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‎tutorials/1_models-quick-fit.html

Lines changed: 34 additions & 34 deletions
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@@ -690,7 +690,7 @@ <h2>2) Fit a Polynomial model: Choose fitter wisely<a class="headerlink" href="#
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<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Text(0, 0.5, &#39;$y_1$&#39;)
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</pre></div>
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</div>
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<img alt="_images/2c7430868a31864c453bf6eeea774904986f6b0a38904187dab38931519020fe.png" src="_images/2c7430868a31864c453bf6eeea774904986f6b0a38904187dab38931519020fe.png" />
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<img alt="_images/b206e7e157616fe49c4578d4e72c813d4fe0ebdbfaf76532566fee6111aacffb.png" src="_images/b206e7e157616fe49c4578d4e72c813d4fe0ebdbfaf76532566fee6111aacffb.png" />
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</div>
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<p>To fit this data let’s remember the three steps: model, fitter and perform fit.</p>
@@ -716,9 +716,9 @@ <h2>2) Fit a Polynomial model: Choose fitter wisely<a class="headerlink" href="#
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Model set size: 1
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Degree: 3
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Parameters:
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c0 c1 c2 c3
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------------------ ------------------ ------------------ ------------------
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-8.474181693465024 11.266137297252593 -5.502843775502853 0.8973360354644486
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c0 c1 c2 c3
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----------------- ----------------- ------------------ ------------------
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-9.12800757901219 12.77469171003877 -6.575706598856835 1.1054564059454586
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</pre></div>
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</div>
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@@ -751,9 +751,9 @@ <h2>2) Fit a Polynomial model: Choose fitter wisely<a class="headerlink" href="#
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Model set size: 1
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Degree: 3
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Parameters:
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c0 c1 c2 c3
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------------------- ------------------- ------------------- -------------------
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-0.0940845418190468 -0.2695751224157016 -0.8510531934902894 0.32231617541725033
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c0 c1 c2 c3
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----------------- -------------------- ------------------- -------------------
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0.448425931971312 -0.19628287661401733 -0.8790022925273284 0.31732388584772475
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</pre></div>
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</div>
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</div>
@@ -788,7 +788,7 @@ <h3>Compare results<a class="headerlink" href="#compare-results" title="Link to
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</div>
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</div>
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<div class="cell_output docutils container">
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Reduced Chi Squared with LinearLSQFitter: 2.0380848248340815
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Reduced Chi Squared with LinearLSQFitter: 1.5151632695641253
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</pre></div>
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</div>
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</div>
@@ -801,7 +801,7 @@ <h3>Compare results<a class="headerlink" href="#compare-results" title="Link to
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</div>
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</div>
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<div class="cell_output docutils container">
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Reduced Chi Squared with SimplexLSQFitter: 4.645859203398919
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Reduced Chi Squared with SimplexLSQFitter: 5.108396459855349
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</pre></div>
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</div>
@@ -820,10 +820,10 @@ <h3>Compare results<a class="headerlink" href="#compare-results" title="Link to
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</div>
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</div>
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<div class="cell_output docutils container">
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<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;matplotlib.legend.Legend at 0x7f5ca2a27e30&gt;
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<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;matplotlib.legend.Legend at 0x7f6f6fc23b90&gt;
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</pre></div>
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</div>
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<img alt="_images/8d0f7ce9cbb7be0373bb7283110b71eb162d92d1e3788929088008f7ec559b79.png" src="_images/8d0f7ce9cbb7be0373bb7283110b71eb162d92d1e3788929088008f7ec559b79.png" />
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<img alt="_images/a778877b480f6d98adf60320ed335116426b5908b8f05bb629cd263e8b15f03f.png" src="_images/a778877b480f6d98adf60320ed335116426b5908b8f05bb629cd263e8b15f03f.png" />
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<p>Results are as espected, the fit performed with the linear fitter is better than the second, non linear one.</p>
@@ -860,7 +860,7 @@ <h2>3) Fit a Gaussian: Let’s compare to scipy<a class="headerlink" href="#fit-
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<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Text(0, 0.5, &#39;$y_2$&#39;)
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</pre></div>
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</div>
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<img alt="_images/c31c511b4804dad58698e20d1a40cf477946ac56000b20e07b23866cf24791d6.png" src="_images/c31c511b4804dad58698e20d1a40cf477946ac56000b20e07b23866cf24791d6.png" />
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<img alt="_images/2490abbcc794c140fa0a5e1f8580b93769ebc35a8ea0d36a888ce01cb3c6ec40.png" src="_images/2490abbcc794c140fa0a5e1f8580b93769ebc35a8ea0d36a888ce01cb3c6ec40.png" />
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<p>Let’s do our three steps to make the fit we want. For this fit we’re going to use a non-linear fitter, <code class="docutils literal notranslate"><span class="pre">LevMarLSQFitter</span></code>, because the model we need (<code class="docutils literal notranslate"><span class="pre">Gaussian1D</span></code>) is non-linear in the parameters.</p>
@@ -885,9 +885,9 @@ <h2>3) Fit a Gaussian: Let’s compare to scipy<a class="headerlink" href="#fit-
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Outputs: (&#39;y&#39;,)
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Model set size: 1
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Parameters:
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amplitude mean stddev
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----------------- ------------------ ------------------
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9.919351213300535 0.3726248055188302 10.319677387647905
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amplitude mean stddev
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----------------- -------------------- -----------------
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10.25380980329387 -0.34280774429380745 9.449824403814645
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</pre></div>
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@@ -913,7 +913,7 @@ <h2>3) Fit a Gaussian: Let’s compare to scipy<a class="headerlink" href="#fit-
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<div class="cell_output docutils container">
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[0.04977461 0.07176987 0.07212312]
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[0.05429624 0.06147289 0.06154842]
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</pre></div>
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@@ -934,9 +934,9 @@ <h2>3) Fit a Gaussian: Let’s compare to scipy<a class="headerlink" href="#fit-
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<div class="cell_output docutils container">
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Amplitude: 9.919351213300535 +\- 0.2231022439896053
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Mean: 0.3726248055188302 +\- 0.26789898297447357
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Standard Deviation: 10.319677387647905 +\- 0.2685574753381447
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Amplitude: 10.25380980329387 +\- 0.2330155370528277
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Mean: -0.34280774429380745 +\- 0.24793727111438463
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Standard Deviation: 9.449824403814645 +\- 0.2480895430045534
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</pre></div>
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<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;&gt;:2: SyntaxWarning: invalid escape sequence &#39;\-&#39;
@@ -945,11 +945,11 @@ <h2>3) Fit a Gaussian: Let’s compare to scipy<a class="headerlink" href="#fit-
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&lt;&gt;:2: SyntaxWarning: invalid escape sequence &#39;\-&#39;
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&lt;&gt;:4: SyntaxWarning: invalid escape sequence &#39;\-&#39;
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&lt;&gt;:6: SyntaxWarning: invalid escape sequence &#39;\-&#39;
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/tmp/ipykernel_3536/1659586526.py:2: SyntaxWarning: invalid escape sequence &#39;\-&#39;
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/tmp/ipykernel_3538/1659586526.py:2: SyntaxWarning: invalid escape sequence &#39;\-&#39;
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&quot;Amplitude: {} +\- {}&quot;.format(best_fit_gauss.amplitude.value, np.sqrt(cov_diag[0]))
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/tmp/ipykernel_3536/1659586526.py:4: SyntaxWarning: invalid escape sequence &#39;\-&#39;
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/tmp/ipykernel_3538/1659586526.py:4: SyntaxWarning: invalid escape sequence &#39;\-&#39;
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print(&quot;Mean: {} +\- {}&quot;.format(best_fit_gauss.mean.value, np.sqrt(cov_diag[1])))
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/tmp/ipykernel_3536/1659586526.py:6: SyntaxWarning: invalid escape sequence &#39;\-&#39;
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/tmp/ipykernel_3538/1659586526.py:6: SyntaxWarning: invalid escape sequence &#39;\-&#39;
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&quot;Standard Deviation: {} +\- {}&quot;.format(
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</pre></div>
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@@ -980,7 +980,7 @@ <h2>3) Fit a Gaussian: Let’s compare to scipy<a class="headerlink" href="#fit-
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[ 9.91935132 0.37262559 10.31967716]
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[10.25380967 -0.3428078 9.44982465]
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@@ -994,9 +994,9 @@ <h2>3) Fit a Gaussian: Let’s compare to scipy<a class="headerlink" href="#fit-
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Amplitude: 9.919351324668995 +\- 0.22692644067578163
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Mean: 0.3726255910714404 +\- 0.27249027313296453
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Standard Deviation: 10.319677158924282 +\- 0.2731600598915281
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Amplitude: 10.253809670516787 +\- 0.22874702438437425
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Mean: -0.3428078046174718 +\- 0.24339562710215684
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Standard Deviation: 9.449824649755104 +\- 0.24354512996537175
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<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;&gt;:1: SyntaxWarning: invalid escape sequence &#39;\-&#39;
@@ -1005,11 +1005,11 @@ <h2>3) Fit a Gaussian: Let’s compare to scipy<a class="headerlink" href="#fit-
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&lt;&gt;:1: SyntaxWarning: invalid escape sequence &#39;\-&#39;
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&lt;&gt;:2: SyntaxWarning: invalid escape sequence &#39;\-&#39;
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&lt;&gt;:3: SyntaxWarning: invalid escape sequence &#39;\-&#39;
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/tmp/ipykernel_3536/2222327920.py:1: SyntaxWarning: invalid escape sequence &#39;\-&#39;
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/tmp/ipykernel_3538/2222327920.py:1: SyntaxWarning: invalid escape sequence &#39;\-&#39;
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print(&quot;Amplitude: {} +\- {}&quot;.format(p_opt[0], np.sqrt(p_cov[0, 0])))
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/tmp/ipykernel_3536/2222327920.py:2: SyntaxWarning: invalid escape sequence &#39;\-&#39;
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print(&quot;Mean: {} +\- {}&quot;.format(p_opt[1], np.sqrt(p_cov[1, 1])))
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/tmp/ipykernel_3536/2222327920.py:3: SyntaxWarning: invalid escape sequence &#39;\-&#39;
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print(&quot;Standard Deviation: {} +\- {}&quot;.format(p_opt[2], np.sqrt(p_cov[2, 2])))
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Reduced Chi Squared using astropy.modeling: 1.034573985888868
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Reduced Chi Squared using astropy.modeling: 0.9636990281912249
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Reduced Chi Squared using scipy: 1.0345739858891707
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Reduced Chi Squared using scipy: 0.9636990281913128
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<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;matplotlib.legend.Legend at 0x7f5ca286fef0&gt;
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<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;matplotlib.legend.Legend at 0x7f6f6f9d6c00&gt;
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<img alt="_images/09c2c445345d0c30586d49171516066734c9d829db36595ef252f7c795b9fb3c.png" src="_images/09c2c445345d0c30586d49171516066734c9d829db36595ef252f7c795b9fb3c.png" />
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<img alt="_images/9a20769891e99632aa5763a2cf8507468858807b9965ba8698e770f70c0e2bf0.png" src="_images/9a20769891e99632aa5763a2cf8507468858807b9965ba8698e770f70c0e2bf0.png" />
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<p><strong>Conclusion:</strong> Choose the method most convenient for every case you need to fit. We recomend <code class="docutils literal notranslate"><span class="pre">astropy.modeling</span></code> because is easier to write the name of the function you want to fit than to remember the expression every time we want to use it. Also, <code class="docutils literal notranslate"><span class="pre">astropy.modeling</span></code> becomes useful with more complicated models like <a class="reference external" href="http://docs.astropy.org/en/stable/modeling/#compound-models">two gaussians</a> plus a <a class="reference external" href="http://docs.astropy.org/en/stable/modeling/#blackbody-radiation">black body</a>, but that is another tutorial.</p>
@@ -1111,7 +1111,7 @@ <h2>4) Exercise: Your turn to choose<a class="headerlink" href="#exercise-your-t
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<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Text(0, 0.5, &#39;$y_3$&#39;)
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<img alt="_images/f69bc99f67f5ea5c1fcc12e802847d267cda08a63da00cf92c1058311a02ab76.png" src="_images/f69bc99f67f5ea5c1fcc12e802847d267cda08a63da00cf92c1058311a02ab76.png" />
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‎tutorials/2_WavelengthCalibration.html

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@@ -856,7 +856,7 @@ <h2>Improving on our guesses<a class="headerlink" href="#improving-on-our-guesse
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<div class="cell_output docutils container">
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<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;&gt;:3: SyntaxWarning: invalid escape sequence &#39;\l&#39;
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&lt;&gt;:3: SyntaxWarning: invalid escape sequence &#39;\l&#39;
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/tmp/ipykernel_4453/1543648565.py:3: SyntaxWarning: invalid escape sequence &#39;\l&#39;
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<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;&gt;:5: SyntaxWarning: invalid escape sequence &#39;\l&#39;
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plt.xlabel(&quot;$\lambda$ [nm]&quot;);
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<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;&gt;:3: SyntaxWarning: invalid escape sequence &#39;\l&#39;
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&lt;&gt;:3: SyntaxWarning: invalid escape sequence &#39;\l&#39;
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<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;&gt;:3: SyntaxWarning: invalid escape sequence &#39;\l&#39;
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plt.xlabel(&quot;$\lambda$ [nm]&quot;)
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