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added dr. zoghbi's example
2017-01-25 06:20:48 +00:00
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<li>First, we load numpy as the clag package. pylab is for plotting</li>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">clag</span>
<span class="o">%</span><span class="k">pylab</span> inline
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<pre>Populating the interactive namespace from numpy and matplotlib
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<li>Now, we read the first light curve. e.g. 1367A.dat, and plot it</li>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">dt</span> <span class="o">=</span> <span class="mf">0.01</span>
<span class="n">t1</span><span class="p">,</span> <span class="n">l1</span><span class="p">,</span> <span class="n">l1e</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">loadtxt</span><span class="p">(</span><span class="s1">&#39;1367A.dat&#39;</span><span class="p">)</span><span class="o">.</span><span class="n">T</span>
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<pre>&lt;Container object of 3 artists&gt;</pre>
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<li>Here, we define the frequency bins in fqL. Here, I use the ones that Ed sent. </li>
<li><p>A general rules for fqL is as follows:</p>
<ul>
<li>define $f_1$, $f_2$ as the two extreme frequencies allowed by the data. i.e. $f_{1} = 1/T$ with $T$ being the length of observation in time units, and $f_{2} = 0.5/\Delta t$</li>
<li>The frequency limits where the psd/lag can be constrained are about ~$0.9f_1 - 0.5f_2$. The 0.9 factor doesn't depend on the data much, but values in the range ~[0.9-1.1] are ok. The factor in front of $f_2$ depends on the quality of the data, for low qualily data, use ~0.1--0.2, and for high quality data, increase it up to $0.9--1$.</li>
<li>Always include two dummy bins at the low and high frequencies and ignore them. The first and last bins are generally biased, So I suggest using the first bin as $0.5f_1 - 0.9 f_1$ (or whatever value you use instead of $0.9 f_1$, see second point above), and the last bin should be $0.5f_2-2*f_2$ (or whatever value instead of $0.5f_2$, see second point above). So the frequency bins should be something like: $[0.5f_1, 0.9f_1, ..., 0.5f_2, 2f_2]$, the bins in between can be devided as desired.</li>
</ul>
</li>
<li><p>fqd is the bin center</p>
</li>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">fqL</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">0.0049999999</span><span class="p">,</span> <span class="mf">0.018619375</span><span class="p">,</span> <span class="mf">0.044733049</span><span class="p">,</span> <span class="mf">0.069336227</span><span class="p">,</span> <span class="mf">0.10747115</span><span class="p">,</span> <span class="mf">0.16658029</span><span class="p">,</span>
<span class="mf">0.25819945</span><span class="p">,</span> <span class="mf">0.40020915</span><span class="p">,</span> <span class="mf">0.62032418</span><span class="p">])</span>
<span class="n">nfq</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">fqL</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span>
<span class="n">fqd</span> <span class="o">=</span> <span class="mi">10</span><span class="o">**</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">log10</span><span class="p">(</span> <span class="p">(</span><span class="n">fqL</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">*</span><span class="n">fqL</span><span class="p">[</span><span class="mi">1</span><span class="p">:])</span> <span class="p">)</span><span class="o">/</span><span class="mf">2.</span><span class="p">)</span>
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<ul>
<li>We create a psd class of type psd10r (i.e. psd in log10 units using the rms normalization, see tutorial of clag for more). Other paramters are given as a list of: time, light curve, error. If you want to fit more than one light curve together, give them as elements of that list.</li>
<li>p1 is an array of the starting parameters</li>
<li>We then call clag.optimize to find the best fit. It takes as parameters, the class of psd or lag, the starting paramters, plus some other parameters whose default values work in most cases. The function returns a tuple of two arrays: the best fit values, and the estimated errors from the Fisher matrix (i.e. approximate errors).</li>
<li>As the fit starts, progress is printed, where for every line, we print: num_of_iteration, max change in parameter values, maximum gradient, change in loglikelihood -- loglikelihood -- list of parameters.</li>
<li>The fit stops when either of the three numbers after iter_number is close to zero.</li>
<li>At the end, the function prints the best fit values, their estimated error and the gradient of the loglikelihood at the those values. For the fit to be valid, the gradient values need to be all close to zero</li>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">P1</span> <span class="o">=</span> <span class="n">clag</span><span class="o">.</span><span class="n">clag</span><span class="p">(</span><span class="s1">&#39;psd10r&#39;</span><span class="p">,</span> <span class="p">[</span><span class="n">t1</span><span class="p">],</span> <span class="p">[</span><span class="n">l1</span><span class="p">],</span> <span class="p">[</span><span class="n">l1e</span><span class="p">],</span> <span class="n">dt</span><span class="p">,</span> <span class="n">fqL</span><span class="p">)</span>
<span class="n">p1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="n">nfq</span><span class="p">)</span>
<span class="n">p1</span><span class="p">,</span> <span class="n">p1e</span> <span class="o">=</span> <span class="n">clag</span><span class="o">.</span><span class="n">optimize</span><span class="p">(</span><span class="n">P1</span><span class="p">,</span> <span class="n">p1</span><span class="p">)</span>
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<pre> 1 4.342e-01 5.106e+01 inf -- 4.956e+03 -- 1 1 1 1 1 1 1 1
2 7.673e-01 5.094e+01 8.346e+01 -- 5.040e+03 -- 0.652988 0.587584 0.568433 0.567574 0.566292 0.566106 0.565781 0.566166
3 3.298e+00 5.072e+01 8.117e+01 -- 5.121e+03 -- 0.414769 0.211226 0.141674 0.138242 0.133442 0.132793 0.131633 0.132768
4 1.606e+00 5.040e+01 7.791e+01 -- 5.199e+03 -- 0.322796 -0.0775344 -0.271946 -0.283286 -0.297439 -0.299306 -0.302453 -0.300418
5 5.910e-01 4.995e+01 7.424e+01 -- 5.273e+03 -- 0.303931 -0.202072 -0.653233 -0.686827 -0.723408 -0.72915 -0.736445 -0.733984
6 3.715e-01 4.907e+01 6.996e+01 -- 5.343e+03 -- 0.288563 -0.184901 -0.963027 -1.05215 -1.1374 -1.1547 -1.17045 -1.16777
7 2.711e-01 4.699e+01 6.310e+01 -- 5.406e+03 -- 0.283941 -0.171583 -1.13016 -1.33783 -1.52092 -1.56818 -1.60449 -1.60156
8 2.136e-01 4.393e+01 5.315e+01 -- 5.459e+03 -- 0.284478 -0.172961 -1.16497 -1.49243 -1.8324 -1.94693 -2.03753 -2.03567
9 1.766e-01 3.793e+01 4.044e+01 -- 5.500e+03 -- 0.290936 -0.172461 -1.18193 -1.52814 -2.02019 -2.2443 -2.46546 -2.47059
10 1.511e-01 2.754e+01 2.660e+01 -- 5.526e+03 -- 0.299556 -0.170594 -1.19171 -1.52653 -2.09181 -2.40938 -2.87374 -2.90691
11 1.353e-01 1.473e+01 1.395e+01 -- 5.540e+03 -- 0.304466 -0.168829 -1.1936 -1.52541 -2.11411 -2.46428 -3.22352 -3.34602
12 1.365e-01 5.346e+00 5.391e+00 -- 5.546e+03 -- 0.306641 -0.168375 -1.1943 -1.52526 -2.12385 -2.4831 -3.45563 -3.7987
13 1.885e-01 1.315e+00 1.631e+00 -- 5.547e+03 -- 0.308259 -0.168765 -1.19466 -1.52395 -2.12898 -2.49063 -3.54795 -4.31734
14 6.419e-01 2.826e-01 4.459e-01 -- 5.548e+03 -- 0.309635 -0.169217 -1.19466 -1.52209 -2.1316 -2.49271 -3.56156 -5.13117
15 3.621e+02 2.692e-01 6.760e-02 -- 5.548e+03 -- 0.310493 -0.16946 -1.19426 -1.52073 -2.13283 -2.49296 -3.55956 -8.13117
16 6.745e-03 2.804e-01 2.200e-04 -- 5.548e+03 -- 0.310716 -0.169438 -1.1942 -1.52027 -2.1332 -2.49291 -3.55848 -11.1312
17 9.379e-04 3.668e-02 3.808e-03 -- 5.548e+03 -- 0.310697 -0.169463 -1.19426 -1.52034 -2.13364 -2.49379 -3.58248 -11.1312
18 1.196e-04 4.629e-03 7.714e-05 -- 5.548e+03 -- 0.310559 -0.169401 -1.1944 -1.52053 -2.13373 -2.49422 -3.58584 -11.1312
********************
0.310559 -0.169401 -1.1944 -1.52053 -2.13373 -2.49422 -3.58584 -11.1312
0.23823 0.201724 0.232207 0.17655 10 0.132676 0.306008 10
-0.000242823 -0.000294102 -0.000203858 -0.0012519 -1.17839e-06 -0.00320256 -0.00462885 -1.49854e-07
********************
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<li>We then call clag.errors to obtain the errors on the parameters. This steps over the parameters, allowing others to change, until the loglikelihood function changes by 1. This gives the 1-sigma error.</li>
<li>The errors can also be obtained using mcmc, though not directly implemeted in clag code, one can use other mcmc packages like emcee, and call the p1.loglikelihood function directly.</li>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">p1</span><span class="p">,</span> <span class="n">p1e</span> <span class="o">=</span> <span class="n">clag</span><span class="o">.</span><span class="n">errors</span><span class="p">(</span><span class="n">P1</span><span class="p">,</span> <span class="n">p1</span><span class="p">,</span> <span class="n">p1e</span><span class="p">)</span>
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<pre> ### errors for param 0 ###
+++ 5.548e+03 5.547e+03 3.105e-01 5.488e-01 0.876 +++
+++ 5.548e+03 5.547e+03 3.105e-01 6.679e-01 1.84 +++
+++ 5.548e+03 5.547e+03 3.105e-01 6.083e-01 1.32 +++
+++ 5.548e+03 5.547e+03 3.105e-01 5.786e-01 1.09 +++
+++ 5.548e+03 5.547e+03 3.105e-01 5.637e-01 0.981 +++
+++ 5.548e+03 5.547e+03 3.105e-01 5.711e-01 1.03 +++
+++ 5.548e+03 5.547e+03 3.105e-01 5.674e-01 1.01 +++
### errors for param 1 ###
+++ 5.548e+03 5.547e+03 -1.694e-01 3.231e-02 0.969 +++
+++ 5.548e+03 5.547e+03 -1.694e-01 1.332e-01 2.06 +++
+++ 5.548e+03 5.547e+03 -1.694e-01 8.274e-02 1.47 +++
+++ 5.548e+03 5.547e+03 -1.694e-01 5.753e-02 1.21 +++
+++ 5.548e+03 5.547e+03 -1.694e-01 4.492e-02 1.09 +++
+++ 5.548e+03 5.547e+03 -1.694e-01 3.862e-02 1.03 +++
+++ 5.548e+03 5.547e+03 -1.694e-01 3.546e-02 0.998 +++
### errors for param 2 ###
+++ 5.548e+03 5.547e+03 -1.194e+00 -9.622e-01 1.03 +++
+++ 5.548e+03 5.548e+03 -1.194e+00 -1.078e+00 0.277 +++
+++ 5.548e+03 5.548e+03 -1.194e+00 -1.020e+00 0.602 +++
+++ 5.548e+03 5.547e+03 -1.194e+00 -9.912e-01 0.805 +++
+++ 5.548e+03 5.547e+03 -1.194e+00 -9.767e-01 0.917 +++
+++ 5.548e+03 5.547e+03 -1.194e+00 -9.695e-01 0.975 +++
+++ 5.548e+03 5.547e+03 -1.194e+00 -9.658e-01 1 +++
### errors for param 3 ###
+++ 5.548e+03 5.547e+03 -1.521e+00 -1.344e+00 0.862 +++
+++ 5.548e+03 5.547e+03 -1.521e+00 -1.256e+00 1.85 +++
+++ 5.548e+03 5.547e+03 -1.521e+00 -1.300e+00 1.32 +++
+++ 5.548e+03 5.547e+03 -1.521e+00 -1.322e+00 1.08 +++
+++ 5.548e+03 5.547e+03 -1.521e+00 -1.333e+00 0.967 +++
+++ 5.548e+03 5.547e+03 -1.521e+00 -1.327e+00 1.02 +++
+++ 5.548e+03 5.547e+03 -1.521e+00 -1.330e+00 0.994 +++
### errors for param 4 ###
+++ 5.548e+03 5.547e+03 -2.134e+00 -1.981e+00 0.868 +++
+++ 5.548e+03 5.547e+03 -2.134e+00 -1.905e+00 1.9 +++
+++ 5.548e+03 5.547e+03 -2.134e+00 -1.943e+00 1.34 +++
+++ 5.548e+03 5.547e+03 -2.134e+00 -1.962e+00 1.09 +++
+++ 5.548e+03 5.547e+03 -2.134e+00 -1.971e+00 0.977 +++
+++ 5.548e+03 5.547e+03 -2.134e+00 -1.967e+00 1.03 +++
+++ 5.548e+03 5.547e+03 -2.134e+00 -1.969e+00 1.01 +++
### errors for param 5 ###
+++ 5.548e+03 5.547e+03 -2.494e+00 -2.362e+00 0.994 +++
### errors for param 6 ###
+++ 5.548e+03 5.547e+03 -3.586e+00 -3.280e+00 1.33 +++
+++ 5.548e+03 5.548e+03 -3.586e+00 -3.433e+00 0.275 +++
+++ 5.548e+03 5.547e+03 -3.586e+00 -3.357e+00 0.683 +++
+++ 5.548e+03 5.547e+03 -3.586e+00 -3.318e+00 0.974 +++
+++ 5.548e+03 5.547e+03 -3.586e+00 -3.299e+00 1.14 +++
+++ 5.548e+03 5.547e+03 -3.586e+00 -3.309e+00 1.06 +++
+++ 5.548e+03 5.547e+03 -3.586e+00 -3.314e+00 1.01 +++
+++ 5.548e+03 5.547e+03 -3.586e+00 -3.316e+00 0.994 +++
### errors for param 7 ###
+++ 5.548e+03 5.548e+03 -1.113e+01 -7.131e+00 0.0013 +++
+++ 5.548e+03 5.548e+03 -1.113e+01 -5.131e+00 0.134 +++
+++ 5.548e+03 5.547e+03 -1.113e+01 -4.131e+00 1.63 +++
+++ 5.548e+03 5.548e+03 -1.113e+01 -4.631e+00 0.451 +++
+++ 5.548e+03 5.547e+03 -1.113e+01 -4.381e+00 0.847 +++
+++ 5.548e+03 5.547e+03 -1.113e+01 -4.256e+00 1.17 +++
+++ 5.548e+03 5.547e+03 -1.113e+01 -4.319e+00 0.995 +++
********************
0.310547 -0.169411 -1.19441 -1.52057 -2.13373 -2.49427 -3.58627 -11.1312
0.256842 0.204876 0.228579 0.190434 0.164654 0.132714 0.270338 6.8125
********************
</pre>
</div>
</div>
</div>
</div>
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<div class="prompt input_prompt">
</div>
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<div class="text_cell_render border-box-sizing rendered_html">
<ul>
<li>Next we plot the results</li>
</ul>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[76]:</div>
<div class="inner_cell">
<div class="input_area">
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">xscale</span><span class="p">(</span><span class="s1">&#39;log&#39;</span><span class="p">);</span> <span class="n">ylim</span><span class="p">(</span><span class="o">-</span><span class="mi">4</span><span class="p">,</span><span class="mi">2</span><span class="p">)</span>
<span class="n">errorbar</span><span class="p">(</span><span class="n">fqd</span><span class="p">,</span> <span class="n">p1</span><span class="p">,</span> <span class="n">yerr</span><span class="o">=</span><span class="n">p1e</span><span class="p">,</span> <span class="n">fmt</span><span class="o">=</span><span class="s1">&#39;o&#39;</span><span class="p">,</span> <span class="n">ms</span><span class="o">=</span><span class="mi">10</span><span class="p">)</span>
</pre></div>
</div>
</div>
</div>
<div class="output_wrapper">
<div class="output">
<div class="output_area"><div class="prompt output_prompt">Out[76]:</div>
<div class="output_text output_subarea output_execute_result">
<pre>&lt;Container object of 3 artists&gt;</pre>
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<div class="output_png output_subarea ">
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"
>
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<div class="input">
<div class="prompt input_prompt">In&nbsp;[&nbsp;]:</div>
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<div class=" highlight hl-ipython2"><pre><span></span>
</pre></div>
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<div class="prompt input_prompt">
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<ul>
<li>Now, we load the second light curve and repeat the process for the second psd</li>
</ul>
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<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[15]:</div>
<div class="inner_cell">
<div class="input_area">
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">t2</span><span class="p">,</span> <span class="n">l2</span><span class="p">,</span> <span class="n">l2e</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">loadtxt</span><span class="p">(</span><span class="s1">&#39;3465A.dat&#39;</span><span class="p">)</span><span class="o">.</span><span class="n">T</span>
<span class="n">errorbar</span><span class="p">(</span><span class="n">t1</span><span class="p">,</span> <span class="n">l1</span><span class="p">,</span> <span class="n">yerr</span><span class="o">=</span><span class="n">l1e</span><span class="p">,</span> <span class="n">fmt</span><span class="o">=</span><span class="s1">&#39;o&#39;</span><span class="p">)</span>
<span class="n">errorbar</span><span class="p">(</span><span class="n">t2</span><span class="p">,</span> <span class="n">l2</span><span class="p">,</span> <span class="n">yerr</span><span class="o">=</span><span class="n">l2e</span><span class="p">,</span> <span class="n">fmt</span><span class="o">=</span><span class="s1">&#39;o&#39;</span><span class="p">)</span>
</pre></div>
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<div class="output">
<div class="output_area"><div class="prompt output_prompt">Out[15]:</div>
<div class="output_text output_subarea output_execute_result">
<pre>&lt;Container object of 3 artists&gt;</pre>
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<div class="output_area"><div class="prompt"></div>
<div class="output_png output_subarea ">
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>
</div>
</div>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[16]:</div>
<div class="inner_cell">
<div class="input_area">
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">P2</span> <span class="o">=</span> <span class="n">clag</span><span class="o">.</span><span class="n">clag</span><span class="p">(</span><span class="s1">&#39;psd10r&#39;</span><span class="p">,</span> <span class="p">[</span><span class="n">t2</span><span class="p">],</span> <span class="p">[</span><span class="n">l2</span><span class="p">],</span> <span class="p">[</span><span class="n">l2e</span><span class="p">],</span> <span class="n">dt</span><span class="p">,</span> <span class="n">fqL</span><span class="p">)</span>
<span class="n">p2</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="n">nfq</span><span class="p">)</span>
<span class="n">p2</span><span class="p">,</span> <span class="n">p2e</span> <span class="o">=</span> <span class="n">clag</span><span class="o">.</span><span class="n">optimize</span><span class="p">(</span><span class="n">P2</span><span class="p">,</span> <span class="n">p2</span><span class="p">)</span>
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<pre> 1 4.365e-01 6.884e+01 inf -- 8.449e+03 -- 1 1 1 1 1 1 1 1
2 7.732e-01 6.807e+01 7.998e+01 -- 8.529e+03 -- 0.596599 0.573944 0.565249 0.565 0.564474 0.564973 0.565061 0.563513
3 3.405e+00 6.725e+01 7.864e+01 -- 8.607e+03 -- 0.244013 0.162113 0.130209 0.130066 0.128738 0.12957 0.129649 0.12783
4 3.360e+01 6.630e+01 7.669e+01 -- 8.684e+03 -- -0.00316365 -0.215478 -0.306172 -0.305067 -0.307606 -0.306662 -0.306644 -0.307445
5 5.927e-01 6.489e+01 7.427e+01 -- 8.758e+03 -- -0.109447 -0.516884 -0.745492 -0.740106 -0.744696 -0.743873 -0.743899 -0.742873
6 3.725e-01 6.264e+01 7.143e+01 -- 8.830e+03 -- -0.143959 -0.685712 -1.18731 -1.17268 -1.18226 -1.18223 -1.18216 -1.17875
7 2.746e-01 5.898e+01 6.767e+01 -- 8.897e+03 -- -0.172747 -0.736257 -1.61838 -1.59549 -1.61983 -1.6226 -1.62219 -1.61642
8 2.229e-01 5.247e+01 6.144e+01 -- 8.959e+03 -- -0.196816 -0.752482 -1.99672 -1.9902 -2.05709 -2.06672 -2.06649 -2.06028
9 1.956e-01 4.085e+01 5.100e+01 -- 9.010e+03 -- -0.215738 -0.754987 -2.24985 -2.31629 -2.49299 -2.51725 -2.52319 -2.51952
10 1.984e-01 2.411e+01 3.583e+01 -- 9.046e+03 -- -0.227795 -0.74941 -2.34289 -2.51344 -2.9179 -2.97306 -3.0163 -3.01235
11 2.720e-01 8.629e+00 1.877e+01 -- 9.064e+03 -- -0.232745 -0.745804 -2.36419 -2.5762 -3.29011 -3.40817 -3.61486 -3.58767
12 1.101e+00 1.216e+00 6.309e+00 -- 9.071e+03 -- -0.23497 -0.744449 -2.37685 -2.59225 -3.51955 -3.73121 -4.59808 -4.44993
13 5.958e+02 2.028e-01 8.420e-01 -- 9.072e+03 -- -0.236431 -0.743626 -2.38453 -2.60022 -3.56793 -3.8266 -7.59808 -7.44993
14 3.292e-02 2.270e-01 1.932e-03 -- 9.072e+03 -- -0.236741 -0.743691 -2.38524 -2.60077 -3.56246 -3.81667 -10.5981 -10.4499
15 2.277e-03 2.223e-02 1.569e-02 -- 9.072e+03 -- -0.237254 -0.744315 -2.3903 -2.60854 -3.6113 -3.94232 -10.5981 -10.4499
16 6.863e-04 3.008e-03 1.056e-04 -- 9.072e+03 -- -0.237548 -0.744546 -2.38911 -2.60708 -3.60308 -3.93728 -10.5981 -10.4499
17 1.050e-04 8.493e-04 4.548e-06 -- 9.072e+03 -- -0.237471 -0.744501 -2.3894 -2.60727 -3.60273 -3.93998 -10.5981 -10.4499
********************
-0.237471 -0.744501 -2.3894 -2.60727 -3.60273 -3.93998 -10.5981 -10.4499
0.264343 0.221316 0.350826 0.274708 0.679297 0.951247 10 10
-0.000202502 2.37574e-05 0.000349669 0.000703071 0.000849318 0.000211385 -6.22057e-07 -1.19394e-06
********************
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">xscale</span><span class="p">(</span><span class="s1">&#39;log&#39;</span><span class="p">);</span> <span class="n">ylim</span><span class="p">(</span><span class="o">-</span><span class="mi">6</span><span class="p">,</span><span class="mi">2</span><span class="p">)</span>
<span class="n">errorbar</span><span class="p">(</span><span class="n">fqd</span><span class="p">,</span> <span class="n">p1</span><span class="p">,</span> <span class="n">yerr</span><span class="o">=</span><span class="n">p1e</span><span class="p">,</span> <span class="n">fmt</span><span class="o">=</span><span class="s1">&#39;o&#39;</span><span class="p">,</span> <span class="n">ms</span><span class="o">=</span><span class="mi">10</span><span class="p">)</span>
<span class="n">errorbar</span><span class="p">(</span><span class="n">fqd</span><span class="p">,</span> <span class="n">p2</span><span class="p">,</span> <span class="n">yerr</span><span class="o">=</span><span class="n">p2e</span><span class="p">,</span> <span class="n">fmt</span><span class="o">=</span><span class="s1">&#39;o&#39;</span><span class="p">,</span> <span class="n">ms</span><span class="o">=</span><span class="mi">10</span><span class="p">)</span>
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<pre>&lt;Container object of 3 artists&gt;</pre>
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mtmzkl6RdGv0IQEA4rLknDwAoHux4hUAEoyQB4AEizonH4mZ/Zakj0haq0op5r3tHA8aY2a3SMpK
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vMZzt0k6LOloHGNB46Icv6q9kj7f3FFiMTEcO7TZCo7heklnqrdLS/Uf15z8mKStlwywT9I/VO9/
m6Q/qk7PyMx2mtndZvZ6dz/k7llJ749pLGjcSo/fr1d3Hj3q7s+0etCQFOF3b7Z5KweLRTV0DFUJ
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eryJY8DKLef43SPpnlYOCsuynGP3kiq7yKIz1TyG7n5e0tByO6KEEgASrJkh/0NJv7Hg+/XV+9Ad
OH7di2PX/WI7hnGGvOnnPwR4WtJbzeyNZna5pPdJysf4eogXx697cey6X9OOYVwllF+SNKXKB6mn
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BCPkASDBCHkASDBCHgASjJAHgAT7f9o3MXBssae1AAAAAElFTkSuQmCC
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">p2</span><span class="p">,</span> <span class="n">p2e</span> <span class="o">=</span> <span class="n">clag</span><span class="o">.</span><span class="n">errors</span><span class="p">(</span><span class="n">P2</span><span class="p">,</span> <span class="n">p2</span><span class="p">,</span> <span class="n">p2e</span><span class="p">)</span>
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<pre> ### errors for param 0 ###
+++ 9.072e+03 9.071e+03 -2.375e-01 2.686e-02 0.913 +++
+++ 9.072e+03 9.071e+03 -2.375e-01 1.590e-01 1.9 +++
+++ 9.072e+03 9.071e+03 -2.375e-01 9.294e-02 1.37 +++
+++ 9.072e+03 9.071e+03 -2.375e-01 5.990e-02 1.13 +++
+++ 9.072e+03 9.071e+03 -2.375e-01 4.338e-02 1.02 +++
+++ 9.072e+03 9.071e+03 -2.375e-01 3.512e-02 0.966 +++
+++ 9.072e+03 9.071e+03 -2.375e-01 3.925e-02 0.993 +++
### errors for param 1 ###
+++ 9.072e+03 9.071e+03 -7.445e-01 -5.232e-01 0.914 +++
+++ 9.072e+03 9.071e+03 -7.445e-01 -4.125e-01 1.94 +++
+++ 9.072e+03 9.071e+03 -7.445e-01 -4.679e-01 1.39 +++
+++ 9.072e+03 9.071e+03 -7.445e-01 -4.955e-01 1.14 +++
+++ 9.072e+03 9.071e+03 -7.445e-01 -5.094e-01 1.02 +++
+++ 9.072e+03 9.071e+03 -7.445e-01 -5.163e-01 0.969 +++
+++ 9.072e+03 9.071e+03 -7.445e-01 -5.128e-01 0.997 +++
### errors for param 2 ###
+++ 9.072e+03 9.071e+03 -2.389e+00 -2.039e+00 1.13 +++
+++ 9.072e+03 9.071e+03 -2.389e+00 -2.214e+00 0.291 +++
+++ 9.072e+03 9.071e+03 -2.389e+00 -2.126e+00 0.647 +++
+++ 9.072e+03 9.071e+03 -2.389e+00 -2.082e+00 0.875 +++
+++ 9.072e+03 9.071e+03 -2.389e+00 -2.060e+00 1 +++
### errors for param 3 ###
+++ 9.072e+03 9.071e+03 -2.607e+00 -2.333e+00 1.17 +++
+++ 9.072e+03 9.071e+03 -2.607e+00 -2.470e+00 0.296 +++
+++ 9.072e+03 9.071e+03 -2.607e+00 -2.401e+00 0.664 +++
+++ 9.072e+03 9.071e+03 -2.607e+00 -2.367e+00 0.901 +++
+++ 9.072e+03 9.071e+03 -2.607e+00 -2.350e+00 1.03 +++
+++ 9.072e+03 9.071e+03 -2.607e+00 -2.358e+00 0.966 +++
+++ 9.072e+03 9.071e+03 -2.607e+00 -2.354e+00 0.999 +++
### errors for param 4 ###
+++ 9.072e+03 9.071e+03 -3.602e+00 -2.923e+00 2.16 +++
+++ 9.072e+03 9.071e+03 -3.602e+00 -3.263e+00 0.353 +++
+++ 9.072e+03 9.071e+03 -3.602e+00 -3.093e+00 0.996 +++
### errors for param 5 ###
+++ 9.072e+03 9.069e+03 -3.940e+00 -2.989e+00 4.49 +++
+++ 9.072e+03 9.071e+03 -3.940e+00 -3.464e+00 0.589 +++
+++ 9.072e+03 9.071e+03 -3.940e+00 -3.227e+00 1.88 +++
+++ 9.072e+03 9.071e+03 -3.940e+00 -3.345e+00 1.1 +++
+++ 9.072e+03 9.071e+03 -3.940e+00 -3.405e+00 0.818 +++
+++ 9.072e+03 9.071e+03 -3.940e+00 -3.375e+00 0.953 +++
+++ 9.072e+03 9.071e+03 -3.940e+00 -3.360e+00 1.03 +++
+++ 9.072e+03 9.071e+03 -3.940e+00 -3.368e+00 0.99 +++
+++ 9.072e+03 9.071e+03 -3.940e+00 -3.364e+00 1.01 +++
### errors for param 6 ###
+++ 9.072e+03 9.072e+03 -1.060e+01 -6.598e+00 0.0054 +++
+++ 9.072e+03 9.071e+03 -1.060e+01 -4.598e+00 0.542 +++
+++ 9.072e+03 9.069e+03 -1.060e+01 -3.598e+00 5.36 +++
+++ 9.072e+03 9.071e+03 -1.060e+01 -4.098e+00 1.72 +++
+++ 9.072e+03 9.071e+03 -1.060e+01 -4.348e+00 0.966 +++
+++ 9.072e+03 9.071e+03 -1.060e+01 -4.223e+00 1.29 +++
+++ 9.072e+03 9.071e+03 -1.060e+01 -4.286e+00 1.12 +++
+++ 9.072e+03 9.071e+03 -1.060e+01 -4.317e+00 1.04 +++
+++ 9.072e+03 9.071e+03 -1.060e+01 -4.332e+00 1 +++
### errors for param 7 ###
+++ 9.072e+03 9.072e+03 -1.045e+01 -7.450e+00 0.00104 +++
+++ 9.072e+03 9.072e+03 -1.045e+01 -5.950e+00 0.0328 +++
+++ 9.072e+03 9.071e+03 -1.045e+01 -5.200e+00 0.185 +++
+++ 9.072e+03 9.071e+03 -1.045e+01 -4.825e+00 0.439 +++
+++ 9.072e+03 9.071e+03 -1.045e+01 -4.637e+00 0.678 +++
+++ 9.072e+03 9.071e+03 -1.045e+01 -4.544e+00 0.842 +++
+++ 9.072e+03 9.071e+03 -1.045e+01 -4.497e+00 0.939 +++
+++ 9.072e+03 9.071e+03 -1.045e+01 -4.473e+00 0.992 +++
********************
-0.237486 -0.744501 -2.38936 -2.60722 -3.60235 -3.93982 -10.5981 -10.4499
0.276735 0.231691 0.328894 0.253241 0.509151 0.575777 2 5.97656
********************
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<li>Next we creat a lag object similar to the psd case. Now we use both light curves and the psd values obtained earlier.</li>
<li>We use cxd10r, becasue we used psd10r above, if that changes, this should change too. Though generally, there is no need to change these.</li>
<li>The light curves, time and error are passed as lists of lists. The outer list contains how many light curve sets we want to fit together, and the inner list contrain the first and second light curves whose lag is to be calculated</li>
<li>p is an array of starting parameters. A start like that should using works fine. Sometimes this need to be tweaked to make sure the fit converges.</li>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">Cx</span> <span class="o">=</span> <span class="n">clag</span><span class="o">.</span><span class="n">clag</span><span class="p">(</span><span class="s1">&#39;cxd10r&#39;</span><span class="p">,</span> <span class="p">[[</span><span class="n">t1</span><span class="p">,</span><span class="n">t2</span><span class="p">]],</span> <span class="p">[[</span><span class="n">l1</span><span class="p">,</span><span class="n">l2</span><span class="p">]],</span> <span class="p">[[</span><span class="n">l1e</span><span class="p">,</span><span class="n">l2e</span><span class="p">]],</span> <span class="n">dt</span><span class="p">,</span> <span class="n">fqL</span><span class="p">,</span> <span class="n">p1</span><span class="p">,</span> <span class="n">p2</span><span class="p">)</span>
<span class="n">p</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">(</span> <span class="p">((</span><span class="n">p1</span><span class="o">+</span><span class="n">p2</span><span class="p">)</span><span class="o">*</span><span class="mf">0.5</span><span class="o">-</span><span class="mf">0.3</span><span class="p">,</span><span class="n">p1</span><span class="o">*</span><span class="mi">0</span><span class="o">+</span><span class="mf">0.1</span><span class="p">)</span> <span class="p">)</span> <span class="c1"># a good starting point generally</span>
<span class="n">p</span><span class="p">,</span> <span class="n">pe</span> <span class="o">=</span> <span class="n">clag</span><span class="o">.</span><span class="n">optimize</span><span class="p">(</span><span class="n">Cx</span><span class="p">,</span> <span class="n">p</span><span class="p">)</span>
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<pre> 1 1.507e+04 9.353e+00 inf -- 1.463e+04 -- -0.263469 -0.756956 -2.09189 -2.3639 -3.16804 -3.51705 -7.39217 -11.0905 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
3 1.162e+04 1.111e+01 2.207e+00 -- 1.464e+04 -- -0.222515 -0.71868 -2.05195 -2.3255 -3.13814 -3.44569 -7.69217 -11.0905 0.0540223 0.146385 0.211107 0.120928 0.22451 0.352806 0.225787 0.1
5 2.572e+03 1.301e+01 1.993e+00 -- 1.464e+04 -- -0.188623 -0.686392 -2.01542 -2.29378 -3.10648 -3.3727 -7.99217 -11.0905 0.0208945 0.18077 0.291002 0.136385 0.324159 0.504178 1.71174 0.1
7 5.499e+03 1.506e+01 1.809e+00 -- 1.464e+04 -- -0.160312 -0.658983 -1.98347 -2.26721 -3.07548 -3.31147 -8.29217 -11.0905 -0.0038816 0.207073 0.349667 0.148222 0.403652 0.596551 2.11801 0.1
9 1.265e+03 1.727e+01 1.655e+00 -- 1.464e+04 -- -0.136444 -0.63555 -1.95597 -2.2447 -3.04632 -3.26203 -8.59217 -11.0905 -0.0229558 0.227707 0.393817 0.157539 0.467517 0.657355 -1.76354 0.1
11 6.386e+02 1.966e+01 1.525e+00 -- 1.464e+04 -- -0.116154 -0.615387 -1.9324 -2.22548 -3.01944 -3.22204 -8.29217 -11.0905 -0.0379751 0.244228 0.427807 0.165034 0.519417 0.700307 -1.76354 0.1
13 3.235e+02 2.224e+01 1.412e+00 -- 1.464e+04 -- -0.0987795 -0.597934 -1.91218 -2.20896 -2.99492 -3.18933 -7.99217 -11.0905 -0.0500122 0.25768 0.454482 0.171164 0.562133 0.732293 -1.76354 0.1
15 1.644e+02 2.500e+01 1.312e+00 -- 1.464e+04 -- -0.0838109 -0.58275 -1.89479 -2.19468 -2.97268 -3.16229 -7.69217 -11.0905 -0.0597936 0.268786 0.475751 0.176246 0.597724 0.757149 -1.76354 0.1
17 8.384e+01 2.795e+01 1.223e+00 -- 1.465e+04 -- -0.0708471 -0.569482 -1.87979 -2.18229 -2.95253 -3.13972 -7.39217 -11.0905 -0.0678276 0.278065 0.492929 0.180509 0.627711 0.777132 -1.76354 0.1
19 4.288e+01 3.109e+01 1.141e+00 -- 1.465e+04 -- -0.059569 -0.557845 -1.86681 -2.17151 -2.93431 -3.12075 -7.09217 -11.0905 -0.0744802 0.285897 0.506948 0.184119 0.653232 0.793647 -1.76354 0.1
21 2.200e+01 3.443e+01 1.066e+00 -- 1.465e+04 -- -0.0497196 -0.547603 -1.85555 -2.1621 -2.91781 -3.1047 -6.79217 -11.0905 -0.0800213 0.292565 0.518486 0.187201 0.675142 0.807615 -1.76354 0.1
23 1.132e+01 3.796e+01 9.959e-01 -- 1.465e+04 -- -0.0410891 -0.538564 -1.84575 -2.15388 -2.90286 -3.09105 -6.49217 -11.0905 -0.084654 0.298288 0.528046 0.189851 0.694098 0.819659 -1.76354 0.1
24 5.898e-01 3.584e+03 1.376e+00 -- 1.465e+04 -- 0.034754 -0.4586 -1.76026 -2.08192 -2.76728 -2.97456 -3.49217 -11.0905 -0.123455 0.34774 0.60772 0.212743 0.859212 0.925291 -2.01201 0.1
25 8.154e-01 5.087e+01 1.095e+01 -- 1.466e+04 -- 0.0315381 -0.463316 -1.78861 -2.14119 -2.7032 -3.06487 -3.50786 -11.0905 -0.080452 0.354068 0.642389 0.0872582 0.929788 0.925607 -1.87766 0.1
26 8.474e-02 4.125e+01 1.295e+00 -- 1.466e+04 -- 0.0313567 -0.462364 -1.77246 -2.09785 -2.72914 -3.01339 -3.63657 -11.0905 -0.0903589 0.346492 0.695621 0.158407 0.937946 1.04186 -1.81 0.1
27 1.402e-01 8.842e+00 5.049e-01 -- 1.466e+04 -- 0.0307976 -0.462048 -1.78087 -2.11005 -2.73093 -3.02079 -3.77705 -11.0905 -0.0859431 0.34971 0.6455 0.156108 0.93052 1.00707 -1.65662 0.1
28 1.151e-01 7.210e+00 1.569e-01 -- 1.466e+04 -- 0.0307692 -0.462203 -1.77706 -2.10191 -2.73633 -3.01355 -3.90775 -11.0905 -0.085448 0.345468 0.669565 0.177991 0.929605 0.996167 -1.50215 0.1
29 8.198e-02 5.268e+00 4.450e-02 -- 1.466e+04 -- 0.0307085 -0.462133 -1.77941 -2.10487 -2.7354 -3.01527 -3.97788 -11.0905 -0.0852619 0.347439 0.650051 0.180002 0.931237 0.991797 -1.32927 0.1
30 4.907e-02 1.673e+00 1.011e-02 -- 1.466e+04 -- 0.0307433 -0.46222 -1.77843 -2.10279 -2.73529 -3.01313 -4.0139 -11.0905 -0.0848026 0.3465 0.657076 0.186301 0.932779 0.989877 -1.2203 0.1
31 2.218e-02 1.737e+00 2.283e-03 -- 1.466e+04 -- 0.0307595 -0.462214 -1.77904 -2.10366 -2.73433 -3.01368 -4.02131 -11.0905 -0.0847916 0.347141 0.651721 0.186854 0.934547 0.990363 -1.16042 0.1
32 1.049e-02 6.278e-01 5.116e-04 -- 1.466e+04 -- 0.0307847 -0.462244 -1.77877 -2.10315 -2.73397 -3.01308 -4.02614 -11.0905 -0.0846378 0.346933 0.653892 0.188201 0.935705 0.990726 -1.13468 0.1
33 4.768e-03 5.593e-01 1.303e-04 -- 1.466e+04 -- 0.0307977 -0.462243 -1.77893 -2.10342 -2.73358 -3.01326 -4.02629 -11.0905 -0.0846303 0.347124 0.652557 0.188172 0.936534 0.991266 -1.12279 0.1
34 2.366e-03 2.813e-01 3.574e-05 -- 1.466e+04 -- 0.0308087 -0.462251 -1.77885 -2.10329 -2.73343 -3.0131 -4.02705 -11.0905 -0.0845834 0.347075 0.653209 0.188435 0.937018 0.991526 -1.11743 0.1
********************
0.0308087 -0.462251 -1.77885 -2.10329 -2.73343 -3.0131 -4.02705 -11.0905 -0.0845834 0.347075 0.653209 0.188435 0.937018 0.991526 -1.11743 0.1
0.00444687 0.00391368 0.0195472 0.0522199 0.0692273 0.0931011 0.600907 10 0.0791371 0.0681671 0.171256 0.248503 0.290782 0.317185 1.41333 10
0.281266 0.00261966 -0.113352 -0.0304571 0.0248402 -0.00516435 0.000469769 2.53754e-07 0.00150497 0.0106824 -0.0107165 -0.00105737 0.003675 0.00209301 0.00132737 2.87086e-08
********************
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<li>We get the errors for the cross spectrum and phase lags</li>
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<span class="n">p</span><span class="p">,</span> <span class="n">pe</span> <span class="o">=</span> <span class="n">clag</span><span class="o">.</span><span class="n">errors</span><span class="p">(</span><span class="n">Cx</span><span class="p">,</span> <span class="n">p</span><span class="p">,</span> <span class="n">pe</span><span class="p">)</span>
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<pre> ### errors for param 0 ###
+++ 1.466e+04 1.466e+04 3.066e-02 3.294e-02 0.176 +++
+++ 1.466e+04 1.466e+04 3.066e-02 3.407e-02 0.514 +++
+++ 1.466e+04 1.466e+04 3.066e-02 3.464e-02 0.828 +++
+++ 1.466e+04 1.466e+04 3.066e-02 3.492e-02 1.05 +++
+++ 1.466e+04 1.466e+04 3.066e-02 3.478e-02 0.932 +++
+++ 1.466e+04 1.466e+04 3.066e-02 3.485e-02 0.989 +++
+++ 1.466e+04 1.466e+04 3.066e-02 3.489e-02 1.02 +++
+++ 1.466e+04 1.466e+04 3.066e-02 3.487e-02 1 +++
### errors for param 1 ###
+++ 1.466e+04 1.466e+04 -4.624e-01 -4.604e-01 0.268 +++
+++ 1.466e+04 1.466e+04 -4.624e-01 -4.594e-01 0.767 +++
+++ 1.466e+04 1.466e+04 -4.624e-01 -4.589e-01 1.2 +++
+++ 1.466e+04 1.466e+04 -4.624e-01 -4.592e-01 0.962 +++
+++ 1.466e+04 1.466e+04 -4.624e-01 -4.590e-01 1.07 +++
+++ 1.466e+04 1.466e+04 -4.624e-01 -4.591e-01 1.02 +++
+++ 1.466e+04 1.466e+04 -4.624e-01 -4.591e-01 0.989 +++
+++ 1.466e+04 1.466e+04 -4.624e-01 -4.591e-01 1 +++
### errors for param 2 ###
+++ 1.466e+04 1.466e+04 -1.780e+00 -1.770e+00 0.503 +++
+++ 1.466e+04 1.466e+04 -1.780e+00 -1.765e+00 1.74 +++
+++ 1.466e+04 1.466e+04 -1.780e+00 -1.767e+00 0.957 +++
+++ 1.466e+04 1.466e+04 -1.780e+00 -1.766e+00 1.3 +++
+++ 1.466e+04 1.466e+04 -1.780e+00 -1.767e+00 1.11 +++
+++ 1.466e+04 1.466e+04 -1.780e+00 -1.767e+00 1.03 +++
+++ 1.466e+04 1.466e+04 -1.780e+00 -1.767e+00 0.995 +++
### errors for param 3 ###
+++ 1.466e+04 1.466e+04 -2.100e+00 -2.075e+00 0.424 +++
+++ 1.466e+04 1.466e+04 -2.100e+00 -2.062e+00 1.24 +++
+++ 1.466e+04 1.466e+04 -2.100e+00 -2.068e+00 0.753 +++
+++ 1.466e+04 1.466e+04 -2.100e+00 -2.065e+00 0.975 +++
+++ 1.466e+04 1.466e+04 -2.100e+00 -2.064e+00 1.1 +++
+++ 1.466e+04 1.466e+04 -2.100e+00 -2.064e+00 1.03 +++
+++ 1.466e+04 1.466e+04 -2.100e+00 -2.065e+00 1 +++
### errors for param 4 ###
+++ 1.466e+04 1.466e+04 -2.728e+00 -2.696e+00 0.209 +++
+++ 1.466e+04 1.466e+04 -2.728e+00 -2.680e+00 0.593 +++
+++ 1.466e+04 1.466e+04 -2.728e+00 -2.672e+00 0.932 +++
+++ 1.466e+04 1.466e+04 -2.728e+00 -2.668e+00 1.17 +++
+++ 1.466e+04 1.466e+04 -2.728e+00 -2.670e+00 1.05 +++
+++ 1.466e+04 1.466e+04 -2.728e+00 -2.671e+00 0.987 +++
+++ 1.466e+04 1.466e+04 -2.728e+00 -2.670e+00 1.02 +++
+++ 1.466e+04 1.466e+04 -2.728e+00 -2.671e+00 1 +++
### errors for param 5 ###
+++ 1.466e+04 1.466e+04 -3.007e+00 -2.964e+00 0.386 +++
+++ 1.466e+04 1.466e+04 -3.007e+00 -2.942e+00 1.12 +++
+++ 1.466e+04 1.466e+04 -3.007e+00 -2.953e+00 0.68 +++
+++ 1.466e+04 1.466e+04 -3.007e+00 -2.947e+00 0.877 +++
+++ 1.466e+04 1.466e+04 -3.007e+00 -2.945e+00 0.991 +++
### errors for param 6 ###
+++ 1.466e+04 1.466e+04 -4.051e+00 -3.738e+00 0.336 +++
+++ 1.466e+04 1.466e+04 -4.051e+00 -3.582e+00 1.27 +++
+++ 1.466e+04 1.466e+04 -4.051e+00 -3.660e+00 0.674 +++
+++ 1.466e+04 1.466e+04 -4.051e+00 -3.621e+00 0.927 +++
+++ 1.466e+04 1.466e+04 -4.051e+00 -3.602e+00 1.09 +++
+++ 1.466e+04 1.466e+04 -4.051e+00 -3.611e+00 1 +++
### errors for param 7 ###
+++ 1.466e+04 1.466e+04 -3.804e+00 -3.719e+00 0.667 +++
+++ 1.466e+04 1.466e+04 -3.804e+00 -3.676e+00 2.74 +++
+++ 1.466e+04 1.466e+04 -3.804e+00 -3.697e+00 1.36 +++
+++ 1.466e+04 1.466e+04 -3.804e+00 -3.708e+00 0.962 +++
+++ 1.466e+04 1.466e+04 -3.804e+00 -3.703e+00 1.14 +++
+++ 1.466e+04 1.466e+04 -3.804e+00 -3.705e+00 1.05 +++
+++ 1.466e+04 1.466e+04 -3.804e+00 -3.707e+00 1.01 +++
### errors for param 8 ###
+++ 1.466e+04 1.466e+04 -8.599e-02 -6.017e-03 1 +++
### errors for param 9 ###
+++ 1.466e+04 1.466e+04 3.480e-01 4.170e-01 0.968 +++
+++ 1.466e+04 1.466e+04 3.480e-01 4.515e-01 1.95 +++
+++ 1.466e+04 1.466e+04 3.480e-01 4.342e-01 1.43 +++
+++ 1.466e+04 1.466e+04 3.480e-01 4.256e-01 1.19 +++
+++ 1.466e+04 1.466e+04 3.480e-01 4.213e-01 1.08 +++
+++ 1.466e+04 1.466e+04 3.480e-01 4.191e-01 1.02 +++
+++ 1.466e+04 1.466e+04 3.480e-01 4.181e-01 0.996 +++
### errors for param 10 ###
+++ 1.466e+04 1.466e+04 6.487e-01 8.233e-01 0.85 +++
+++ 1.466e+04 1.466e+04 6.487e-01 9.105e-01 1.66 +++
+++ 1.466e+04 1.466e+04 6.487e-01 8.669e-01 1.24 +++
+++ 1.466e+04 1.466e+04 6.487e-01 8.451e-01 1.04 +++
+++ 1.466e+04 1.466e+04 6.487e-01 8.342e-01 0.944 +++
+++ 1.466e+04 1.466e+04 6.487e-01 8.396e-01 0.992 +++
### errors for param 11 ###
+++ 1.466e+04 1.466e+04 1.842e-01 4.266e-01 0.925 +++
+++ 1.466e+04 1.466e+04 1.842e-01 5.478e-01 1.96 +++
+++ 1.466e+04 1.466e+04 1.842e-01 4.872e-01 1.41 +++
+++ 1.466e+04 1.466e+04 1.842e-01 4.569e-01 1.16 +++
+++ 1.466e+04 1.466e+04 1.842e-01 4.417e-01 1.04 +++
+++ 1.466e+04 1.466e+04 1.842e-01 4.342e-01 0.98 +++
+++ 1.466e+04 1.466e+04 1.842e-01 4.380e-01 1.01 +++
### errors for param 12 ###
+++ 1.466e+04 1.466e+04 9.450e-01 1.226e+00 0.62 +++
+++ 1.466e+04 1.466e+04 9.450e-01 1.367e+00 1.36 +++
+++ 1.466e+04 1.466e+04 9.450e-01 1.297e+00 0.96 +++
+++ 1.466e+04 1.466e+04 9.450e-01 1.332e+00 1.15 +++
+++ 1.466e+04 1.466e+04 9.450e-01 1.314e+00 1.06 +++
+++ 1.466e+04 1.466e+04 9.450e-01 1.305e+00 1.01 +++
### errors for param 13 ###
+++ 1.466e+04 1.466e+04 1.013e+00 1.320e+00 0.825 +++
+++ 1.466e+04 1.466e+04 1.013e+00 1.474e+00 1.81 +++
+++ 1.466e+04 1.466e+04 1.013e+00 1.397e+00 1.28 +++
+++ 1.466e+04 1.466e+04 1.013e+00 1.358e+00 1.04 +++
+++ 1.466e+04 1.466e+04 1.013e+00 1.339e+00 0.93 +++
+++ 1.466e+04 1.466e+04 1.013e+00 1.349e+00 0.984 +++
+++ 1.466e+04 1.466e+04 1.013e+00 1.354e+00 1.01 +++
+++ 1.466e+04 1.466e+04 1.013e+00 1.351e+00 0.998 +++
### errors for param 14 ###
### errors for param 15 ###
+++ 1.466e+04 1.466e+04 6.767e-01 1.187e+00 0.535 +++
+++ 1.466e+04 1.466e+04 6.767e-01 1.442e+00 1.32 +++
+++ 1.466e+04 1.466e+04 6.767e-01 1.314e+00 0.875 +++
+++ 1.466e+04 1.466e+04 6.767e-01 1.378e+00 1.08 +++
+++ 1.466e+04 1.466e+04 6.767e-01 1.346e+00 0.974 +++
+++ 1.466e+04 1.466e+04 6.767e-01 1.362e+00 1.03 +++
+++ 1.466e+04 1.466e+04 6.767e-01 1.354e+00 1 +++
********************
0.030665 -0.46243 -1.78021 -2.09957 -2.72838 -3.0075 -4.05118 -3.80382 -0.0859876 0.347974 0.648709 0.184157 0.945002 1.01285 -1.02557 0.67675
0.00420635 0.00330811 0.0128812 0.0346945 0.0578177 0.0629875 0.439838 0.0971903 0.0799706 0.0700847 0.190914 0.253798 0.360451 0.338322 2 0.677385
********************
</pre>
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<div class="prompt input_prompt">In&nbsp;[99]:</div>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">phi</span><span class="p">,</span> <span class="n">phie</span> <span class="o">=</span> <span class="n">p</span><span class="p">[</span><span class="n">nfq</span><span class="p">:],</span> <span class="n">pe</span><span class="p">[</span><span class="n">nfq</span><span class="p">:]</span>
<span class="n">lag</span><span class="p">,</span> <span class="n">lage</span> <span class="o">=</span> <span class="n">phi</span><span class="o">/</span><span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="o">*</span><span class="n">fqd</span><span class="p">),</span> <span class="n">phie</span><span class="o">/</span><span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="o">*</span><span class="n">fqd</span><span class="p">)</span>
<span class="n">cx</span><span class="p">,</span> <span class="n">cxe</span> <span class="o">=</span> <span class="n">p</span><span class="p">[:</span><span class="n">nfq</span><span class="p">],</span> <span class="n">pe</span><span class="p">[:</span><span class="n">nfq</span><span class="p">]</span>
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<div class="prompt input_prompt">In&nbsp;[100]:</div>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">xscale</span><span class="p">(</span><span class="s1">&#39;log&#39;</span><span class="p">);</span> <span class="n">ylim</span><span class="p">(</span><span class="o">-</span><span class="mi">10</span><span class="p">,</span><span class="mi">10</span><span class="p">)</span>
<span class="n">errorbar</span><span class="p">(</span><span class="n">fqd</span><span class="p">,</span> <span class="n">lag</span><span class="p">,</span> <span class="n">yerr</span><span class="o">=</span><span class="n">lage</span><span class="p">,</span> <span class="n">fmt</span><span class="o">=</span><span class="s1">&#39;o&#39;</span><span class="p">,</span> <span class="n">ms</span><span class="o">=</span><span class="mi">10</span><span class="p">)</span>
</pre></div>
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<div class="output">
<div class="output_area"><div class="prompt output_prompt">Out[100]:</div>
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<pre>&lt;Container object of 3 artists&gt;</pre>
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ss24rI/+e8fM/l7SJ/jPID/d9p+kJ1X/zH1H0pF2+8/jhO/yi76d07Irfrr7c1p2mWgURif9Ny1p
epCNQsc66b//lvRng2wUOrZq/7n7eUm7Ot0RUz0BIKA8wv8NSb/e9HzVi76hkOi/cqP/yi2z/htE
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3/HrpZTtQG/ov3Kj/8otdf8VepEXACANTvgCQECEPwAERPgDQECEPwAERPgDQECEPwAERPgDQECE
PwAE9H9r3y+QQfII/gAAAABJRU5ErkJggg==
"
>
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<div class="prompt input_prompt">In&nbsp;[&nbsp;]:</div>
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<div class=" highlight hl-ipython2"><pre><span></span>
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