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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">1.04·ms·+-·89.5·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each)</span>541 <span·class="go">1.03·ms·+-·51·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each)</span>
542 <span·class="go">2.54·ms·+-·27.3·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each)</span>542 <span·class="go">2.52·ms·+-·31.3·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">997·us·+-·10.7·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each)</span>548 <span·class="go">967·us·+-·57.5·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each)</span>
549 <span·class="go">1.88·ms·+-·15.2·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each)</span>549 <span·class="go">1.76·ms·+-·14.6·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">2.46·ms·+-·22.2·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each)</span>555 <span·class="go">2.47·ms·+-·13.8·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each)</span>
556 <span·class="go">4.48·ms·+-·20.1·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each)</span>556 <span·class="go">4.48·ms·+-·14.2·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([0.96688587,·0.66836792,·0.82700037])</span>592 <span·class="gh">Out[7]:·</span><span·class="go">array([0.99809434,·0.78831731,·0.01278104])</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([0.5898092,·0.7809597,·0.8570909],·dtype=float32)</span>594 <span·class="gh">Out[8]:·</span><span·class="go">array([0.81170803,·0.9937773·,·0.4398616·],·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([39,··6,·85],·dtype=uint8)</span>596 <span·class="gh">Out[9]:·</span><span·class="go">array([102,·169,··79],·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([0.90719441,·0.86518206])</span>618 <span·class="gh">Out[12]:·</span><span·class="go">array([0.54036979,·0.97249852])</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">[0.90719441·0.86518206·0.·········0.········]</span>620 <span·class="go">[0.54036979·0.97249852·0.·········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([[·0,··2,··3,··1,··1],</span>642 <span·class="go">array([[·1,··2,··3,··1,··1],</span>
643 <span·class="go">·······[·4,··6,··7,··5,··5],</span>643 <span·class="go">·······[·5,··6,··7,··5,··5],</span>
644 <span·class="go">·······[·8,·10,·11,··9,··9]])</span>644 <span·class="go">·······[·9,·10,·11,··9,··9]])</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([[·3,··0,··1,··2],</span>648 <span·class="go">array([[·1,··2,··0,··3],</span>
649 <span·class="go">·······[·7,··4,··5,··6],</span>649 <span·class="go">·······[·5,··6,··4,··7],</span>
650 <span·class="go">·······[11,··8,··9,·10]])</span>650 <span·class="go">·······[·9,·10,··8,·11]])</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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Offset 102, 26 lines modifiedOffset 102, 26 lines modified
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 1.04·ms·+-·89.5·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each)107 1.03·ms·+-·51·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each)
108 2.54·ms·+-·27.3·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each)108 2.52·ms·+-·31.3·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 ···...:
112 997·us·+-·10.7·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each)112 967·us·+-·57.5·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each)
113 1.88·ms·+-·15.2·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each)113 1.76·ms·+-·14.6·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 2.46·ms·+-·22.2·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each)117 2.47·ms·+-·13.8·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each)
118 4.48·ms·+-·20.1·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each)118 4.48·ms·+-·14.2·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([0.96688587,·0.66836792,·0.82700037])146 Out[7]:·array([0.99809434,·0.78831731,·0.01278104])
  
147 In·[8]:·rng.random(3,·dtype=np.float32)147 In·[8]:·rng.random(3,·dtype=np.float32)
148 Out[8]:·array([0.5898092,·0.7809597,·0.8570909],·dtype=float32)148 Out[8]:·array([0.81170803,·0.9937773·,·0.4398616·],·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([39,··6,·85],·dtype=uint8)150 Out[9]:·array([102,·169,··79],·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([0.90719441,·0.86518206])162 Out[12]:·array([0.54036979,·0.97249852])
  
163 In·[13]:·print(existing)163 In·[13]:·print(existing)
164 [0.90719441·0.86518206·0.·········0.········]164 [0.54036979·0.97249852·0.·········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([[·0,··2,··3,··1,··1],185 array([[·1,··2,··3,··1,··1],
186 ·······[·4,··6,··7,··5,··5],186 ·······[·5,··6,··7,··5,··5],
187 ·······[·8,·10,·11,··9,··9]])187 ·······[·9,·10,·11,··9,··9]])
  
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([[·3,··0,··1,··2],191 array([[·1,··2,··0,··3],
192 ·······[·7,··4,··5,··6],192 ·······[·5,··6,··4,··7],
193 ·······[11,··8,··9,·10]])193 ·······[·9,·10,··8,·11]])
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([0.91752844,·0.85628547])</span>615 <span·class="gh">Out[4]:·</span><span·class="go">array([0.92432591,·0.51143531])</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([4.98516344,·4.12887796],·domain=[0.,·9.],·window=[-1.,··1.],·symbol=&#39;x&#39;)</span>622 <span·class="gh">Out[6]:·</span><span·class="go">Polynomial([4.67090189,·4.15946659],·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([0.85628547,·0.91752844],·domain=[-1.,··1.],·window=[-1.,··1.],·symbol=&#39;x&#39;)</span>630 <span·class="gh">Out[7]:·</span><span·class="go">Polynomial([0.51143531,·0.92432591],·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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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([0.91752844,·0.85628547])155 Out[4]:·array([0.92432591,·0.51143531])
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([4.98516344,·4.12887796],·domain=[0.,·9.],·window=[-1.,159 Out[6]:·Polynomial([4.67090189,·4.15946659],·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([0.85628547,·0.91752844],·domain=[-1.,··1.],·window=[-1.,165 Out[7]:·Polynomial([0.51143531,·0.92432591],·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
32.6 KB
./usr/share/doc/python-numpy/html/searchindex.js
32.5 KB
js-beautify {}
    
Offset 32344, 14 lines modifiedOffset 32344, 15 lines modified
32344 ········"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],32344 ········"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 ········"010":·[653,·1602,·1659,·1716,·1773,·1830,·1886],32345 ········"010":·[653,·1602,·1659,·1716,·1773,·1830,·1886],
32346 ········"0100":·1519,32346 ········"0100":·1519,
32347 ········"01041667":·1585,32347 ········"01041667":·1585,
32348 ········"011":·[1602,·1659,·1716,·1773,·1830,·1886],32348 ········"011":·[1602,·1659,·1716,·1773,·1830,·1886],
32349 ········"012":·[1602,·1659,·1716,·1773,·1830,·1886],32349 ········"012":·[1602,·1659,·1716,·1773,·1830,·1886],
32350 ········"0123456789":·[303,·2132],32350 ········"0123456789":·[303,·2132],
 32351 ········"01278104":·2461,
32351 ········"01280782":·[2335,·2378,·2425],32352 ········"01280782":·[2335,·2378,·2425],
32352 ········"016":·[648,·653],32353 ········"016":·[648,·653],
32353 ········"01652764":·2635,32354 ········"01652764":·2635,
32354 ········"01666667":·1544,32355 ········"01666667":·1544,
32355 ········"016j":·2105,32356 ········"016j":·2105,
32356 ········"01831564":·1660,32357 ········"01831564":·1660,
32357 ········"018318":·[2353,·2400,·2450],32358 ········"018318":·[2353,·2400,·2450],
Offset 32368, 24 lines modifiedOffset 32369, 24 lines modified
32368 ········"0253":·2652,32369 ········"0253":·2652,
32369 ········"02654825":·1891,32370 ········"02654825":·1891,
32370 ········"02658058e":·2666,32371 ········"02658058e":·2666,
32371 ········"02755911":·2666,32372 ········"02755911":·2666,
32372 ········"027559113243068367":·2666,32373 ········"027559113243068367":·2666,
32373 ········"02785049":·1867,32374 ········"02785049":·1867,
32374 ········"02i":·[513,·2644],32375 ········"02i":·[513,·2644],
32375 ········"03":·[55,·67,·163,·566,·669,·1335,·1586,·1816,·2658],32376 ········"03":·[55,·67,·163,·566,·669,·1335,·1586,·1816,·2461,·2658],
32376 ········"03125":·[1585,·2491],32377 ········"03125":·[1585,·2491],
32377 ········"0326911":·[2335,·2378,·2425],32378 ········"0326911":·[2335,·2378,·2425],
32378 ········"0361":·2607,32379 ········"0361":·2607,
32379 ········"03703704":·1809,32380 ········"03703704":·1809,
32380 ········"03943254e":·2104,32381 ········"03943254e":·2104,
32381 ········"03968254":·[1113,·1543],32382 ········"03968254":·[1113,·1543],
32382 ········"0396842":·680,32383 ········"0396842":·680,
32383 ········"03t13":·55,32384 ········"03t13":·55,
32384 ········"04":·[54,·55,·164,·410,·547,·1586,·2461,·2463,·2594,·2659],32385 ········"04":·[54,·55,·164,·410,·547,·1586,·2463,·2594,·2659],
32385 ········"0400":·360,32386 ········"0400":·360,
32386 ········"04097352":·2635,32387 ········"04097352":·2635,
32387 ········"04166667":·[1544,·1585],32388 ········"04166667":·[1544,·1585],
32388 ········"04211c6":·2521,32389 ········"04211c6":·2521,
32389 ········"04551152e":·2104,32390 ········"04551152e":·2104,
32390 ········"04719755":·1911,32391 ········"04719755":·1911,
32391 ········"05":·[55,·91,·163,·410,·548,·669,·896,·1095,·1871,·2083,·2173,·2353,·2400,·2450,·2648],32392 ········"05":·[55,·91,·163,·410,·548,·669,·896,·1095,·1871,·2083,·2173,·2353,·2400,·2450,·2648],
Offset 32500, 15 lines modifiedOffset 32501, 15 lines modified
32500 ········"100j":·1909,32501 ········"100j":·1909,
32501 ········"100x5":·652,32502 ········"100x5":·652,
32502 ········"101":·[86,·137,·138,·143,·145,·570,·1325,·2077,·2463,·2666],32503 ········"101":·[86,·137,·138,·143,·145,·570,·1325,·2077,·2463,·2666],
32503 ········"1010":·[145,·1519,·2077],32504 ········"1010":·[145,·1519,·2077],
32504 ········"10100":·[143,·570],32505 ········"10100":·[143,·570],
32505 ········"1015":·2592,32506 ········"1015":·2592,
32506 ········"10151":·2560,32507 ········"10151":·2560,
32507 ········"102":·[2463,·2637,·2666],32508 ········"102":·[2461,·2463,·2637,·2666],
32508 ········"1023":·[141,·2583],32509 ········"1023":·[141,·2583],
32509 ········"1024":·[66,·72,·2658],32510 ········"1024":·[66,·72,·2658],
32510 ········"10240":·977,32511 ········"10240":·977,
32511 ········"103":·2463,32512 ········"103":·2463,
32512 ········"10330":·55,32513 ········"10330":·55,
32513 ········"10339":·[2536,·2542],32514 ········"10339":·[2536,·2542],
32514 ········"1035":·[1643,·1655],32515 ········"1035":·[1643,·1655],
Offset 32734, 15 lines modifiedOffset 32735, 14 lines modified
32734 ········"12769":·2548,32735 ········"12769":·2548,
32735 ········"12773":·2548,32736 ········"12773":·2548,
32736 ········"128":·[56,·62,·69,·114,·514,·863,·1048,·1098,·1116,·1335,·1904,·2091,·2162,·2270,·2275,·2280,·2285,·2290,·2299,·2300,·2301,·2302,·2303,·2348,·2458,·2462,·2463,·2464,·2525,·2535,·2566,·2583,·2622,·2639,·2648],32737 ········"128":·[56,·62,·69,·114,·514,·863,·1048,·1098,·1116,·1335,·1904,·2091,·2162,·2270,·2275,·2280,·2285,·2290,·2299,·2300,·2301,·2302,·2303,·2348,·2458,·2462,·2463,·2464,·2525,·2535,·2566,·2583,·2622,·2639,·2648],
32737 ········"12811363":·[349,·2457,·2639],32738 ········"12811363":·[349,·2457,·2639],
32738 ········"12820":·2548,32739 ········"12820":·2548,
32739 ········"1284":·[287,·1241,·1324,·1478,·1998],32740 ········"1284":·[287,·1241,·1324,·1478,·1998],
32740 ········"12852":·[2533,·2534],32741 ········"12852":·[2533,·2534],
32741 ········"12887796":·2488, 
32742 ········"12890":·2548,32742 ········"12890":·2548,
32743 ········"129":·[863,·1048,·1116,·1904,·2463,·2639],32743 ········"129":·[863,·1048,·1116,·1904,·2463,·2639],
32744 ········"12909":·2549,32744 ········"12909":·2549,
32745 ········"12923":·2549,32745 ········"12923":·2549,
32746 ········"12945251":·2666,32746 ········"12945251":·2666,
32747 ········"13":·[5,·26,·28,·30,·31,·36,·38,·47,·54,·55,·58,·61,·98,·107,·108,·114,·140,·141,·142,·144,·146,·163,·270,·336,·366,·367,·370,·374,·375,·409,·433,·530,·543,·546,·628,·647,·880,·949,·963,·1069,·1157,·1229,·1247,·1312,·1466,·1752,·1761,·1870,·1913,·1986,·2089,·2091,·2205,·2206,·2208,·2209,·2210,·2224,·2225,·2236,·2237,·2246,·2342,·2457,·2461,·2463,·2477,·2513,·2516,·2519,·2529,·2535,·2555,·2556,·2557,·2558,·2560,·2561,·2571,·2583,·2592,·2595,·2600,·2601,·2602,·2603,·2604,·2606,·2622,·2624,·2626,·2627,·2628,·2629,·2630,·2631,·2632,·2633,·2635,·2637,·2638,·2641,·2645,·2647,·2657,·2666],32747 ········"13":·[5,·26,·28,·30,·31,·36,·38,·47,·54,·55,·58,·61,·98,·107,·108,·114,·140,·141,·142,·144,·146,·163,·270,·336,·366,·367,·370,·374,·375,·409,·433,·530,·543,·546,·628,·647,·880,·949,·963,·1069,·1157,·1229,·1247,·1312,·1466,·1752,·1761,·1870,·1913,·1986,·2089,·2091,·2205,·2206,·2208,·2209,·2210,·2224,·2225,·2236,·2237,·2246,·2342,·2457,·2461,·2463,·2477,·2513,·2516,·2519,·2529,·2535,·2555,·2556,·2557,·2558,·2560,·2561,·2571,·2583,·2592,·2595,·2600,·2601,·2602,·2603,·2604,·2606,·2622,·2624,·2626,·2627,·2628,·2629,·2630,·2631,·2632,·2633,·2635,·2637,·2638,·2641,·2645,·2647,·2657,·2666],
32748 ········"130":·409,32748 ········"130":·409,
Offset 33062, 14 lines modifiedOffset 33062, 15 lines modified
33062 ········"15886":·2572,33062 ········"15886":·2572,
33063 ········"15888336":·680,33063 ········"15888336":·680,
33064 ········"159":·2463,33064 ········"159":·2463,
33065 ········"15900":·2572,33065 ········"15900":·2572,
33066 ········"15916":·2563,33066 ········"15916":·2563,
33067 ········"15929":·2563,33067 ········"15929":·2563,
33068 ········"15930":·2563,33068 ········"15930":·2563,
 33069 ········"15946659":·2488,
33069 ········"15954":·2563,33070 ········"15954":·2563,
33070 ········"1597":·28,33071 ········"1597":·28,
33071 ········"1599":·1643,33072 ········"1599":·1643,
33072 ········"15997":·2572,33073 ········"15997":·2572,
33073 ········"15cb66f":·2521,33074 ········"15cb66f":·2521,
33074 ········"15e":·2086,33075 ········"15e":·2086,
33075 ········"15ej":·2086,33076 ········"15ej":·2086,
Offset 33156, 14 lines modifiedOffset 33157, 15 lines modified
33156 ········"168":·2463,33157 ········"168":·2463,
33157 ········"16815":·2572,33158 ········"16815":·2572,
33158 ········"16830":·2588,33159 ········"16830":·2588,
33159 ········"16832":·2567,33160 ········"16832":·2567,
33160 ········"16841":·2572,33161 ········"16841":·2572,
33161 ········"16872":·2567,33162 ········"16872":·2567,
33162 ········"16875":·2567,33163 ········"16875":·2567,
 33164 ········"169":·2461,
33163 ········"16904":·2567,33165 ········"16904":·2567,
33164 ········"16905":·2567,33166 ········"16905":·2567,
33165 ········"16906":·2567,33167 ········"16906":·2567,
33166 ········"16916":·2567,33168 ········"16916":·2567,
33167 ········"16922":·2567,33169 ········"16922":·2567,
33168 ········"16938":·2572,33170 ········"16938":·2572,
33169 ········"16959":·2568,33171 ········"16959":·2568,
Offset 33514, 15 lines modifiedOffset 33516, 15 lines modified
33514 ········"1l_0":·1822,33516 ········"1l_0":·1822,
33515 ········"1rc1":·577,33517 ········"1rc1":·577,
33516 ········"1st":·[36,·74,·642,·2616,·2637,·2641],33518 ········"1st":·[36,·74,·642,·2616,·2637,·2641],
33517 ········"1th":·[661,·2168],33519 ········"1th":·[661,·2168],
33518 ········"1type":·2554,33520 ········"1type":·2554,
33519 ········"1xn":·2665,33521 ········"1xn":·2665,
33520 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33521 ········"20":·[0,·22,·24,·32,·38,·47,·54,·55,·57,·58,·59,·60,·74,·78,·90,·95,·98,·99,·113,·120,·121,·123,·124,·137,·141,·143,·160,·163,·270,·287,·336,·341,·342,·349,·354,·356,·358,·371,·420,·436,·438,·439,·441,·443,·444,·445,·446,·448,·449,·450,·451,·452,·453,·454,·455,·480,·481,·482,·483,·486,·487,·489,·513,·527,·534,·540,·548,·567,·568,·569,·570,·628,·653,·661,·667,·669,·820,·848,·851,·855,·857,·860,·864,·866,·870,·880,·893,·896,·897,·900,·901,·905,·906,·912,·913,·917,·933,·937,·940,·941,·947,·951,·956,·958,·965,·967,·977,·985,·986,·990,·1019,·1024,·1025,·1026,·1031,·1038,·1040,·1044,·1049,·1051,·1056,·1069,·1083,·1088,·1089,·1094,·1097,·1100,·1101,·1106,·1109,·1114,·1117,·1118,·1123,·1124,·1131,·1143,·1145,·1146,·1229,·1241,·1247,·1312,·1324,·1466,·1478,·1482,·1516,·1808,·1867,·1871,·1906,·1986,·1998,·2073,·2089,·2115,·2165,·2168,·2172,·2174,·2203,·2204,·2208,·2223,·2224,·2237,·2238,·2240,·2249,·2256,·2257,·2270,·2300,·2316,·2319,·2321,·2323,·2328,·2333,·2337,·2338,·2342,·2348,·2361,·2365,·2377,·2380,·2381,·2383,·2388,·2390,·2408,·2412,·2424,·2427,·2428,·2430,·2435,·2438,·2461,·2462,·2463,·2470,·2513,·2517,·2519,·2533,·2535,·2542,·2560,·2571,·2576,·2577,·2583,·2584,·2594,·2599,·2602,·2603,·2608,·2622,·2627,·2635,·2637,·2641,·2642,·2645,·2657,·2658,·2666],33523 ········"20":·[0,·22,·24,·32,·38,·47,·54,·55,·57,·58,·59,·60,·74,·78,·90,·95,·98,·99,·113,·120,·121,·123,·124,·137,·141,·143,·160,·163,·270,·287,·336,·341,·342,·349,·354,·356,·358,·371,·420,·436,·438,·439,·441,·443,·444,·445,·446,·448,·449,·450,·451,·452,·453,·454,·455,·480,·481,·482,·483,·486,·487,·489,·513,·527,·534,·540,·548,·567,·568,·569,·570,·628,·653,·661,·667,·669,·820,·848,·851,·855,·857,·860,·864,·866,·870,·880,·893,·896,·897,·900,·901,·905,·906,·912,·913,·917,·933,·937,·940,·941,·947,·951,·956,·958,·965,·967,·977,·985,·986,·990,·1019,·1024,·1025,·1026,·1031,·1038,·1040,·1044,·1049,·1051,·1056,·1069,·1083,·1088,·1089,·1094,·1097,·1100,·1101,·1106,·1109,·1114,·1117,·1118,·1123,·1124,·1131,·1143,·1145,·1146,·1229,·1241,·1247,·1312,·1324,·1466,·1478,·1482,·1516,·1808,·1867,·1871,·1906,·1986,·1998,·2073,·2089,·2115,·2165,·2168,·2172,·2174,·2203,·2204,·2208,·2223,·2224,·2237,·2238,·2240,·2249,·2256,·2257,·2270,·2300,·2316,·2319,·2321,·2323,·2328,·2333,·2337,·2338,·2342,·2348,·2361,·2365,·2377,·2380,·2381,·2383,·2388,·2390,·2408,·2412,·2424,·2427,·2428,·2430,·2435,·2438,·2462,·2463,·2470,·2513,·2517,·2519,·2533,·2535,·2542,·2560,·2571,·2576,·2577,·2583,·2584,·2594,·2599,·2602,·2603,·2608,·2622,·2627,·2635,·2637,·2641,·2642,·2645,·2657,·2658,·2666],
33522 ········"200":·[441,·446,·2337,·2339,·2346,·2354,·2357,·2380,·2382,·2392,·2401,·2404,·2427,·2429,·2441,·2451,·2454,·2645,·2648,·2666],33524 ········"200":·[441,·446,·2337,·2339,·2346,·2354,·2357,·2380,·2382,·2392,·2401,·2404,·2427,·2429,·2441,·2451,·2454,·2645,·2648,·2666],
33523 ········"2000":·[514,·526,·2525,·2613],33525 ········"2000":·[514,·526,·2525,·2613],
33524 ········"20000":·[2316,·2359,·2361,·2406,·2408,·2456,·2583],33526 ········"20000":·[2316,·2359,·2361,·2406,·2408,·2456,·2583],
33525 ········"2000000":·2635,33527 ········"2000000":·2635,
33526 ········"20000000e":·897,33528 ········"20000000e":·897,
33527 ········"2001":·[55,·2322,·2326,·2329,·2330,·2331,·2335,·2339,·2340,·2366,·2371,·2373,·2374,·2375,·2378,·2382,·2383,·2413,·2418,·2420,·2421,·2422,·2425,·2429,·2430],33529 ········"2001":·[55,·2322,·2326,·2329,·2330,·2331,·2335,·2339,·2340,·2366,·2371,·2373,·2374,·2375,·2378,·2382,·2383,·2413,·2418,·2420,·2421,·2422,·2425,·2429,·2430],
33528 ········"2002":·[55,·360,·2316,·2323,·2353,·2361,·2367,·2400,·2408,·2414,·2450],33530 ········"2002":·[55,·360,·2316,·2323,·2353,·2361,·2367,·2400,·2408,·2414,·2450],
Offset 33748, 15 lines modifiedOffset 33750, 15 lines modified
33748 ········"219":·2463,33750 ········"219":·2463,
33749 ········"21925":·2594,33751 ········"21925":·2594,
33750 ········"21949":·2589,33752 ········"21949":·2589,
33751 ········"21951":·2589,33753 ········"21951":·2589,
33752 ········"21952":·2589,33754 ········"21952":·2589,
33753 ········"21976":·2594,33755 ········"21976":·2594,
Max diff block lines reached; 17970/33261 bytes (54.03%) of diff not shown.