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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">1.0 | 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">2.5 | 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">9 | 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. | 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">2.4 | 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·+-· | 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·integer | 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·integer |
561 | random·numbers·from·a·discrete·uniform·distribution.·This·replaces·both | 561 | 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·legacy | 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·legacy |
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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([0.9 | 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. | 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([ | 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·for | 600 | <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 modified | Offset 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. | 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. | 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·which | 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·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 modified | Offset 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([[· | 642 | <span·class="go">array([[·1,··2,··3,··1,··1],</span> |
643 | <span·class="go">·······[· | 643 | <span·class="go">·······[·5,··6,··7,··5,··5],</span> |
644 | <span·class="go">·······[· | 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([[· | 648 | <span·class="go">array([[·1,··2,··0,··3],</span> |
649 | <span·class="go">·······[· | 649 | <span·class="go">·······[·5,··6,··4,··7],</span> |
650 | <span·class="go">·······[ | 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·distribution | 654 | <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> |
Offset 102, 26 lines modified | Offset 102, 26 lines modified | ||
102 | In·[1]:·import·numpy.random | 102 | 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 | 1.0 | 107 | 1.03·ms·+-·51·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each) |
108 | 2.5 | 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 | 9 | 112 | 967·us·+-·57.5·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each) |
113 | 1. | 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 | 2.4 | 117 | 2.47·ms·+-·13.8·us·per·loop·(mean·+-·std.·dev.·of·7·runs,·1·loop·each) |
118 | 4.48·ms·+-· | 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·from | 119 | ····*·_\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·the | 120 | ······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·legacy | 122 | ····*·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-point | 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-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,·and | 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,·and |
Offset 140, 38 lines modified | Offset 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([0.9 | 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. | 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([ | 150 | Out[9]:·array([102,·169,··79],·dtype=uint8) |
151 | ····*·Optional·out·argument·that·allows·existing·arrays·to·be·filled·for·select | 151 | ····*·Optional·out·argument·that·allows·existing·arrays·to·be·filled·for·select |
152 | ······distributions | 152 | ······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·suitable | 157 | ······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. | 162 | Out[12]:·array([0.54036979,·0.97249852]) |
163 | In·[13]:·print(existing) | 163 | In·[13]:·print(existing) |
164 | [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_\x8e | 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_\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 modified | Offset 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([[· | 185 | array([[·1,··2,··3,··1,··1], |
186 | ·······[· | 186 | ·······[·5,··6,··7,··5,··5], |
187 | ·······[· | 187 | ·······[·9,·10,·11,··9,··9]]) |
188 | In·[18]:·rng.shuffle(a,·axis=1)········#·Shuffle·in-place | 188 | In·[18]:·rng.shuffle(a,·axis=1)········#·Shuffle·in-place |
189 | In·[19]:·a | 189 | In·[19]:·a |
190 | Out[19]: | 190 | Out[19]: |
191 | array([[· | 191 | array([[·1,··2,··0,··3], |
192 | ·······[· | 192 | ·······[·5,··6,··4,··7], |
193 | ·······[ | 193 | ·······[·9,·10,··8,·11]]) |
194 | ····*·Added·a·method·to·sample·from·the·complex·normal·distribution | 194 | ····*·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_\x8s | 196 | _\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_\x8n | 197 | _\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_\x8t | 198 | _\x8n_\x8e_\x8x_\x8t |
199 | _\x8P_\x8e_\x8r_\x8f_\x8o_\x8r_\x8m_\x8a_\x8n_\x8c_\x8e | 199 | _\x8P_\x8e_\x8r_\x8f_\x8o_\x8r_\x8m_\x8a_\x8n_\x8c_\x8e |
200 | ©·Copyright·2008-2025,·NumPy·Developers. | 200 | ©·Copyright·2008-2025,·NumPy·Developers. |
Offset 609, 31 lines modified | Offset 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([0.9 | 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. | 622 | <span·class="gh">Out[6]:·</span><span·class="go">Polynomial([4.67090189,·4.15946659],·domain=[0.,·9.],·window=[-1.,··1.],·symbol='x')</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·the | 625 | <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·the | 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·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. | 630 | <span·class="gh">Out[7]:·</span><span·class="go">Polynomial([0.51143531,·0.92432591],·domain=[-1.,··1.],·window=[-1.,··1.],·symbol='x')</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·package | 637 | <p>In·addition·to·standard·power·series·polynomials,·the·polynomial·package |
Offset 150, 26 lines modified | Offset 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([0.9 | 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_fitted | 158 | In·[6]:·p_fitted |
159 | Out[6]:·Polynomial([4. | 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·linear | 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·linear |
162 | mapping·between·the·window·and·domain.·_\x8c_\x8o_\x8n_\x8v_\x8e_\x8r_\x8t·can·be·used·to·get·the | 162 | 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. | 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·package | 168 | In·addition·to·standard·power·series·polynomials,·the·polynomial·package |
169 | provides·several·additional·kinds·of·polynomials·including·Chebyshev,·Hermite | 169 | provides·several·additional·kinds·of·polynomials·including·Chebyshev,·Hermite |
170 | (two·subtypes),·Laguerre,·and·Legendre·polynomials.·Each·of·these·has·an | 170 | (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·that | 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·that |
172 | provides·a·consistent·interface·for·working·with·polynomials·regardless·of | 172 | provides·a·consistent·interface·for·working·with·polynomials·regardless·of |
Offset 32344, 14 lines modified | Offset 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 modified | Offset 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,·246 | 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 modified | Offset 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 modified | Offset 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 modified | Offset 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 modified | Offset 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 modified | Offset 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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| 33522 | 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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,·246 | 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 modified | Offset 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. |