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536 <div·class="highlight-ipython·notranslate"><div·class="highlight"><pre><span></span><span·class="gp">In·[1]:·</span><span·class="kn">import</span>·<span·class="nn">numpy.random</span>536 <div·class="highlight-ipython·notranslate"><div·class="highlight"><pre><span></span><span·class="gp">In·[1]:·</span><span·class="kn">import</span>·<span·class="nn">numpy.random</span>
  
537 <span·class="gp">In·[2]:·</span><span·class="n">rng</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">default_rng</span><span·class="p">()</span>537 <span·class="gp">In·[2]:·</span><span·class="n">rng</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">default_rng</span><span·class="p">()</span>
  
538 <span·class="gp">In·[3]:·</span><span·class="o">%</span><span·class="k">timeit</span>·-n·1·rng.standard_normal(100000)538 <span·class="gp">In·[3]:·</span><span·class="o">%</span><span·class="k">timeit</span>·-n·1·rng.standard_normal(100000)
539 <span·class="gp">···...:·</span><span·class="o">%</span><span·class="k">timeit</span>·-n·1·numpy.random.standard_normal(100000)539 <span·class="gp">···...:·</span><span·class="o">%</span><span·class="k">timeit</span>·-n·1·numpy.random.standard_normal(100000)
540 <span·class="gp">···...:·</span>540 <span·class="gp">···...:·</span>
541 <span·class="go">1.14·ms·+-·28.9·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each)</span>541 <span·class="go">1.16·ms·+-·9.2·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each)</span>
542 <span·class="go">2.26·ms·+-·148·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each)</span>542 <span·class="go">2.03·ms·+-·15.8·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each)</span>
543 </pre></div>543 </pre></div>
544 </div>544 </div>
545 <div·class="highlight-ipython·notranslate"><div·class="highlight"><pre><span></span><span·class="gp">In·[4]:·</span><span·class="o">%</span><span·class="k">timeit</span>·-n·1·rng.standard_exponential(100000)545 <div·class="highlight-ipython·notranslate"><div·class="highlight"><pre><span></span><span·class="gp">In·[4]:·</span><span·class="o">%</span><span·class="k">timeit</span>·-n·1·rng.standard_exponential(100000)
546 <span·class="gp">···...:·</span><span·class="o">%</span><span·class="k">timeit</span>·-n·1·numpy.random.standard_exponential(100000)546 <span·class="gp">···...:·</span><span·class="o">%</span><span·class="k">timeit</span>·-n·1·numpy.random.standard_exponential(100000)
547 <span·class="gp">···...:·</span>547 <span·class="gp">···...:·</span>
548 <span·class="go">545·us·+-·16.2·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each)</span>548 <span·class="go">524·us·+-·21·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each)</span>
549 <span·class="go">1.61·ms·+-·69.9·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each)</span>549 <span·class="go">1.38·ms·+-·12.7·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each)</span>
550 </pre></div>550 </pre></div>
551 </div>551 </div>
552 <div·class="highlight-ipython·notranslate"><div·class="highlight"><pre><span></span><span·class="gp">In·[5]:·</span><span·class="o">%</span><span·class="k">timeit</span>·-n·1·rng.standard_gamma(3.0,·100000)552 <div·class="highlight-ipython·notranslate"><div·class="highlight"><pre><span></span><span·class="gp">In·[5]:·</span><span·class="o">%</span><span·class="k">timeit</span>·-n·1·rng.standard_gamma(3.0,·100000)
553 <span·class="gp">···...:·</span><span·class="o">%</span><span·class="k">timeit</span>·-n·1·numpy.random.standard_gamma(3.0,·100000)553 <span·class="gp">···...:·</span><span·class="o">%</span><span·class="k">timeit</span>·-n·1·numpy.random.standard_gamma(3.0,·100000)
554 <span·class="gp">···...:·</span>554 <span·class="gp">···...:·</span>
555 <span·class="go">2.2·ms·+-·18.5·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each)</span>555 <span·class="go">2.14·ms·+-·33.3·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each)</span>
556 <span·class="go">4.44·ms·+-·29.9·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each)</span>556 <span·class="go">4.16·ms·+-·24.4·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each)</span>
557 </pre></div>557 </pre></div>
558 </div>558 </div>
559 <ul·class="simple">559 <ul·class="simple">
560 <li><p><a·class="reference·internal"·href="generated/numpy.random.Generator.integers.html#numpy.random.Generator.integers"·title="numpy.random.Generator.integers"><code·class="xref·py·py-obj·docutils·literal·notranslate"><span·class="pre">integers</span></code></a>·is·now·the·canonical·way·to·generate·integer560 <li><p><a·class="reference·internal"·href="generated/numpy.random.Generator.integers.html#numpy.random.Generator.integers"·title="numpy.random.Generator.integers"><code·class="xref·py·py-obj·docutils·literal·notranslate"><span·class="pre">integers</span></code></a>·is·now·the·canonical·way·to·generate·integer
561 random·numbers·from·a·discrete·uniform·distribution.·This·replaces·both561 random·numbers·from·a·discrete·uniform·distribution.·This·replaces·both
562 <a·class="reference·internal"·href="generated/numpy.random.randint.html#numpy.random.randint"·title="numpy.random.randint"><code·class="xref·py·py-obj·docutils·literal·notranslate"><span·class="pre">randint</span></code></a>·and·the·deprecated·<a·class="reference·internal"·href="generated/numpy.random.random_integers.html#numpy.random.random_integers"·title="numpy.random.random_integers"><code·class="xref·py·py-obj·docutils·literal·notranslate"><span·class="pre">random_integers</span></code></a>.</p></li>562 <a·class="reference·internal"·href="generated/numpy.random.randint.html#numpy.random.randint"·title="numpy.random.randint"><code·class="xref·py·py-obj·docutils·literal·notranslate"><span·class="pre">randint</span></code></a>·and·the·deprecated·<a·class="reference·internal"·href="generated/numpy.random.random_integers.html#numpy.random.random_integers"·title="numpy.random.random_integers"><code·class="xref·py·py-obj·docutils·literal·notranslate"><span·class="pre">random_integers</span></code></a>.</p></li>
563 <li><p>The·<a·class="reference·internal"·href="generated/numpy.random.rand.html#numpy.random.rand"·title="numpy.random.rand"><code·class="xref·py·py-obj·docutils·literal·notranslate"><span·class="pre">rand</span></code></a>·and·<a·class="reference·internal"·href="generated/numpy.random.randn.html#numpy.random.randn"·title="numpy.random.randn"><code·class="xref·py·py-obj·docutils·literal·notranslate"><span·class="pre">randn</span></code></a>·methods·are·only·available·through·the·legacy563 <li><p>The·<a·class="reference·internal"·href="generated/numpy.random.rand.html#numpy.random.rand"·title="numpy.random.rand"><code·class="xref·py·py-obj·docutils·literal·notranslate"><span·class="pre">rand</span></code></a>·and·<a·class="reference·internal"·href="generated/numpy.random.randn.html#numpy.random.randn"·title="numpy.random.randn"><code·class="xref·py·py-obj·docutils·literal·notranslate"><span·class="pre">randn</span></code></a>·methods·are·only·available·through·the·legacy
Offset 586, 21 lines modifiedOffset 586, 21 lines modified
586 <li><p>Standard·Exponentials·(<a·class="reference·internal"·href="generated/numpy.random.Generator.standard_exponential.html#numpy.random.Generator.standard_exponential"·title="numpy.random.Generator.standard_exponential"><code·class="xref·py·py-obj·docutils·literal·notranslate"><span·class="pre">standard_exponential</span></code></a>)</p></li>586 <li><p>Standard·Exponentials·(<a·class="reference·internal"·href="generated/numpy.random.Generator.standard_exponential.html#numpy.random.Generator.standard_exponential"·title="numpy.random.Generator.standard_exponential"><code·class="xref·py·py-obj·docutils·literal·notranslate"><span·class="pre">standard_exponential</span></code></a>)</p></li>
587 </ul>587 </ul>
588 </li>588 </li>
589 </ul>589 </ul>
590 <div·class="highlight-ipython·notranslate"><div·class="highlight"><pre><span></span><span·class="gp">In·[6]:·</span><span·class="n">rng</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">default_rng</span><span·class="p">()</span>590 <div·class="highlight-ipython·notranslate"><div·class="highlight"><pre><span></span><span·class="gp">In·[6]:·</span><span·class="n">rng</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">default_rng</span><span·class="p">()</span>
  
591 <span·class="gp">In·[7]:·</span><span·class="n">rng</span><span·class="o">.</span><span·class="n">random</span><span·class="p">(</span><span·class="mi">3</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>591 <span·class="gp">In·[7]:·</span><span·class="n">rng</span><span·class="o">.</span><span·class="n">random</span><span·class="p">(</span><span·class="mi">3</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>
592 <span·class="gh">Out[7]:·</span><span·class="go">array([0.52982092,·0.42295032,·0.24147651])</span>592 <span·class="gh">Out[7]:·</span><span·class="go">array([0.29293961,·0.65281904,·0.13724775])</span>
  
593 <span·class="gp">In·[8]:·</span><span·class="n">rng</span><span·class="o">.</span><span·class="n">random</span><span·class="p">(</span><span·class="mi">3</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">float32</span><span·class="p">)</span>593 <span·class="gp">In·[8]:·</span><span·class="n">rng</span><span·class="o">.</span><span·class="n">random</span><span·class="p">(</span><span·class="mi">3</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">float32</span><span·class="p">)</span>
594 <span·class="gh">Out[8]:·</span><span·class="go">array([0.9568871·,·0.1235407·,·0.99757785],·dtype=float32)</span>594 <span·class="gh">Out[8]:·</span><span·class="go">array([0.96676505,·0.3154664·,·0.50938195],·dtype=float32)</span>
  
595 <span·class="gp">In·[9]:·</span><span·class="n">rng</span><span·class="o">.</span><span·class="n">integers</span><span·class="p">(</span><span·class="mi">0</span><span·class="p">,</span>·<span·class="mi">256</span><span·class="p">,</span>·<span·class="n">size</span><span·class="o">=</span><span·class="mi">3</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">uint8</span><span·class="p">)</span>595 <span·class="gp">In·[9]:·</span><span·class="n">rng</span><span·class="o">.</span><span·class="n">integers</span><span·class="p">(</span><span·class="mi">0</span><span·class="p">,</span>·<span·class="mi">256</span><span·class="p">,</span>·<span·class="n">size</span><span·class="o">=</span><span·class="mi">3</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">uint8</span><span·class="p">)</span>
596 <span·class="gh">Out[9]:·</span><span·class="go">array([·71,·215,··84],·dtype=uint8)</span>596 <span·class="gh">Out[9]:·</span><span·class="go">array([33,·49,·40],·dtype=uint8)</span>
597 </pre></div>597 </pre></div>
598 </div>598 </div>
599 <ul>599 <ul>
600 <li><p>Optional·<code·class="docutils·literal·notranslate"><span·class="pre">out</span></code>·argument·that·allows·existing·arrays·to·be·filled·for600 <li><p>Optional·<code·class="docutils·literal·notranslate"><span·class="pre">out</span></code>·argument·that·allows·existing·arrays·to·be·filled·for
601 select·distributions</p>601 select·distributions</p>
602 <ul·class="simple">602 <ul·class="simple">
603 <li><p>Uniforms·(<a·class="reference·internal"·href="generated/numpy.random.Generator.random.html#numpy.random.Generator.random"·title="numpy.random.Generator.random"><code·class="xref·py·py-obj·docutils·literal·notranslate"><span·class="pre">random</span></code></a>)</p></li>603 <li><p>Uniforms·(<a·class="reference·internal"·href="generated/numpy.random.Generator.random.html#numpy.random.Generator.random"·title="numpy.random.Generator.random"><code·class="xref·py·py-obj·docutils·literal·notranslate"><span·class="pre">random</span></code></a>)</p></li>
Offset 613, 18 lines modifiedOffset 613, 18 lines modified
613 </li>613 </li>
614 </ul>614 </ul>
615 <div·class="highlight-ipython·notranslate"><div·class="highlight"><pre><span></span><span·class="gp">In·[10]:·</span><span·class="n">rng</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">default_rng</span><span·class="p">()</span>615 <div·class="highlight-ipython·notranslate"><div·class="highlight"><pre><span></span><span·class="gp">In·[10]:·</span><span·class="n">rng</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">default_rng</span><span·class="p">()</span>
  
616 <span·class="gp">In·[11]:·</span><span·class="n">existing</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">4</span><span·class="p">)</span>616 <span·class="gp">In·[11]:·</span><span·class="n">existing</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">4</span><span·class="p">)</span>
  
617 <span·class="gp">In·[12]:·</span><span·class="n">rng</span><span·class="o">.</span><span·class="n">random</span><span·class="p">(</span><span·class="n">out</span><span·class="o">=</span><span·class="n">existing</span><span·class="p">[:</span><span·class="mi">2</span><span·class="p">])</span>617 <span·class="gp">In·[12]:·</span><span·class="n">rng</span><span·class="o">.</span><span·class="n">random</span><span·class="p">(</span><span·class="n">out</span><span·class="o">=</span><span·class="n">existing</span><span·class="p">[:</span><span·class="mi">2</span><span·class="p">])</span>
618 <span·class="gh">Out[12]:·</span><span·class="go">array([0.62682846,·0.76426864])</span>618 <span·class="gh">Out[12]:·</span><span·class="go">array([0.5231906·,·0.65732983])</span>
  
619 <span·class="gp">In·[13]:·</span><span·class="nb">print</span><span·class="p">(</span><span·class="n">existing</span><span·class="p">)</span>619 <span·class="gp">In·[13]:·</span><span·class="nb">print</span><span·class="p">(</span><span·class="n">existing</span><span·class="p">)</span>
620 <span·class="go">[0.62682846·0.76426864·0.·········0.········]</span>620 <span·class="go">[0.5231906··0.65732983·0.·········0.········]</span>
621 </pre></div>621 </pre></div>
622 </div>622 </div>
623 <ul·class="simple">623 <ul·class="simple">
624 <li><p>Optional·<code·class="docutils·literal·notranslate"><span·class="pre">axis</span></code>·argument·for·methods·like·<a·class="reference·internal"·href="generated/numpy.random.Generator.choice.html#numpy.random.Generator.choice"·title="numpy.random.Generator.choice"><code·class="xref·py·py-obj·docutils·literal·notranslate"><span·class="pre">choice</span></code></a>,624 <li><p>Optional·<code·class="docutils·literal·notranslate"><span·class="pre">axis</span></code>·argument·for·methods·like·<a·class="reference·internal"·href="generated/numpy.random.Generator.choice.html#numpy.random.Generator.choice"·title="numpy.random.Generator.choice"><code·class="xref·py·py-obj·docutils·literal·notranslate"><span·class="pre">choice</span></code></a>,
625 <a·class="reference·internal"·href="generated/numpy.random.Generator.permutation.html#numpy.random.Generator.permutation"·title="numpy.random.Generator.permutation"><code·class="xref·py·py-obj·docutils·literal·notranslate"><span·class="pre">permutation</span></code></a>·and·<a·class="reference·internal"·href="generated/numpy.random.Generator.shuffle.html#numpy.random.Generator.shuffle"·title="numpy.random.Generator.shuffle"><code·class="xref·py·py-obj·docutils·literal·notranslate"><span·class="pre">shuffle</span></code></a>·that·controls·which625 <a·class="reference·internal"·href="generated/numpy.random.Generator.permutation.html#numpy.random.Generator.permutation"·title="numpy.random.Generator.permutation"><code·class="xref·py·py-obj·docutils·literal·notranslate"><span·class="pre">permutation</span></code></a>·and·<a·class="reference·internal"·href="generated/numpy.random.Generator.shuffle.html#numpy.random.Generator.shuffle"·title="numpy.random.Generator.shuffle"><code·class="xref·py·py-obj·docutils·literal·notranslate"><span·class="pre">shuffle</span></code></a>·that·controls·which
626 axis·an·operation·is·performed·over·for·multi-dimensional·arrays.</p></li>626 axis·an·operation·is·performed·over·for·multi-dimensional·arrays.</p></li>
627 </ul>627 </ul>
Offset 636, 25 lines modifiedOffset 636, 25 lines modified
636 <span·class="gh">Out[16]:·</span>636 <span·class="gh">Out[16]:·</span>
637 <span·class="go">array([[·0,··1,··2,··3],</span>637 <span·class="go">array([[·0,··1,··2,··3],</span>
638 <span·class="go">·······[·4,··5,··6,··7],</span>638 <span·class="go">·······[·4,··5,··6,··7],</span>
639 <span·class="go">·······[·8,··9,·10,·11]])</span>639 <span·class="go">·······[·8,··9,·10,·11]])</span>
  
640 <span·class="gp">In·[17]:·</span><span·class="n">rng</span><span·class="o">.</span><span·class="n">choice</span><span·class="p">(</span><span·class="n">a</span><span·class="p">,</span>·<span·class="n">axis</span><span·class="o">=</span><span·class="mi">1</span><span·class="p">,</span>·<span·class="n">size</span><span·class="o">=</span><span·class="mi">5</span><span·class="p">)</span>640 <span·class="gp">In·[17]:·</span><span·class="n">rng</span><span·class="o">.</span><span·class="n">choice</span><span·class="p">(</span><span·class="n">a</span><span·class="p">,</span>·<span·class="n">axis</span><span·class="o">=</span><span·class="mi">1</span><span·class="p">,</span>·<span·class="n">size</span><span·class="o">=</span><span·class="mi">5</span><span·class="p">)</span>
641 <span·class="gh">Out[17]:·</span>641 <span·class="gh">Out[17]:·</span>
642 <span·class="go">array([[·2,··1,··0,··3,··2],</span>642 <span·class="go">array([[·3,··2,··2,··2,··0],</span>
643 <span·class="go">·······[·6,··5,··4,··7,··6],</span> 
644 <span·class="go">·······[10,··9,··8,·11,·10]])</span>643 <span·class="go">·······[·7,··6,··6,··6,··4],</span>
 644 <span·class="go">·······[11,·10,·10,·10,··8]])</span>
  
645 <span·class="gp">In·[18]:·</span><span·class="n">rng</span><span·class="o">.</span><span·class="n">shuffle</span><span·class="p">(</span><span·class="n">a</span><span·class="p">,</span>·<span·class="n">axis</span><span·class="o">=</span><span·class="mi">1</span><span·class="p">)</span>········<span·class="c1">#·Shuffle·in-place</span>645 <span·class="gp">In·[18]:·</span><span·class="n">rng</span><span·class="o">.</span><span·class="n">shuffle</span><span·class="p">(</span><span·class="n">a</span><span·class="p">,</span>·<span·class="n">axis</span><span·class="o">=</span><span·class="mi">1</span><span·class="p">)</span>········<span·class="c1">#·Shuffle·in-place</span>
  
646 <span·class="gp">In·[19]:·</span><span·class="n">a</span>646 <span·class="gp">In·[19]:·</span><span·class="n">a</span>
647 <span·class="gh">Out[19]:·</span>647 <span·class="gh">Out[19]:·</span>
648 <span·class="go">array([[·1,··2,··3,··0],</span>648 <span·class="go">array([[·1,··3,··2,··0],</span>
649 <span·class="go">·······[·5,··6,··7,··4],</span>649 <span·class="go">·······[·5,··7,··6,··4],</span>
650 <span·class="go">·······[·9,·10,·11,··8]])</span>650 <span·class="go">·······[·9,·11,·10,··8]])</span>
651 </pre></div>651 </pre></div>
652 </div>652 </div>
653 <ul·class="simple">653 <ul·class="simple">
654 <li><p>Added·a·method·to·sample·from·the·complex·normal·distribution654 <li><p>Added·a·method·to·sample·from·the·complex·normal·distribution
655 (<em·class="xref·py·py-obj">complex_normal</em>)</p></li>655 (<em·class="xref·py·py-obj">complex_normal</em>)</p></li>
656 </ul>656 </ul>
657 </section>657 </section>
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102 In·[1]:·import·numpy.random102 In·[1]:·import·numpy.random
  
103 In·[2]:·rng·=·np.random.default_rng()103 In·[2]:·rng·=·np.random.default_rng()
  
104 In·[3]:·%timeit·-n·1·rng.standard_normal(100000)104 In·[3]:·%timeit·-n·1·rng.standard_normal(100000)
105 ···...:·%timeit·-n·1·numpy.random.standard_normal(100000)105 ···...:·%timeit·-n·1·numpy.random.standard_normal(100000)
106 ···...:106 ···...:
107 1.14·ms·+-·28.9·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each)107 1.16·ms·+-·9.2·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each)
108 2.26·ms·+-·148·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each)108 2.03·ms·+-·15.8·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each)
109 In·[4]:·%timeit·-n·1·rng.standard_exponential(100000)109 In·[4]:·%timeit·-n·1·rng.standard_exponential(100000)
110 ···...:·%timeit·-n·1·numpy.random.standard_exponential(100000)110 ···...:·%timeit·-n·1·numpy.random.standard_exponential(100000)
111 ···...:111 ···...:
112 545·us·+-·16.2·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each)112 524·us·+-·21·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each)
113 1.61·ms·+-·69.9·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each)113 1.38·ms·+-·12.7·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each)
114 In·[5]:·%timeit·-n·1·rng.standard_gamma(3.0,·100000)114 In·[5]:·%timeit·-n·1·rng.standard_gamma(3.0,·100000)
115 ···...:·%timeit·-n·1·numpy.random.standard_gamma(3.0,·100000)115 ···...:·%timeit·-n·1·numpy.random.standard_gamma(3.0,·100000)
116 ···...:116 ···...:
117 2.2·ms·+-·18.5·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each)117 2.14·ms·+-·33.3·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each)
118 4.44·ms·+-·29.9·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each)118 4.16·ms·+-·24.4·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each)
119 ····*·_\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r_\x8s·is·now·the·canonical·way·to·generate·integer·random·numbers·from119 ····*·_\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r_\x8s·is·now·the·canonical·way·to·generate·integer·random·numbers·from
120 ······a·discrete·uniform·distribution.·This·replaces·both·_\x8r_\x8a_\x8n_\x8d_\x8i_\x8n_\x8t·and·the120 ······a·discrete·uniform·distribution.·This·replaces·both·_\x8r_\x8a_\x8n_\x8d_\x8i_\x8n_\x8t·and·the
121 ······deprecated·_\x8r_\x8a_\x8n_\x8d_\x8o_\x8m_\x8__\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r_\x8s.121 ······deprecated·_\x8r_\x8a_\x8n_\x8d_\x8o_\x8m_\x8__\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r_\x8s.
122 ····*·The·_\x8r_\x8a_\x8n_\x8d·and·_\x8r_\x8a_\x8n_\x8d_\x8n·methods·are·only·available·through·the·legacy122 ····*·The·_\x8r_\x8a_\x8n_\x8d·and·_\x8r_\x8a_\x8n_\x8d_\x8n·methods·are·only·available·through·the·legacy
123 ······_\x8R_\x8a_\x8n_\x8d_\x8o_\x8m_\x8S_\x8t_\x8a_\x8t_\x8e.123 ······_\x8R_\x8a_\x8n_\x8d_\x8o_\x8m_\x8S_\x8t_\x8a_\x8t_\x8e.
124 ····*·_\x8G_\x8e_\x8n_\x8e_\x8r_\x8a_\x8t_\x8o_\x8r_\x8._\x8r_\x8a_\x8n_\x8d_\x8o_\x8m·is·now·the·canonical·way·to·generate·floating-point124 ····*·_\x8G_\x8e_\x8n_\x8e_\x8r_\x8a_\x8t_\x8o_\x8r_\x8._\x8r_\x8a_\x8n_\x8d_\x8o_\x8m·is·now·the·canonical·way·to·generate·floating-point
125 ······random·numbers,·which·replaces·_\x8R_\x8a_\x8n_\x8d_\x8o_\x8m_\x8S_\x8t_\x8a_\x8t_\x8e_\x8._\x8r_\x8a_\x8n_\x8d_\x8o_\x8m_\x8__\x8s_\x8a_\x8m_\x8p_\x8l_\x8e,·_\x8s_\x8a_\x8m_\x8p_\x8l_\x8e,·and125 ······random·numbers,·which·replaces·_\x8R_\x8a_\x8n_\x8d_\x8o_\x8m_\x8S_\x8t_\x8a_\x8t_\x8e_\x8._\x8r_\x8a_\x8n_\x8d_\x8o_\x8m_\x8__\x8s_\x8a_\x8m_\x8p_\x8l_\x8e,·_\x8s_\x8a_\x8m_\x8p_\x8l_\x8e,·and
Offset 140, 38 lines modifiedOffset 140, 38 lines modified
140 ··········o·Uniforms·(_\x8r_\x8a_\x8n_\x8d_\x8o_\x8m·and·_\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r_\x8s)140 ··········o·Uniforms·(_\x8r_\x8a_\x8n_\x8d_\x8o_\x8m·and·_\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r_\x8s)
141 ··········o·Normals·(_\x8s_\x8t_\x8a_\x8n_\x8d_\x8a_\x8r_\x8d_\x8__\x8n_\x8o_\x8r_\x8m_\x8a_\x8l)141 ··········o·Normals·(_\x8s_\x8t_\x8a_\x8n_\x8d_\x8a_\x8r_\x8d_\x8__\x8n_\x8o_\x8r_\x8m_\x8a_\x8l)
142 ··········o·Standard·Gammas·(_\x8s_\x8t_\x8a_\x8n_\x8d_\x8a_\x8r_\x8d_\x8__\x8g_\x8a_\x8m_\x8m_\x8a)142 ··········o·Standard·Gammas·(_\x8s_\x8t_\x8a_\x8n_\x8d_\x8a_\x8r_\x8d_\x8__\x8g_\x8a_\x8m_\x8m_\x8a)
143 ··········o·Standard·Exponentials·(_\x8s_\x8t_\x8a_\x8n_\x8d_\x8a_\x8r_\x8d_\x8__\x8e_\x8x_\x8p_\x8o_\x8n_\x8e_\x8n_\x8t_\x8i_\x8a_\x8l)143 ··········o·Standard·Exponentials·(_\x8s_\x8t_\x8a_\x8n_\x8d_\x8a_\x8r_\x8d_\x8__\x8e_\x8x_\x8p_\x8o_\x8n_\x8e_\x8n_\x8t_\x8i_\x8a_\x8l)
144 In·[6]:·rng·=·np.random.default_rng()144 In·[6]:·rng·=·np.random.default_rng()
  
145 In·[7]:·rng.random(3,·dtype=np.float64)145 In·[7]:·rng.random(3,·dtype=np.float64)
146 Out[7]:·array([0.52982092,·0.42295032,·0.24147651])146 Out[7]:·array([0.29293961,·0.65281904,·0.13724775])
  
147 In·[8]:·rng.random(3,·dtype=np.float32)147 In·[8]:·rng.random(3,·dtype=np.float32)
148 Out[8]:·array([0.9568871·,·0.1235407·,·0.99757785],·dtype=float32)148 Out[8]:·array([0.96676505,·0.3154664·,·0.50938195],·dtype=float32)
  
149 In·[9]:·rng.integers(0,·256,·size=3,·dtype=np.uint8)149 In·[9]:·rng.integers(0,·256,·size=3,·dtype=np.uint8)
150 Out[9]:·array([·71,·215,··84],·dtype=uint8)150 Out[9]:·array([33,·49,·40],·dtype=uint8)
151 ····*·Optional·out·argument·that·allows·existing·arrays·to·be·filled·for·select151 ····*·Optional·out·argument·that·allows·existing·arrays·to·be·filled·for·select
152 ······distributions152 ······distributions
153 ··········o·Uniforms·(_\x8r_\x8a_\x8n_\x8d_\x8o_\x8m)153 ··········o·Uniforms·(_\x8r_\x8a_\x8n_\x8d_\x8o_\x8m)
154 ··········o·Normals·(_\x8s_\x8t_\x8a_\x8n_\x8d_\x8a_\x8r_\x8d_\x8__\x8n_\x8o_\x8r_\x8m_\x8a_\x8l)154 ··········o·Normals·(_\x8s_\x8t_\x8a_\x8n_\x8d_\x8a_\x8r_\x8d_\x8__\x8n_\x8o_\x8r_\x8m_\x8a_\x8l)
155 ··········o·Standard·Gammas·(_\x8s_\x8t_\x8a_\x8n_\x8d_\x8a_\x8r_\x8d_\x8__\x8g_\x8a_\x8m_\x8m_\x8a)155 ··········o·Standard·Gammas·(_\x8s_\x8t_\x8a_\x8n_\x8d_\x8a_\x8r_\x8d_\x8__\x8g_\x8a_\x8m_\x8m_\x8a)
156 ··········o·Standard·Exponentials·(_\x8s_\x8t_\x8a_\x8n_\x8d_\x8a_\x8r_\x8d_\x8__\x8e_\x8x_\x8p_\x8o_\x8n_\x8e_\x8n_\x8t_\x8i_\x8a_\x8l)156 ··········o·Standard·Exponentials·(_\x8s_\x8t_\x8a_\x8n_\x8d_\x8a_\x8r_\x8d_\x8__\x8e_\x8x_\x8p_\x8o_\x8n_\x8e_\x8n_\x8t_\x8i_\x8a_\x8l)
157 ······This·allows·multithreading·to·fill·large·arrays·in·chunks·using·suitable157 ······This·allows·multithreading·to·fill·large·arrays·in·chunks·using·suitable
158 ······BitGenerators·in·parallel.158 ······BitGenerators·in·parallel.
159 In·[10]:·rng·=·np.random.default_rng()159 In·[10]:·rng·=·np.random.default_rng()
  
160 In·[11]:·existing·=·np.zeros(4)160 In·[11]:·existing·=·np.zeros(4)
  
161 In·[12]:·rng.random(out=existing[:2])161 In·[12]:·rng.random(out=existing[:2])
162 Out[12]:·array([0.62682846,·0.76426864])162 Out[12]:·array([0.5231906·,·0.65732983])
  
163 In·[13]:·print(existing)163 In·[13]:·print(existing)
164 [0.62682846·0.76426864·0.·········0.········]164 [0.5231906··0.65732983·0.·········0.········]
165 ····*·Optional·axis·argument·for·methods·like·_\x8c_\x8h_\x8o_\x8i_\x8c_\x8e,·_\x8p_\x8e_\x8r_\x8m_\x8u_\x8t_\x8a_\x8t_\x8i_\x8o_\x8n·and·_\x8s_\x8h_\x8u_\x8f_\x8f_\x8l_\x8e165 ····*·Optional·axis·argument·for·methods·like·_\x8c_\x8h_\x8o_\x8i_\x8c_\x8e,·_\x8p_\x8e_\x8r_\x8m_\x8u_\x8t_\x8a_\x8t_\x8i_\x8o_\x8n·and·_\x8s_\x8h_\x8u_\x8f_\x8f_\x8l_\x8e
166 ······that·controls·which·axis·an·operation·is·performed·over·for·multi-166 ······that·controls·which·axis·an·operation·is·performed·over·for·multi-
167 ······dimensional·arrays.167 ······dimensional·arrays.
168 In·[14]:·rng·=·np.random.default_rng()168 In·[14]:·rng·=·np.random.default_rng()
  
169 In·[15]:·a·=·np.arange(12).reshape((3,·4))169 In·[15]:·a·=·np.arange(12).reshape((3,·4))
  
Offset 179, 25 lines modifiedOffset 179, 25 lines modified
179 Out[16]:179 Out[16]:
180 array([[·0,··1,··2,··3],180 array([[·0,··1,··2,··3],
181 ·······[·4,··5,··6,··7],181 ·······[·4,··5,··6,··7],
182 ·······[·8,··9,·10,·11]])182 ·······[·8,··9,·10,·11]])
  
183 In·[17]:·rng.choice(a,·axis=1,·size=5)183 In·[17]:·rng.choice(a,·axis=1,·size=5)
184 Out[17]:184 Out[17]:
185 array([[·2,··1,··0,··3,··2], 
186 ·······[·6,··5,··4,··7,··6], 
187 ·······[10,··9,··8,·11,·10]])185 array([[·3,··2,··2,··2,··0],
 186 ·······[·7,··6,··6,··6,··4],
 187 ·······[11,·10,·10,·10,··8]])
  
188 In·[18]:·rng.shuffle(a,·axis=1)········#·Shuffle·in-place188 In·[18]:·rng.shuffle(a,·axis=1)········#·Shuffle·in-place
  
189 In·[19]:·a189 In·[19]:·a
190 Out[19]:190 Out[19]:
191 array([[·1,··2,··3,··0],191 array([[·1,··3,··2,··0],
192 ·······[·5,··6,··7,··4],192 ·······[·5,··7,··6,··4],
193 ·······[·9,·10,·11,··8]])193 ·······[·9,·11,·10,··8]])
194 ····*·Added·a·method·to·sample·from·the·complex·normal·distribution194 ····*·Added·a·method·to·sample·from·the·complex·normal·distribution
195 ······(c\x8co\x8om\x8mp\x8pl\x8le\x8ex\x8x_\x8_n\x8no\x8or\x8rm\x8ma\x8al\x8l)195 ······(c\x8co\x8om\x8mp\x8pl\x8le\x8ex\x8x_\x8_n\x8no\x8or\x8rm\x8ma\x8al\x8l)
196 _\x8p_\x8r_\x8e_\x8v_\x8i_\x8o_\x8u_\x8s196 _\x8p_\x8r_\x8e_\x8v_\x8i_\x8o_\x8u_\x8s
197 _\x8M_\x8u_\x8l_\x8t_\x8i_\x8t_\x8h_\x8r_\x8e_\x8a_\x8d_\x8e_\x8d_\x8·_\x8g_\x8e_\x8n_\x8e_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n197 _\x8M_\x8u_\x8l_\x8t_\x8i_\x8t_\x8h_\x8r_\x8e_\x8a_\x8d_\x8e_\x8d_\x8·_\x8g_\x8e_\x8n_\x8e_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n
198 _\x8n_\x8e_\x8x_\x8t198 _\x8n_\x8e_\x8x_\x8t
199 _\x8P_\x8e_\x8r_\x8f_\x8o_\x8r_\x8m_\x8a_\x8n_\x8c_\x8e199 _\x8P_\x8e_\x8r_\x8f_\x8o_\x8r_\x8m_\x8a_\x8n_\x8c_\x8e
200 ©·Copyright·2008-2025,·NumPy·Developers.200 ©·Copyright·2008-2025,·NumPy·Developers.
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./usr/share/doc/python-numpy/html/reference/routines.polynomials.html
    
Offset 609, 31 lines modifiedOffset 609, 31 lines modified
  
609 <span·class="gp">In·[3]:·</span><span·class="n">y</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="o">+</span>·<span·class="n">rng</span><span·class="o">.</span><span·class="n">standard_normal</span><span·class="p">(</span><span·class="mi">10</span><span·class="p">)</span>609 <span·class="gp">In·[3]:·</span><span·class="n">y</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="o">+</span>·<span·class="n">rng</span><span·class="o">.</span><span·class="n">standard_normal</span><span·class="p">(</span><span·class="mi">10</span><span·class="p">)</span>
610 </pre></div>610 </pre></div>
611 </div>611 </div>
612 <p>With·the·legacy·polynomial·module,·a·linear·fit·(i.e.·polynomial·of·degree·1)612 <p>With·the·legacy·polynomial·module,·a·linear·fit·(i.e.·polynomial·of·degree·1)
613 could·be·applied·to·these·data·with·<a·class="reference·internal"·href="generated/numpy.polyfit.html#numpy.polyfit"·title="numpy.polyfit"><code·class="xref·py·py-obj·docutils·literal·notranslate"><span·class="pre">polyfit</span></code></a>:</p>613 could·be·applied·to·these·data·with·<a·class="reference·internal"·href="generated/numpy.polyfit.html#numpy.polyfit"·title="numpy.polyfit"><code·class="xref·py·py-obj·docutils·literal·notranslate"><span·class="pre">polyfit</span></code></a>:</p>
614 <div·class="highlight-ipython·notranslate"><div·class="highlight"><pre><span></span><span·class="gp">In·[4]:·</span><span·class="n">np</span><span·class="o">.</span><span·class="n">polyfit</span><span·class="p">(</span><span·class="n">x</span><span·class="p">,</span>·<span·class="n">y</span><span·class="p">,</span>·<span·class="n">deg</span><span·class="o">=</span><span·class="mi">1</span><span·class="p">)</span>614 <div·class="highlight-ipython·notranslate"><div·class="highlight"><pre><span></span><span·class="gp">In·[4]:·</span><span·class="n">np</span><span·class="o">.</span><span·class="n">polyfit</span><span·class="p">(</span><span·class="n">x</span><span·class="p">,</span>·<span·class="n">y</span><span·class="p">,</span>·<span·class="n">deg</span><span·class="o">=</span><span·class="mi">1</span><span·class="p">)</span>
615 <span·class="gh">Out[4]:·</span><span·class="go">array([1.00621178,·0.14101989])</span>615 <span·class="gh">Out[4]:·</span><span·class="go">array([·0.91501666,·-0.00424889])</span>
616 </pre></div>616 </pre></div>
617 </div>617 </div>
618 <p>With·the·new·polynomial·API,·the·<a·class="reference·internal"·href="generated/numpy.polynomial.polynomial.Polynomial.fit.html#numpy.polynomial.polynomial.Polynomial.fit"·title="numpy.polynomial.polynomial.Polynomial.fit"><code·class="xref·py·py-obj·docutils·literal·notranslate"><span·class="pre">fit</span></code></a>618 <p>With·the·new·polynomial·API,·the·<a·class="reference·internal"·href="generated/numpy.polynomial.polynomial.Polynomial.fit.html#numpy.polynomial.polynomial.Polynomial.fit"·title="numpy.polynomial.polynomial.Polynomial.fit"><code·class="xref·py·py-obj·docutils·literal·notranslate"><span·class="pre">fit</span></code></a>
619 class·method·is·preferred:</p>619 class·method·is·preferred:</p>
620 <div·class="highlight-ipython·notranslate"><div·class="highlight"><pre><span></span><span·class="gp">In·[5]:·</span><span·class="n">p_fitted</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">polynomial</span><span·class="o">.</span><span·class="n">Polynomial</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">(</span><span·class="n">x</span><span·class="p">,</span>·<span·class="n">y</span><span·class="p">,</span>·<span·class="n">deg</span><span·class="o">=</span><span·class="mi">1</span><span·class="p">)</span>620 <div·class="highlight-ipython·notranslate"><div·class="highlight"><pre><span></span><span·class="gp">In·[5]:·</span><span·class="n">p_fitted</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">polynomial</span><span·class="o">.</span><span·class="n">Polynomial</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">(</span><span·class="n">x</span><span·class="p">,</span>·<span·class="n">y</span><span·class="p">,</span>·<span·class="n">deg</span><span·class="o">=</span><span·class="mi">1</span><span·class="p">)</span>
  
621 <span·class="gp">In·[6]:·</span><span·class="n">p_fitted</span>621 <span·class="gp">In·[6]:·</span><span·class="n">p_fitted</span>
622 <span·class="gh">Out[6]:·</span><span·class="go">Polynomial([4.66897291,·4.52795303],·domain=[0.,·9.],·window=[-1.,··1.],·symbol=&#39;x&#39;)</span>622 <span·class="gh">Out[6]:·</span><span·class="go">Polynomial([4.11332609,·4.11757499],·domain=[0.,·9.],·window=[-1.,··1.],·symbol=&#39;x&#39;)</span>
623 </pre></div>623 </pre></div>
624 </div>624 </div>
625 <p>Note·that·the·coefficients·are·given·<em>in·the·scaled·domain</em>·defined·by·the625 <p>Note·that·the·coefficients·are·given·<em>in·the·scaled·domain</em>·defined·by·the
626 linear·mapping·between·the·<code·class="docutils·literal·notranslate"><span·class="pre">window</span></code>·and·<code·class="docutils·literal·notranslate"><span·class="pre">domain</span></code>.626 linear·mapping·between·the·<code·class="docutils·literal·notranslate"><span·class="pre">window</span></code>·and·<code·class="docutils·literal·notranslate"><span·class="pre">domain</span></code>.
627 <a·class="reference·internal"·href="generated/numpy.polynomial.polynomial.Polynomial.convert.html#numpy.polynomial.polynomial.Polynomial.convert"·title="numpy.polynomial.polynomial.Polynomial.convert"><code·class="xref·py·py-obj·docutils·literal·notranslate"><span·class="pre">convert</span></code></a>·can·be·used·to·get·the627 <a·class="reference·internal"·href="generated/numpy.polynomial.polynomial.Polynomial.convert.html#numpy.polynomial.polynomial.Polynomial.convert"·title="numpy.polynomial.polynomial.Polynomial.convert"><code·class="xref·py·py-obj·docutils·literal·notranslate"><span·class="pre">convert</span></code></a>·can·be·used·to·get·the
628 coefficients·in·the·unscaled·data·domain.</p>628 coefficients·in·the·unscaled·data·domain.</p>
629 <div·class="highlight-ipython·notranslate"><div·class="highlight"><pre><span></span><span·class="gp">In·[7]:·</span><span·class="n">p_fitted</span><span·class="o">.</span><span·class="n">convert</span><span·class="p">()</span>629 <div·class="highlight-ipython·notranslate"><div·class="highlight"><pre><span></span><span·class="gp">In·[7]:·</span><span·class="n">p_fitted</span><span·class="o">.</span><span·class="n">convert</span><span·class="p">()</span>
630 <span·class="gh">Out[7]:·</span><span·class="go">Polynomial([0.14101989,·1.00621178],·domain=[-1.,··1.],·window=[-1.,··1.],·symbol=&#39;x&#39;)</span>630 <span·class="gh">Out[7]:·</span><span·class="go">Polynomial([-0.00424889,··0.91501666],·domain=[-1.,··1.],·window=[-1.,··1.],·symbol=&#39;x&#39;)</span>
631 </pre></div>631 </pre></div>
632 </div>632 </div>
633 </section>633 </section>
634 </section>634 </section>
635 <section·id="documentation-for-the-polynomial-package">635 <section·id="documentation-for-the-polynomial-package">
636 <h2>Documentation·for·the·<a·class="reference·internal"·href="routines.polynomials-package.html#module-numpy.polynomial"·title="numpy.polynomial"><code·class="xref·py·py-obj·docutils·literal·notranslate"><span·class="pre">polynomial</span></code></a>·package<a·class="headerlink"·href="#documentation-for-the-polynomial-package"·title="Link·to·this·heading">#</a></h2>636 <h2>Documentation·for·the·<a·class="reference·internal"·href="routines.polynomials-package.html#module-numpy.polynomial"·title="numpy.polynomial"><code·class="xref·py·py-obj·docutils·literal·notranslate"><span·class="pre">polynomial</span></code></a>·package<a·class="headerlink"·href="#documentation-for-the-polynomial-package"·title="Link·to·this·heading">#</a></h2>
637 <p>In·addition·to·standard·power·series·polynomials,·the·polynomial·package637 <p>In·addition·to·standard·power·series·polynomials,·the·polynomial·package
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Offset 150, 26 lines modifiedOffset 150, 26 lines modified
  
150 In·[2]:·x·=·np.arange(10)150 In·[2]:·x·=·np.arange(10)
  
151 In·[3]:·y·=·np.arange(10)·+·rng.standard_normal(10)151 In·[3]:·y·=·np.arange(10)·+·rng.standard_normal(10)
152 With·the·legacy·polynomial·module,·a·linear·fit·(i.e.·polynomial·of·degree·1)152 With·the·legacy·polynomial·module,·a·linear·fit·(i.e.·polynomial·of·degree·1)
153 could·be·applied·to·these·data·with·_\x8p_\x8o_\x8l_\x8y_\x8f_\x8i_\x8t:153 could·be·applied·to·these·data·with·_\x8p_\x8o_\x8l_\x8y_\x8f_\x8i_\x8t:
154 In·[4]:·np.polyfit(x,·y,·deg=1)154 In·[4]:·np.polyfit(x,·y,·deg=1)
155 Out[4]:·array([1.00621178,·0.14101989])155 Out[4]:·array([·0.91501666,·-0.00424889])
156 With·the·new·polynomial·API,·the·_\x8f_\x8i_\x8t·class·method·is·preferred:156 With·the·new·polynomial·API,·the·_\x8f_\x8i_\x8t·class·method·is·preferred:
157 In·[5]:·p_fitted·=·np.polynomial.Polynomial.fit(x,·y,·deg=1)157 In·[5]:·p_fitted·=·np.polynomial.Polynomial.fit(x,·y,·deg=1)
  
158 In·[6]:·p_fitted158 In·[6]:·p_fitted
159 Out[6]:·Polynomial([4.66897291,·4.52795303],·domain=[0.,·9.],·window=[-1.,159 Out[6]:·Polynomial([4.11332609,·4.11757499],·domain=[0.,·9.],·window=[-1.,
160 1.],·symbol='x')160 1.],·symbol='x')
161 Note·that·the·coefficients·are·given·i\x8in\x8n·t\x8th\x8he\x8e·s\x8sc\x8ca\x8al\x8le\x8ed\x8d·d\x8do\x8om\x8ma\x8ai\x8in\x8n·defined·by·the·linear161 Note·that·the·coefficients·are·given·i\x8in\x8n·t\x8th\x8he\x8e·s\x8sc\x8ca\x8al\x8le\x8ed\x8d·d\x8do\x8om\x8ma\x8ai\x8in\x8n·defined·by·the·linear
162 mapping·between·the·window·and·domain.·_\x8c_\x8o_\x8n_\x8v_\x8e_\x8r_\x8t·can·be·used·to·get·the162 mapping·between·the·window·and·domain.·_\x8c_\x8o_\x8n_\x8v_\x8e_\x8r_\x8t·can·be·used·to·get·the
163 coefficients·in·the·unscaled·data·domain.163 coefficients·in·the·unscaled·data·domain.
164 In·[7]:·p_fitted.convert()164 In·[7]:·p_fitted.convert()
165 Out[7]:·Polynomial([0.14101989,·1.00621178],·domain=[-1.,··1.],·window=[-1.,165 Out[7]:·Polynomial([-0.00424889,··0.91501666],·domain=[-1.,··1.],·window=[-1.,
166 1.],·symbol='x')166 1.],·symbol='x')
167 *\x8**\x8**\x8**\x8**\x8*·D\x8Do\x8oc\x8cu\x8um\x8me\x8en\x8nt\x8ta\x8at\x8ti\x8io\x8on\x8n·f\x8fo\x8or\x8r·t\x8th\x8he\x8e·_\x8p\x8p_\x8o\x8o_\x8l\x8l_\x8y\x8y_\x8n\x8n_\x8o\x8o_\x8m\x8m_\x8i\x8i_\x8a\x8a_\x8l\x8l·p\x8pa\x8ac\x8ck\x8ka\x8ag\x8ge\x8e_\x8#\x8#·*\x8**\x8**\x8**\x8**\x8*167 *\x8**\x8**\x8**\x8**\x8*·D\x8Do\x8oc\x8cu\x8um\x8me\x8en\x8nt\x8ta\x8at\x8ti\x8io\x8on\x8n·f\x8fo\x8or\x8r·t\x8th\x8he\x8e·_\x8p\x8p_\x8o\x8o_\x8l\x8l_\x8y\x8y_\x8n\x8n_\x8o\x8o_\x8m\x8m_\x8i\x8i_\x8a\x8a_\x8l\x8l·p\x8pa\x8ac\x8ck\x8ka\x8ag\x8ge\x8e_\x8#\x8#·*\x8**\x8**\x8**\x8**\x8*
168 In·addition·to·standard·power·series·polynomials,·the·polynomial·package168 In·addition·to·standard·power·series·polynomials,·the·polynomial·package
169 provides·several·additional·kinds·of·polynomials·including·Chebyshev,·Hermite169 provides·several·additional·kinds·of·polynomials·including·Chebyshev,·Hermite
170 (two·subtypes),·Laguerre,·and·Legendre·polynomials.·Each·of·these·has·an170 (two·subtypes),·Laguerre,·and·Legendre·polynomials.·Each·of·these·has·an
171 associated·c\x8co\x8on\x8nv\x8ve\x8en\x8ni\x8ie\x8en\x8nc\x8ce\x8e·c\x8cl\x8la\x8as\x8ss\x8s·available·from·the·_\x8n_\x8u_\x8m_\x8p_\x8y_\x8._\x8p_\x8o_\x8l_\x8y_\x8n_\x8o_\x8m_\x8i_\x8a_\x8l·namespace·that171 associated·c\x8co\x8on\x8nv\x8ve\x8en\x8ni\x8ie\x8en\x8nc\x8ce\x8e·c\x8cl\x8la\x8as\x8ss\x8s·available·from·the·_\x8n_\x8u_\x8m_\x8p_\x8y_\x8._\x8p_\x8o_\x8l_\x8y_\x8n_\x8o_\x8m_\x8i_\x8a_\x8l·namespace·that
172 provides·a·consistent·interface·for·working·with·polynomials·regardless·of172 provides·a·consistent·interface·for·working·with·polynomials·regardless·of
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32327 ········"0010":·1519,32327 ········"0010":·1519,
32328 ········"0011":·138,32328 ········"0011":·138,
32329 ········"001637457145670096":·2315,32329 ········"001637457145670096":·2315,
32330 ········"001j":·[1596,·1653,·1710,·1767,·1824,·1879,·1893],32330 ········"001j":·[1596,·1653,·1710,·1767,·1824,·1879,·1893],
32331 ········"002":·[1335,·1602,·1659,·1716,·1773,·1830,·1886],32331 ········"002":·[1335,·1602,·1659,·1716,·1773,·1830,·1886],
32332 ········"0024":·477,32332 ········"0024":·477,
32333 ········"003":·[2327,·2372,·2419],32333 ········"003":·[2327,·2372,·2419],
 32334 ········"00424889":·2488,
32334 ········"005":·2188,32335 ········"005":·2188,
32335 ········"0050000029":·[357,·359],32336 ········"0050000029":·[357,·359],
32336 ········"0050045159":·[357,·359],32337 ········"0050045159":·[357,·359],
32337 ········"00578369":·1754,32338 ········"00578369":·1754,
32338 ········"00621178":·2488, 
32339 ········"00625":·1585,32339 ········"00625":·1585,
32340 ········"007000999997857":·1541,32340 ········"007000999997857":·1541,
32341 ········"00867716":·[2319,·2363,·2410],32341 ········"00867716":·[2319,·2363,·2410],
32342 ········"00950034":·[2339,·2352,·2382,·2389,·2399,·2429,·2436,·2449],32342 ········"00950034":·[2339,·2352,·2382,·2389,·2399,·2429,·2436,·2449],
32343 ········"009a87ff44bf":·42,32343 ········"009a87ff44bf":·42,
32344 ········"00j":·[514,·642,·2167],32344 ········"00j":·[514,·642,·2167],
32345 ········"01":·[41,·42,·45,·54,·55,·62,·147,·162,·163,·164,·335,·361,·410,·514,·547,·557,·566,·669,·897,·1088,·1094,·1586,·1594,·1601,·1658,·1715,·1772,·1829,·1885,·2104,·2160,·2252,·2323,·2329,·2367,·2373,·2414,·2420,·2525,·2658],32345 ········"01":·[41,·42,·45,·54,·55,·62,·147,·162,·163,·164,·335,·361,·410,·514,·547,·557,·566,·669,·897,·1088,·1094,·1586,·1594,·1601,·1658,·1715,·1772,·1829,·1885,·2104,·2160,·2252,·2323,·2329,·2367,·2373,·2414,·2420,·2525,·2658],
Offset 32369, 15 lines modifiedOffset 32369, 15 lines modified
32369 ········"0253":·2652,32369 ········"0253":·2652,
32370 ········"02654825":·1891,32370 ········"02654825":·1891,
32371 ········"02658058e":·2666,32371 ········"02658058e":·2666,
32372 ········"02755911":·2666,32372 ········"02755911":·2666,
32373 ········"027559113243068367":·2666,32373 ········"027559113243068367":·2666,
32374 ········"02785049":·1867,32374 ········"02785049":·1867,
32375 ········"02i":·[513,·2644],32375 ········"02i":·[513,·2644],
32376 ········"03":·[55,·67,·163,·566,·669,·1335,·1586,·1816,·2658],32376 ········"03":·[55,·67,·163,·566,·669,·1335,·1586,·1816,·2461,·2658],
32377 ········"03125":·[1585,·2491],32377 ········"03125":·[1585,·2491],
32378 ········"0326911":·[2335,·2378,·2425],32378 ········"0326911":·[2335,·2378,·2425],
32379 ········"0361":·2607,32379 ········"0361":·2607,
32380 ········"03703704":·1809,32380 ········"03703704":·1809,
32381 ········"03943254e":·2104,32381 ········"03943254e":·2104,
32382 ········"03968254":·[1113,·1543],32382 ········"03968254":·[1113,·1543],
32383 ········"0396842":·680,32383 ········"0396842":·680,
Offset 32615, 14 lines modifiedOffset 32615, 15 lines modified
32615 ········"11218":·2542,32615 ········"11218":·2542,
32616 ········"11219":·2539,32616 ········"11219":·2539,
32617 ········"11251":·2539,32617 ········"11251":·2539,
32618 ········"11274":·2540,32618 ········"11274":·2540,
32619 ········"11294":·2540,32619 ········"11294":·2540,
32620 ········"113":·[674,·2463,·2666],32620 ········"113":·[674,·2463,·2666],
32621 ········"11308":·2542,32621 ········"11308":·2542,
 32622 ········"11332609":·2488,
32622 ········"1138":·2612,32623 ········"1138":·2612,
32623 ········"114":·2463,32624 ········"114":·2463,
32624 ········"11407192":·1822,32625 ········"11407192":·1822,
32625 ········"1142":·[2353,·2400,·2450],32626 ········"1142":·[2353,·2400,·2450],
32626 ········"1149":·2612,32627 ········"1149":·2612,
32627 ········"115":·[1654,·2463],32628 ········"115":·[1654,·2463],
32628 ········"1151":·657,32629 ········"1151":·657,
Offset 32639, 14 lines modifiedOffset 32640, 15 lines modified
32639 ········"11682":·2543,32640 ········"11682":·2543,
32640 ········"11698":·2543,32641 ········"11698":·2543,
32641 ········"11700":·2543,32642 ········"11700":·2543,
32642 ········"11719":·2543,32643 ········"11719":·2543,
32643 ········"11720":·2543,32644 ········"11720":·2543,
32644 ········"11746":·2543,32645 ········"11746":·2543,
32645 ········"11757":·2543,32646 ········"11757":·2543,
 32647 ········"11757499":·2488,
32646 ········"11758":·2543,32648 ········"11758":·2543,
32647 ········"11759":·2543,32649 ········"11759":·2543,
32648 ········"11760":·2543,32650 ········"11760":·2543,
32649 ········"11761":·2543,32651 ········"11761":·2543,
32650 ········"11763":·2543,32652 ········"11763":·2543,
32651 ········"11769564":·2635,32653 ········"11769564":·2635,
32652 ········"117696":·2635,32654 ········"117696":·2635,
Offset 32716, 15 lines modifiedOffset 32718, 14 lines modified
32716 ········"123456789":·[2091,·2393,·2644],32718 ········"123456789":·[2091,·2393,·2644],
32717 ········"12345678903141592653589793":·2299,32719 ········"12345678903141592653589793":·2299,
32718 ········"123456789a12":·25,32720 ········"123456789a12":·25,
32719 ········"123456789a123456789b":·25,32721 ········"123456789a123456789b":·25,
32720 ········"1234567e":·2172,32722 ········"1234567e":·2172,
32721 ········"12346":·2462,32723 ········"12346":·2462,
32722 ········"1235":·2091,32724 ········"1235":·2091,
32723 ········"1235407":·2461, 
32724 ········"123abc":·[302,·305,·2131,·2134],32725 ········"123abc":·[302,·305,·2131,·2134],
32725 ········"124":·[98,·905],32726 ········"124":·[98,·905],
32726 ········"125":·[470,·660,·1114,·1142,·1645,·1651,·1899,·1900,·2239,·2339,·2382,·2429,·2460,·2491,·2659,·2666],32727 ········"125":·[470,·660,·1114,·1142,·1645,·1651,·1899,·1900,·2239,·2339,·2382,·2429,·2460,·2491,·2659,·2666],
32727 ········"12589991e":·645,32728 ········"12589991e":·645,
32728 ········"126":·[863,·1048,·1116,·1904],32729 ········"126":·[863,·1048,·1116,·1904],
32729 ········"1261":·2612,32730 ········"1261":·2612,
32730 ········"12658":·2560,32731 ········"12658":·2560,
Offset 32787, 14 lines modifiedOffset 32788, 15 lines modified
32787 ········"13610":·2560,32788 ········"13610":·2560,
32788 ········"13620":·2551,32789 ········"13620":·2551,
32789 ········"13641":·2551,32790 ········"13641":·2551,
32790 ········"13644":·2551,32791 ········"13644":·2551,
32791 ········"1366":·36,32792 ········"1366":·36,
32792 ········"13698":·2560,32793 ········"13698":·2560,
32793 ········"13710533":·[2319,·2363,·2410],32794 ········"13710533":·[2319,·2363,·2410],
 32795 ········"13724775":·2461,
32794 ········"13742":·2552,32796 ········"13742":·2552,
32795 ········"1377":·2612,32797 ········"1377":·2612,
32796 ········"13794":·2560,32798 ········"13794":·2560,
32797 ········"138":·2463,32799 ········"138":·2463,
32798 ········"13808":·[2553,·2558],32800 ········"13808":·[2553,·2558],
32799 ········"13823":·2552,32801 ········"13823":·2552,
32800 ········"13829":·2560,32802 ········"13829":·2560,
Offset 32825, 15 lines modifiedOffset 32827, 14 lines modified
32825 ········"14052":·2552,32827 ········"14052":·2552,
32826 ········"14056":·2552,32828 ········"14056":·2552,
32827 ········"14057":·2552,32829 ········"14057":·2552,
32828 ········"14058":·2552,32830 ········"14058":·2552,
32829 ········"14084":·2552,32831 ········"14084":·2552,
32830 ········"141":·669,32832 ········"141":·669,
32831 ········"14100":·2560,32833 ········"14100":·2560,
32832 ········"14101989":·2488, 
32833 ········"141120":·2642,32834 ········"141120":·2642,
32834 ········"14112001":·2666,32835 ········"14112001":·2666,
32835 ········"14142":·2560,32836 ········"14142":·2560,
32836 ········"14156":·2555,32837 ········"14156":·2555,
32837 ········"14157":·2555,32838 ········"14157":·2555,
32838 ········"141571941375841":·2202,32839 ········"141571941375841":·2202,
32839 ········"14158":·2555,32840 ········"14158":·2555,
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32945 ········"14720":·2560,32946 ········"14720":·2560,
32946 ········"14730":·2560,32947 ········"14730":·2560,
32947 ········"14758":·2558,32948 ········"14758":·2558,
32948 ········"14771":·2560,32949 ········"14771":·2560,
32949 ········"14777":·2560,32950 ········"14777":·2560,
32950 ········"14781":·2558,32951 ········"14781":·2558,
32951 ········"14787":·2569,32952 ········"14787":·2569,
32952 ········"148":·[2344,·2386,·2433,·2461,·2463],32953 ········"148":·[2344,·2386,·2433,·2463],
32953 ········"14812":·3,32954 ········"14812":·3,
32954 ········"148293216":·2666,32955 ········"148293216":·2666,
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