">])</span> <span class="c1"># INDICES WHERE CONDITION</span> <span class="nb">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="n">a</span> <span class="o">></span> <span class="mi">2</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="c1"># (CONDITION, IF(CONDITION), ELSE)</span> <span class="nb">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">median</span><span class="p">(</span><span class="n">a</span><span class="p">))</span> <span class="c1"># MEDIAN</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <h2 id="Basta-teoria!-E'-ora-di-sporcarsi-un-po'-le-mani-scrivendo-del-codice!">Basta teoria! E' ora di sporcarsi un po' le mani scrivendo del codice!<a class="anchor-link" href="#Basta-teoria!-E'-ora-di-sporcarsi-un-po'-le-mani-scrivendo-del-codice!">¶</a></h2><p>Da quello che abbiamo imparato dovreste essere in grado di vettorizzare facilmente il codice seguente per il calcolo del $\pi$. Controllate anche il tempo di esecuzione delle due versioni dell'algoritmo!</p> </div> </div> </div></section></section><section><section> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [16]:</div> <div class="inner_cell"> <div class="input_area"> <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> <span class="kn">import</span> <span class="nn">time</span> <span class="n">N</span> <span class="o">=</span> <span class="mi">100000</span> <span class="c1"># number of MC events</span> <span class="n">N_run</span> <span class="o">=</span> <span class="mi">100</span> <span class="c1"># number of runs</span> <span class="n">Nhits</span> <span class="o">=</span> <span class="mf">0.0</span> <span class="c1"># number of points accepted</span> <span class="n">pi</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">N_run</span><span class="p">)</span> <span class="c1"># values of pi</span> <span class="n">start_time</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span> <span class="c1"># start clock </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="n">N_run</span><span class="p">):</span> <span class="n">Nhits</span> <span class="o">=</span> <span class="mf">0.0</span> ................................................................................ <span class="n">res</span> <span class="o">=</span> <span class="n">x</span><span class="o">*</span><span class="n">x</span> <span class="o">+</span> <span class="n">y</span><span class="o">*</span><span class="n">y</span> <span class="k">if</span> <span class="n">res</span> <span class="o"><</span> <span class="mi">1</span><span class="p">:</span> <span class="n">Nhits</span> <span class="o">+=</span> <span class="mf">1.0</span> <span class="n">pi</span><span class="p">[</span><span class="n">I</span><span class="p">]</span> <span class="o">+=</span> <span class="mf">4.</span> <span class="o">*</span> <span class="n">Nhits</span><span class="o">/</span><span class="n">N</span> <span class="n">run_time</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"pi with "</span><span class="p">,</span> <span class="n">N</span><span class="p">,</span> <span class="s2">" steps for "</span><span class="p">,</span> <span class="n">N_run</span><span class="p">,</span> <span class="s2">" runs is "</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">pi</span><span class="p">),</span> <span class="s2">" in "</span><span class="p">,</span> <span class="n">run_time</span><span class="o">-</span><span class="n">start_time</span><span class="p">,</span> <span class="s2">" sec"</span><span class="p">)</span> <span class="nb">print</span> <span class="p">(</span><span class="s2">"Precision computation : "</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">pi</span><span class="p">)</span><span class="o">-</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">))</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> |
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12012 12013 12014 12015 12016 12017 12018 12019 12020 12021 12022 12023 12024 12025 12026 12027 12028 12029 12030 12031 12032 ..... 12080 12081 12082 12083 12084 12085 12086 12087 12088 12089 12090 12091 12092 12093 12094 12095 12096 12097 12098 12099 12100 12101 ..... 12102 12103 12104 12105 12106 12107 12108 12109 12110 12111 12112 12113 12114 12115 12116 12117 12118 12119 12120 12121 12122 12123 12124 12125 12126 12127 12128 12129 12130 12131 ..... 12202 12203 12204 12205 12206 12207 12208 12209 12210 12211 12212 12213 12214 12215 12216 12217 12218 12219 12220 ..... 12242 12243 12244 12245 12246 12247 12248 12249 12250 12251 12252 12253 12254 12255 12256 12257 12258 12259 12260 12261 12262 12263 12264 12265 12266 12267 12268 12269 12270 12271 12272 ..... 12273 12274 12275 12276 12277 12278 12279 12280 12281 12282 12283 12284 12285 12286 12287 ..... 12299 12300 12301 12302 12303 12304 12305 12306 12307 12308 12309 12310 12311 12312 12313 12314 12315 12316 12317 12318 12319 12320 12321 12322 12323 12324 12325 12326 12327 12328 12329 12330 12331 12332 12333 12334 12335 12336 12337 12338 12339 12340 12341 12342 12343 12344 12345 12346 12347 12348 12349 12350 12351 12352 12353 12354 12355 12356 12357 12358 12359 12360 12361 12362 12363 12364 12365 12366 12367 12368 12369 12370 12371 12372 12373 12374 12375 12376 ..... 12428 12429 12430 12431 12432 12433 12434 12435 12436 12437 12438 12439 12440 12441 12442 ..... 12451 12452 12453 12454 12455 12456 12457 12458 12459 12460 12461 12462 12463 12464 12465 12466 12467 12468 12469 12470 12471 ..... 12508 12509 12510 12511 12512 12513 12514 12515 12516 12517 12518 12519 12520 12521 12522 12523 12524 12525 12526 12527 12528 12529 ..... 12559 12560 12561 12562 12563 12564 12565 12566 12567 12568 12569 12570 12571 12572 12573 12574 12575 12576 12577 12578 12579 12580 12581 12582 12583 12584 12585 12586 12587 12588 12589 12590 12591 12592 12593 12594 12595 12596 12597 12598 12599 ..... 12607 12608 12609 12610 12611 12612 12613 12614 12615 12616 12617 12618 12619 12620 12621 12622 12623 12624 12625 12626 12627 12628 12629 12630 12631 12632 12633 ..... 12635 12636 12637 12638 12639 12640 12641 12642 12643 12644 12645 12646 12647 12648 12649 12650 12651 12652 12653 12654 12655 12656 ..... 12676 12677 12678 12679 12680 12681 12682 12683 12684 12685 12686 12687 12688 12689 12690 12691 12692 12693 12694 12695 12696 12697 12698 ..... 12712 12713 12714 12715 12716 12717 12718 12719 12720 12721 12722 12723 12724 12725 12726 12727 12728 12729 12730 12731 12732 12733 12734 12735 12736 12737 ..... 12742 12743 12744 12745 12746 12747 12748 12749 12750 12751 12752 12753 12754 12755 12756 ..... 12765 12766 12767 12768 12769 12770 12771 12772 12773 12774 12775 12776 12777 12778 12779 12780 12781 12782 12783 12784 12785 12786 12787 12788 12789 12790 12791 12792 12793 12794 12795 ..... 12811 12812 12813 12814 12815 12816 12817 12818 12819 12820 12821 12822 12823 12824 12825 ..... 12832 12833 12834 12835 12836 12837 12838 12839 12840 12841 12842 12843 12844 12845 12846 12847 12848 12849 12850 12851 12852 12853 12854 12855 12856 ..... 12882 12883 12884 12885 12886 12887 12888 12889 12890 12891 12892 12893 12894 12895 12896 12897 12898 12899 12900 12901 12902 12903 ..... 12928 12929 12930 12931 12932 12933 12934 12935 12936 12937 12938 12939 12940 12941 12942 12943 12944 12945 12946 12947 12948 12949 12950 ..... 12984 12985 12986 12987 12988 12989 12990 12991 12992 12993 12994 12995 12996 12997 12998 12999 13000 13001 13002 13003 13004 13005 13006 13007 13008 13009 13010 13011 13012 13013 13014 13015 13016 13017 13018 ..... 13019 13020 13021 13022 13023 13024 13025 13026 13027 13028 13029 13030 13031 13032 13033 13034 13035 13036 13037 ..... 13045 13046 13047 13048 13049 13050 13051 13052 13053 13054 13055 13056 13057 13058 13059 13060 13061 13062 13063 13064 13065 13066 ..... 13067 13068 13069 13070 13071 13072 13073 13074 13075 13076 13077 13078 13079 13080 13081 13082 13083 13084 13085 ..... 13092 13093 13094 13095 13096 13097 13098 13099 13100 13101 13102 13103 13104 13105 13106 13107 13108 13109 13110 13111 13112 13113 13114 13115 13116 13117 13118 ..... 13135 13136 13137 13138 13139 13140 13141 13142 13143 13144 13145 13146 13147 13148 13149 13150 13151 13152 13153 13154 13155 13156 13157 13158 13159 13160 13161 13162 13163 13164 13165 13166 13167 13168 13169 13170 ..... 13190 13191 13192 13193 13194 13195 13196 13197 13198 13199 13200 13201 13202 13203 13204 13205 13206 13207 13208 13209 13210 13211 13212 13213 13214 13215 ..... 13263 13264 13265 13266 13267 13268 13269 13270 13271 13272 13273 13274 13275 13276 13277 13278 13279 13280 13281 13282 13283 13284 13285 13286 13287 13288 13289 13290 13291 13292 13293 13294 13295 13296 13297 13298 13299 13300 13301 13302 13303 13304 13305 13306 13307 13308 13309 13310 13311 13312 13313 13314 ..... 13318 13319 13320 13321 13322 13323 13324 13325 13326 13327 13328 13329 13330 13331 13332 13333 |
<p>Ad esempio?</p> </div> </div> </div></div></section></section><section><section> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [13]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="k">print</span> <span class="p">(</span><span class="s2">"</span><span class="si">%f</span><span class="s2"> = </span><span class="si">%.32f</span><span class="s2">"</span><span class="o">%</span><span class="p">(</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">))</span> <span class="c1">#scrittura del numero 0.1 con 32 cifre decimali</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"</span><span class="si">%.17f</span><span class="s2"> + </span><span class="si">%.17f</span><span class="s2"> = </span><span class="si">%.17f</span><span class="s2">"</span><span class="o">%</span><span class="p">(</span><span class="mf">0.1</span><span class="p">,</span><span class="mf">0.2</span><span class="p">,</span><span class="mf">0.1</span> <span class="o">+</span> <span class="mf">0.2</span><span class="p">))</span> <span class="k">print</span> <span class="p">(</span><span class="mf">0.1</span><span class="p">)</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ </ul> </div> </div> </div></section></section><section><section> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [14]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="mf">0.1</span> <span class="n">b</span> <span class="o">=</span> <span class="mf">0.2</span> <span class="n">c</span> <span class="o">=</span> <span class="mf">0.3</span> <span class="k">print</span> <span class="p">((</span><span class="n">a</span> <span class="o">+</span> <span class="n">b</span><span class="p">)</span> <span class="o">+</span> <span class="n">c</span><span class="p">,</span> <span class="n">a</span> <span class="o">+</span> <span class="p">(</span><span class="n">b</span> <span class="o">+</span> <span class="n">c</span><span class="p">))</span> <span class="k">assert</span><span class="p">((</span><span class="n">a</span> <span class="o">+</span> <span class="n">b</span><span class="p">)</span> <span class="o">+</span> <span class="n">c</span> <span class="o">==</span> <span class="n">a</span> <span class="o">+</span> <span class="p">(</span><span class="n">b</span> <span class="o">+</span> <span class="n">c</span><span class="p">))</span> <span class="c1">#verifica della proprietà associativa(+) considerando tutti i bit</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <div class="output"> <div class="output_area"> <div class="prompt"></div> <div class="output_subarea output_stream output_stdout output_text"> <pre>0.6 0.6 </pre> </div> </div> <div class="output_area"> <div class="prompt"></div> <div class="output_subarea output_text output_error"> <pre> <span class="ansi-red-fg">---------------------------------------------------------------------------</span> <span class="ansi-red-fg">AssertionError</span> Traceback (most recent call last) <span class="ansi-green-fg"><ipython-input-14-65fc2234e42f></span> in <span class="ansi-cyan-fg"><module></span><span class="ansi-blue-fg">()</span> <span class="ansi-green-intense-fg ansi-bold"> 3</span> c <span class="ansi-yellow-intense-fg ansi-bold">=</span> <span class="ansi-cyan-intense-fg ansi-bold">0.3</span> <span class="ansi-green-intense-fg ansi-bold"> 4</span> <span class="ansi-green-intense-fg ansi-bold">print</span> <span class="ansi-yellow-intense-fg ansi-bold">(</span><span class="ansi-yellow-intense-fg ansi-bold">(</span>a <span class="ansi-yellow-intense-fg ansi-bold">+</span> b<span class="ansi-yellow-intense-fg ansi-bold">)</span> <span class="ansi-yellow-intense-fg ansi-bold">+</span> c<span class="ansi-yellow-intense-fg ansi-bold">,</span> a <span class="ansi-yellow-intense-fg ansi-bold">+</span> <span class="ansi-yellow-intense-fg ansi-bold">(</span>b <span class="ansi-yellow-intense-fg ansi-bold">+</span> c<span class="ansi-yellow-intense-fg ansi-bold">)</span><span class="ansi-yellow-intense-fg ansi-bold">)</span> <span class="ansi-green-fg">----> 5</span><span class="ansi-red-fg"> </span><span class="ansi-green-intense-fg ansi-bold">assert</span><span class="ansi-yellow-intense-fg ansi-bold">(</span><span class="ansi-yellow-intense-fg ansi-bold">(</span>a <span class="ansi-yellow-intense-fg ansi-bold">+</span> b<span class="ansi-yellow-intense-fg ansi-bold">)</span> <span class="ansi-yellow-intense-fg ansi-bold">+</span> c <span class="ansi-yellow-intense-fg ansi-bold">==</span> a <span class="ansi-yellow-intense-fg ansi-bold">+</span> <span class="ansi-yellow-intense-fg ansi-bold">(</span>b <span class="ansi-yellow-intense-fg ansi-bold">+</span> c<span class="ansi-yellow-intense-fg ansi-bold">)</span><span class="ansi-yellow-intense-fg ansi-bold">)</span> <span class="ansi-red-fg">AssertionError</span>: </pre> </div> </div> </div> </div> ................................................................................ <p>Chiunque (sfido il contrario!) utilizzerebbe la formula esattamente com'è scritta!</p> </div> </div> </div></div></section></section><section><section> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [15]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span> <span class="k">print</span> <span class="p">(</span><span class="mf">1.</span><span class="o">/</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">4</span><span class="p">))</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <h2 id="MA...">MA...<a class="anchor-link" href="#MA...">¶</a></h2><p>Qualcuno (non so davvero chi...decisamente me incluso) potrebbe pensare di calcolarla sviluppando il rapporto come:</p> </div> </div> </div></div></section></section><section><section> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [16]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="k">def</span> <span class="nf">isqrt</span><span class="p">(</span><span class="n">number</span><span class="p">):</span> <span class="k">assert</span> <span class="n">number</span> <span class="o">></span> <span class="mi">0</span> <span class="n">threehalfs</span> <span class="o">=</span> <span class="mf">1.5</span> <span class="n">x2</span> <span class="o">=</span> <span class="n">number</span> <span class="o">*</span> <span class="mf">0.5</span> <span class="n">y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">float32</span><span class="p">(</span><span class="n">number</span><span class="p">)</span> <span class="c1">#conversione a float32 del numero</span> <span class="n">i</span> <span class="o">=</span> <span class="n">y</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">int32</span><span class="p">)</span> <span class="c1">#"vedi" y come una variabile int32</span> <span class="n">i</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">int32</span><span class="p">(</span><span class="mh">0x5f3759df</span><span class="p">)</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">int32</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="c1">#differenza tra numeri in bit-format</span> <span class="n">y</span> <span class="o">=</span> <span class="n">i</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span> <span class="n">y</span> <span class="o">=</span> <span class="n">y</span> <span class="o">*</span> <span class="p">(</span><span class="n">threehalfs</span> <span class="o">-</span> <span class="p">(</span><span class="n">x2</span> <span class="o">*</span> <span class="n">y</span> <span class="o">*</span> <span class="n">y</span><span class="p">))</span> <span class="k">return</span> <span class="nb">float</span><span class="p">(</span><span class="n">y</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="n">isqrt</span><span class="p">(</span><span class="mi">4</span><span class="p">))</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <div class="output"> <div class="output_area"> <div class="prompt"></div> <div class="output_subarea output_stream output_stdout output_text"> <pre>0.499153574792 </pre> </div> </div> </div> </div> ................................................................................ </div></section></section><section><section> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> <div class="inner_cell"> <div class="text_cell_render border-box-sizing rendered_html"> <h2 id="Un-esempio-più-comune">Un esempio più comune<a class="anchor-link" href="#Un-esempio-più-comune">¶</a></h2><p>Supponiamo di voler calcolare il valore medio di un vettore $x$. Saremo tutti d'accordo che questo sia calcolabile come:</p> <p>$E[x] = \sum_{i=1}^N \frac{x_i}{N}$</p> <p>che è certamente equivalente a</p> <p>$E[x] = \frac{1}{N}\sum_{i=1}^N x_i$</p> <p>Bene...proviamo allora</p> </div> </div> </div></section></section><section><section> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [17]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span> <span class="n">N</span> <span class="o">=</span> <span class="mi">10000</span> <span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">N</span><span class="p">)</span> <span class="c1">#vettore contenente N numeri random estratti uniformemente in [0,1]</span> <span class="n">mean_1</span> <span class="o">=</span> <span class="mf">0.0</span> <span class="n">mean_2</span> <span class="o">=</span> <span class="mf">0.0</span> <span class="k">for</span> <span class="n">x_i</span> <span class="ow">in</span> <span class="n">x</span><span class="p">:</span> <span class="n">mean_1</span> <span class="o">+=</span> <span class="n">x_i</span> <span class="o">/</span> <span class="n">N</span> <span class="n">mean_2</span> <span class="o">+=</span> <span class="n">x_i</span> <span class="n">mean_2</span> <span class="o">/=</span> <span class="n">N</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"Media 1 = </span><span class="si">%.32f</span><span class="s2">"</span><span class="o">%</span><span class="p">(</span><span class="n">mean_1</span><span class="p">))</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"Media 2 = </span><span class="si">%.32f</span><span class="s2">"</span><span class="o">%</span><span class="p">(</span><span class="n">mean_2</span><span class="p">))</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> <div class="output"> <div class="output_area"> <div class="prompt"></div> <div class="output_subarea output_stream output_stdout output_text"> <pre>Media 1 = 0.49977160834157097202279373959755 Media 2 = 0.49977160834156963975516418940970 </pre> </div> </div> </div> </div> </div></section></section><section><section> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> <div class="inner_cell"> <div class="text_cell_render border-box-sizing rendered_html"> <h2 id="Cost-of-Operations">Cost of Operations<a class="anchor-link" href="#Cost-of-Operations">¶</a></h2><p><img src="./immagini/time.png" alt="alt text" title="## Cost of Operations"></p> </div> </div> </div></section></section><section><section> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> <div class="inner_cell"> <div class="text_cell_render border-box-sizing rendered_html"> <h2 id="Cost-of-Functions">Cost of Functions<a class="anchor-link" href="#Cost-of-Functions">¶</a></h2><p><img src="./immagini/time2.png" alt="alt text" title="## Cost of Operations"></p> </div> </div> </div></section></section><section><section> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> ................................................................................ </div> </div></div></section></section><section><section> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> <div class="inner_cell"> <div class="text_cell_render border-box-sizing rendered_html"> <h2 id="Ad-esempio">Ad esempio<a class="anchor-link" href="#Ad-esempio">¶</a></h2><p><img src="./immagini/vec.png" alt="alt text" title="## Cost of Operations"></p> </div> </div> </div></section></section><section><section> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> ................................................................................ <p><strong>NOTA</strong>: la vettorizzazione di un loop è uno dei metodi più rapidi da implementare e con il miglior guadagno in tempi di calcolo...soprattutto nei linguaggi ad alto livello!</p> </div> </div> </div><div class="fragment"> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [18]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="k">print</span> <span class="p">(</span><span class="s1">'true'</span> <span class="k">if</span> <span class="bp">True</span> <span class="k">else</span> <span class="s1">'false'</span><span class="p">)</span> <span class="c1"># operatore ternario del C++ in Python: la sintassi è "output1 se condizione, altrimenti output2</span> <span class="k">print</span> <span class="p">(</span><span class="s1">'false'</span> <span class="k">if</span> <span class="bp">False</span> <span class="k">else</span> <span class="s1">'false'</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s1">'odd'</span> <span class="k">if</span> <span class="mi">5</span><span class="o">%</span><span class="k">2</span> else 'even') <span class="k">print</span> <span class="p">(</span><span class="s1">'odd'</span> <span class="k">if</span> <span class="mi">4</span><span class="o">%</span><span class="k">2</span> else 'even') </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <h2 id="I-NumPy-array-e-ndarray">I NumPy array e ndarray<a class="anchor-link" href="#I-NumPy-array-e-ndarray">¶</a></h2><p>Proprio come gli std::vector<type> del C++, NumPy mette a disposizione i suoi contenitori per i vettori, chiamati np.ndarray (N-dimensional array object), contenitori <strong>veloci</strong>, <strong>flessibili</strong> per <strong>grandi data sets</strong>.</p> </div> </div> </div><div class="fragment"> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [19]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span> <span class="n">a</span> <span class="o">=</span> <span class="n">np</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">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">])</span> <span class="c1"># vettore 1x4</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"a = "</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span> <span class="n">b</span> <span class="o">=</span> <span class="n">np</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">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">],[</span><span class="mi">5</span><span class="p">,</span><span class="mi">6</span><span class="p">,</span><span class="mi">7</span><span class="p">,</span><span class="mi">8</span><span class="p">]])</span> <span class="c1"># matrice 2x4</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"b = "</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ </ul> </div> </div> </div></section></section><section><section> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [20]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">]</span> <span class="n">a_array</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="n">b_array</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">a</span><span class="p">))</span> <span class="k">print</span> <span class="p">(</span><span class="n">a_array</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="n">b_array</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="n">a_array</span><span class="o">.</span><span class="n">dtype</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">a_array</span><span class="p">))</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> <div class="output"> <div class="output_area"> <div class="prompt"></div> <div class="output_subarea output_stream output_stdout output_text"> <pre>(4L,) (4L,) int32 4 </pre> </div> </div> </div> </div> ................................................................................ <h2 id="Creare-array">Creare array<a class="anchor-link" href="#Creare-array">¶</a></h2><p>Ci sono 3 funzioni importanti per la creazione di array e l'inizializzazione di array.</p> </div> </div> </div><div class="fragment"> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [21]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="n">array_zeros</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span> <span class="c1"># vettore 1x10 di zeri</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"array_zeros = "</span><span class="p">,</span> <span class="n">array_zeros</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"array_zeros ha dimensioni : "</span><span class="p">,</span> <span class="n">array_zeros</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span> <span class="n">a_matzeros</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">2</span><span class="p">,</span><span class="mi">10</span><span class="p">))</span> <span class="c1"># matrice 2x10 di zeri</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"a_matzeros ha dimensioni : "</span><span class="p">,</span> <span class="n">a_matzeros</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span> <span class="n">array_ones</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span> <span class="c1"># vettore 1x10 di uno</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"aarray_ones = "</span><span class="p">,</span> <span class="n">array_ones</span><span class="p">)</span> <span class="n">a_empty</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">empty</span><span class="p">(</span><span class="mi">20</span><span class="p">)</span> <span class="c1"># vettore 1x20 di valori "vuoti"=locazioni di memoria libere</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"a_empty = "</span><span class="p">,</span> <span class="n">a_empty</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"a_empty contiene oggetti di tipo : "</span><span class="p">,</span> <span class="n">a_empty</span><span class="o">.</span><span class="n">dtype</span><span class="p">)</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <div class="output_area"> <div class="prompt"></div> <div class="output_subarea output_stream output_stdout output_text"> <pre>array_zeros = [ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.] array_zeros ha dimensioni : (10L,) a_matzeros ha dimensioni : (2L, 10L) aarray_ones = [ 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.] a_empty = [ 2.85808557e-316 6.22522714e-322 0.00000000e+000 0.00000000e+000 1.90979621e-313 5.30276956e+180 7.70748458e-043 2.99877042e-066 3.65961324e-086 4.25757156e-096 2.64936654e+180 3.80884741e+180 8.03704417e-095 9.97328607e-143 1.47278628e+179 8.37170573e-144 6.53456787e-042 3.21430743e-057 4.46920458e-090 1.72171244e+184] a_empty contiene oggetti di tipo : float64 </pre> </div> </div> </div> </div> ................................................................................ <p>Le principali funzioni sono 2: np.arange e np.linspace</p> </div> </div> </div></section></section><section><section> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [22]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span> <span class="c1"># vettore di 10 elementi con numeri crescenti da 0(default) e 10</span> <span class="k">print</span> <span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span> <span class="c1"># (valore iniziale, valore finale, step)</span> <span class="k">print</span> <span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">4</span><span class="p">)</span> <span class="c1"># (valore iniziale, valore finale, numero di punti)</span> <span class="k">print</span> <span class="p">(</span><span class="n">a</span><span class="p">)</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ </div> </div> </div></section></section><section><section> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [23]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="n">np</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">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"a = "</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"a contiene elementi di tipo : "</span><span class="p">,</span> <span class="n">a</span><span class="o">.</span><span class="n">dtype</span><span class="p">)</span> <span class="n">a</span> <span class="o">=</span> <span class="n">np</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">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">uint32</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"a = "</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"a contiene elementi di tipo : "</span><span class="p">,</span> <span class="n">a</span><span class="o">.</span><span class="n">dtype</span><span class="p">)</span> <span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="s1">'1.21'</span><span class="p">,</span> <span class="s1">'.2'</span><span class="p">,</span> <span class="s1">'-.4'</span><span class="p">],</span> <span class="n">dtype</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">string_</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"a di stringhe = "</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"a cast 2 float = "</span><span class="p">,</span> <span class="n">a</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">))</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <div class="prompt"></div> <div class="output_subarea output_stream output_stdout output_text"> <pre>a = [ 1. 2. 3. 4.] a contiene elementi di tipo : float64 a = [1 2 3 4] a contiene elementi di tipo : uint32 a di stringhe = ['1.21' '.2' '-.4'] a cast 2 float = [ 1.21 0.2 -0.4 ] </pre> </div> </div> </div> </div> ................................................................................ <p>...ma soprattutto hanno tutta una serie di operazioni <strong>già vettorizzate</strong>!!</p> </div> </div> </div></section></section><section><section> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [24]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="n">np</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">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">])</span> <span class="n">b</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">5</span><span class="p">])</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"</span><span class="se">\n</span><span class="s2"> OPERAZIONI ARITMETICHE</span><span class="se">\n</span><span class="s2">"</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"a = "</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"b = "</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"a * 10 : "</span><span class="p">,</span> <span class="n">a</span> <span class="o">*</span> <span class="mi">10</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"a + 2 : "</span><span class="p">,</span> <span class="n">a</span> <span class="o">+</span> <span class="mi">2</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"a^2 : "</span><span class="p">,</span> <span class="n">a</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"</span><span class="se">\n</span><span class="s2"> OPERAZIONI TRA ARRAY</span><span class="se">\n</span><span class="s2">"</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"a * b : "</span><span class="p">,</span> <span class="n">a</span><span class="o">*</span><span class="n">b</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"a + b : "</span><span class="p">,</span> <span class="n">a</span><span class="o">+</span><span class="n">b</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"a - b : "</span><span class="p">,</span> <span class="n">a</span><span class="o">-</span><span class="n">b</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"1. / a : "</span><span class="p">,</span> <span class="mf">1.</span><span class="o">/</span><span class="n">a</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"1 / a : "</span><span class="p">,</span> <span class="mi">1</span><span class="o">/</span><span class="n">a</span><span class="p">)</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ OPERAZIONI TRA ARRAY a * b : [ 2 6 12 20] a + b : [3 5 7 9] a - b : [-1 -1 -1 -1] 1. / a : [ 1. 0.5 0.33333333 0.25 ] 1 / a : [1 0 0 0] </pre> </div> </div> </div> </div> ................................................................................ <p>Posso anche prendere pezzi dei vettori e combinarli insieme.</p> </div> </div> </div><div class="fragment"> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [162]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">20</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="n">a</span><span class="p">[</span><span class="mi">8</span><span class="p">])</span> <span class="c1"># ottavo elemento del vettore</span> <span class="k">print</span> <span class="p">(</span><span class="n">a</span><span class="p">[:</span><span class="mi">8</span><span class="p">])</span> <span class="c1"># primi 8 elementi</span> <span class="k">print</span> <span class="p">(</span><span class="n">a</span><span class="p">[</span><span class="mi">8</span><span class="p">:</span><span class="mi">12</span><span class="p">])</span> <span class="c1"># elementi compresi tra l'ottavo e il dodicesimo</span> <span class="k">print</span> <span class="p">(</span><span class="n">a</span><span class="p">[</span><span class="mi">12</span><span class="p">:</span><span class="o">-</span><span class="mi">4</span><span class="p">])</span> <span class="c1"># elementi compresi tra il 12esimo e il quart'ultimo</span> <span class="k">print</span> <span class="p">(</span><span class="n">a</span><span class="p">[</span><span class="o">-</span><span class="mi">4</span><span class="p">:])</span> <span class="c1"># elementi dal quart'ultimo e la fine</span> <span class="k">assert</span><span class="p">(</span> <span class="n">np</span><span class="o">.</span><span class="n">all</span><span class="p">(</span><span class="n">a</span><span class="p">[</span><span class="o">-</span><span class="mi">15</span><span class="p">:</span><span class="o">-</span><span class="mi">10</span><span class="p">]</span> <span class="o">==</span> <span class="n">a</span><span class="p">[</span><span class="mi">5</span><span class="p">:</span><span class="mi">10</span><span class="p">]))</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <div class="text_cell_render border-box-sizing rendered_html"> <h2 id="ATTENZIONE!">ATTENZIONE!<a class="anchor-link" href="#ATTENZIONE!">¶</a></h2> </div> </div> </div><div class="fragment"> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [165]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="n">arr_slice</span> <span class="o">=</span> <span class="n">a</span><span class="p">[</span><span class="mi">2</span><span class="p">:</span><span class="mi">5</span><span class="p">]</span> <span class="c1"># pezzo del vettore a</span> <span class="n">arr_slice</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="mi">10000</span> <span class="c1"># modifica del secondo elemento del pezzo di a</span> <span class="k">print</span> <span class="p">(</span><span class="n">a</span><span class="p">)</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <pre><code> arr[2:5].copy()</code></pre> </div> </div> </div></div></section></section><section><section> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [176]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="n">arr3d</span> <span class="o">=</span> <span class="n">np</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">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">]],</span> <span class="p">[[</span><span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">9</span><span class="p">],</span> <span class="p">[</span><span class="mi">10</span><span class="p">,</span> <span class="mi">11</span><span class="p">,</span> <span class="mi">12</span><span class="p">]]])</span> <span class="k">print</span> <span class="p">(</span><span class="s2">" a = "</span><span class="p">,</span> <span class="n">arr3d</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"primo elemento : "</span><span class="p">,</span> <span class="n">arr3d</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="k">print</span> <span class="p">(</span><span class="s2">"prima riga : "</span><span class="p">,</span> <span class="n">arr3d</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="k">print</span> <span class="p">(</span><span class="s2">"prima matrice : "</span><span class="p">,</span> <span class="n">arr3d</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"profondità : "</span><span class="p">,</span> <span class="n">arr3d</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <pre><code> np.mean(array)</code></pre> </div> </div> </div></section></section><section><section> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [15]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="kn">import</span> <span class="nn">time</span> <span class="n">start_time</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span> <span class="c1"># inizia a contare il tempo</span> <span class="n">N</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="mf">1e7</span><span class="p">)</span> <span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">N</span><span class="p">)</span> <span class="n">mean_for_1</span> <span class="o">=</span> <span class="mf">0.0</span> <span class="n">mean_for_2</span> <span class="o">=</span> <span class="mf">0.0</span> <span class="k">for</span> <span class="n">x_i</span> <span class="ow">in</span> <span class="n">x</span><span class="p">:</span> <span class="n">mean_for_1</span> <span class="o">+=</span> <span class="n">x_i</span><span class="o">/</span><span class="n">N</span> <span class="n">mean_for_2</span> <span class="o">+=</span> <span class="n">x_i</span> <span class="n">mean_for_2</span> <span class="o">/=</span> <span class="n">N</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"Mean 1 = </span><span class="si">%.32f</span><span class="s2">"</span><span class="o">%</span><span class="p">(</span><span class="n">mean_for_1</span><span class="p">))</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"Mean 2 = </span><span class="si">%.32f</span><span class="s2">"</span><span class="o">%</span><span class="p">(</span><span class="n">mean_for_2</span><span class="p">))</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"Calcolate in </span><span class="si">%.32f</span><span class="s2"> sec"</span><span class="o">%</span><span class="p">(</span><span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span><span class="o">-</span><span class="n">start_time</span><span class="p">))</span> <span class="n">start_time</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span> <span class="n">mean_vec</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"Mean vettorizzata = </span><span class="si">%.32f</span><span class="s2">"</span><span class="o">%</span><span class="p">(</span><span class="n">mean_vec</span><span class="p">))</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"Calcolata in </span><span class="si">%.32f</span><span class="s2"> sec"</span><span class="o">%</span><span class="p">(</span><span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span><span class="o">-</span><span class="n">start_time</span><span class="p">))</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <div class="output"> <div class="output_area"> <div class="prompt"></div> <div class="output_subarea output_stream output_stdout output_text"> <pre>Mean 1 = 0.50003546594170067418616554277833 Mean 2 = 0.50003546594162207039602208169526 Calcolate in 33.26500010490417480468750000000000 sec Mean vettorizzata = 0.50003546594165892980043963689241 Calcolata in 0.04699993133544921875000000000000 sec </pre> </div> </div> </div> </div> ................................................................................ <p>Numpy predispone già un'ampia gamma di generatori!</p> </div> </div> </div><div class="fragment"> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [193]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="kn">from</span> <span class="nn">numpy</span> <span class="kn">import</span> <span class="n">random</span> <span class="k">print</span> <span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">())</span> <span class="c1"># uniform distribution</span> <span class="k">print</span> <span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">())</span> <span class="c1"># normal distribution</span> <span class="k">print</span> <span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">exponential</span><span class="p">())</span> <span class="c1"># exponential distribution</span> <span class="k">print</span> <span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">))</span> <span class="c1"># random matrix</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <div class="output"> <div class="output_area"> <div class="prompt"></div> <div class="output_subarea output_stream output_stdout output_text"> <pre>0.0803586638819 -1.11673488584 0.466184685074 [[ 0.73152502 0.59559674 0.73434003] [ 0.18037221 0.05359538 0.28565275]] </pre> </div> </div> </div> </div> ................................................................................ <h2 id="Una-carrellata-di-altre-funzioni-utili...">Una carrellata di altre funzioni utili...<a class="anchor-link" href="#Una-carrellata-di-altre-funzioni-utili...">¶</a></h2><p><strong>NOTA</strong> In Matlab la nomenclatura è <strong>quasi sempre</strong> la stessa, ovviamente senza l'np davanti!</p> </div> </div> </div><div class="fragment"> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [30]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="n">np</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="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="mf">3.444</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="mf">4.29</span><span class="p">,</span> <span class="mf">6.98</span><span class="p">])</span> <span class="n">b</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">2</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="mf">3.44</span><span class="p">,</span> <span class="o">-</span><span class="mf">2.</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">7</span><span class="p">])</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"</span><span class="se">\n</span><span class="s2"> ALCUNE altre operazioni </span><span class="se">\n</span><span class="s2">"</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">a</span><span class="p">))</span> <span class="c1"># absolute value </span> <span class="k">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">fabs</span><span class="p">(</span><span class="n">a</span><span class="p">))</span> <span class="c1"># absolute value </span> <span class="k">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">a</span><span class="p">))</span> <span class="c1"># square root</span> <span class="k">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">floor</span><span class="p">(</span><span class="n">a</span><span class="p">))</span> <span class="c1"># the largest integer value less than or equal to x</span> <span class="k">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">ceil</span><span class="p">(</span><span class="n">a</span><span class="p">))</span> <span class="c1"># smallest integer value greater than or equal to x</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ </div> </div> <div class="output_area"> <div class="prompt"></div> <div class="output_subarea output_stream output_stderr output_text"> <pre>C:\Users\NICO\Anaconda2\lib\site-packages\ipykernel\__main__.py:8: RuntimeWarning: invalid value encountered in sqrt </pre> </div> </div> </div> </div> </div></div></section></section><section><section> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [27]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="k">print</span> <span class="p">(</span><span class="s2">"a = "</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"b = "</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"</span><span class="se">\n</span><span class="s2"> ALCUNE operazioni logiche </span><span class="se">\n</span><span class="s2">"</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">logical_and</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">))</span> <span class="c1"># AND</span> <span class="k">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">logical_or</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">))</span> <span class="c1"># OR</span> <span class="k">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">greater</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">))</span> <span class="c1"># ></span> <span class="k">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">equal</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">))</span> <span class="c1"># ==</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ </div> </div> </div></section></section><section><section> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [29]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="k">print</span> <span class="p">(</span><span class="s2">"a = "</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"b = "</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"</span><span class="se">\n</span><span class="s2"> ALCUNE operazioni sul posizionamento </span><span class="se">\n</span><span class="s2">"</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sort</span><span class="p">(</span><span class="n">a</span><span class="p">))</span> <span class="c1"># SORTING ELEMENTS</span> <span class="k">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">argsort</span><span class="p">(</span><span class="n">a</span><span class="p">))</span> <span class="c1"># SORTING INDICES</span> <span class="k">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="n">a</span> <span class="o"><</span> <span class="mi">2</span><span class="p">)[</span><span class="mi">0</span><span class="p">])</span> <span class="c1"># INDICES WHERE CONDITION</span> <span class="k">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="n">a</span> <span class="o">></span> <span class="mi">2</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="c1"># (CONDITION, IF(CONDITION), ELSE)</span> <span class="k">print</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">median</span><span class="p">(</span><span class="n">a</span><span class="p">))</span> <span class="c1"># MEDIAN</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> ................................................................................ <h2 id="Basta-teoria!-E'-ora-di-sporcarsi-un-po'-le-mani-scrivendo-del-codice!">Basta teoria! E' ora di sporcarsi un po' le mani scrivendo del codice!<a class="anchor-link" href="#Basta-teoria!-E'-ora-di-sporcarsi-un-po'-le-mani-scrivendo-del-codice!">¶</a></h2><p>Da quello che abbiamo imparato dovreste essere in grado di vettorizzare facilmente il codice seguente per il calcolo del $\pi$. Controllate anche il tempo di esecuzione delle due versioni dell'algoritmo!</p> </div> </div> </div></section></section><section><section> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [ ]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span> <span class="kn">import</span> <span class="nn">time</span> <span class="sd">"""</span> <span class="sd">Metropolis Algorithm</span> <span class="sd">Algoritmo per il calcolo dell'integrale di una funzione attraverso un campionamento Monte Carlo. </span> <span class="sd">In questo esempio viene utilizzato per il calcolo del valore del pi-greco. Si consideri al proposito un cerchio di</span> <span class="sd">raggio unitario (r = 1) centrato nell'origine, inscritto in un quadrato. In questo modo il quadrato avrà lato pari a 2</span> <span class="sd">e la sua area sarà uguale a 4. Andando ad estrarre in modo uniforme nell'intervallo [-1,1] una coppia di numeri (x, y),</span> <span class="sd">qualora le coordinate risultino appartenenti al cerchio verrà conteggiato un Hit. La condizione da imporre sarà quindi:</span> <span class="sd"> x^2 + y^2 < 1</span> <span class="sd"> </span> <span class="sd">Secondo la teoria dei metodi Monte Carlo, il numero di Hit rispetto al totale sarà equivalente (per un numero tendente</span> <span class="sd">all'infinito di estrazioni) al rapporto tra le aree. In questo caso quindi</span> <span class="sd"> Hit/Tot = pi/4</span> <span class="sd"> </span> <span class="sd">Volendo estrarre un risultato più robusto si consiglia di campionare il valore di pi un numero N_runs di volte, in modo</span> <span class="sd">che il corretto valore di pi sia dato dalla media della distribuzione di più campionamenti Monte Carlo.</span> <span class="sd">"""</span> </pre></div> </div> </div> </div> </div></section></section><section><section> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [16]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython2"><pre><span></span><span class="n">N</span> <span class="o">=</span> <span class="mi">100000</span> <span class="c1"># number of MC events</span> <span class="n">N_run</span> <span class="o">=</span> <span class="mi">100</span> <span class="c1"># number of runs</span> <span class="n">Nhits</span> <span class="o">=</span> <span class="mf">0.0</span> <span class="c1"># number of points accepted</span> <span class="n">pi</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">N_run</span><span class="p">)</span> <span class="c1"># values of pi</span> <span class="n">start_time</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span> <span class="c1"># start clock </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="n">N_run</span><span class="p">):</span> <span class="n">Nhits</span> <span class="o">=</span> <span class="mf">0.0</span> ................................................................................ <span class="n">res</span> <span class="o">=</span> <span class="n">x</span><span class="o">*</span><span class="n">x</span> <span class="o">+</span> <span class="n">y</span><span class="o">*</span><span class="n">y</span> <span class="k">if</span> <span class="n">res</span> <span class="o"><</span> <span class="mi">1</span><span class="p">:</span> <span class="n">Nhits</span> <span class="o">+=</span> <span class="mf">1.0</span> <span class="n">pi</span><span class="p">[</span><span class="n">I</span><span class="p">]</span> <span class="o">+=</span> <span class="mf">4.</span> <span class="o">*</span> <span class="n">Nhits</span><span class="o">/</span><span class="n">N</span> <span class="n">run_time</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"pi with "</span><span class="p">,</span> <span class="n">N</span><span class="p">,</span> <span class="s2">" steps for "</span><span class="p">,</span> <span class="n">N_run</span><span class="p">,</span> <span class="s2">" runs is "</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">pi</span><span class="p">),</span> <span class="s2">" in "</span><span class="p">,</span> <span class="n">run_time</span><span class="o">-</span><span class="n">start_time</span><span class="p">,</span> <span class="s2">" sec"</span><span class="p">)</span> <span class="k">print</span> <span class="p">(</span><span class="s2">"Precision computation : "</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">pi</span><span class="p">)</span><span class="o">-</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">))</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> |
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