<p>Determine the coefficients of a linear combination of noises and comapre with lscov</p>
<h2>Contents</h2>
<div>
  <ul>
    <li><a href="#1">Make data</a></li>
    <li><a href="#2">Do fit and check results</a></li>
  </ul>
</div>

<h2>Make data<a name="1"></a></h2>

<div class="fragment"><pre>
  
  fs    = 10;
  nsecs = 10;

  <span class="comment">% Elements of the fit basis</span>
  B1 = ao(plist(<span class="string">'tsfcn'</span>, <span class="string">'randn(size(t))'</span>, <span class="string">'fs'</span>, fs, <span class="string">'nsecs'</span>, nsecs, <span class="string">'yunits'</span>, <span class="string">'T'</span>));
  B1.setName;
  B2 = ao(plist(<span class="string">'tsfcn'</span>, <span class="string">'randn(size(t))'</span>, <span class="string">'fs'</span>, fs, <span class="string">'nsecs'</span>, nsecs, <span class="string">'yunits'</span>, <span class="string">'T'</span>));
  B2.setName;
  B3 = ao(plist(<span class="string">'tsfcn'</span>, <span class="string">'randn(size(t))'</span>, <span class="string">'fs'</span>, fs, <span class="string">'nsecs'</span>, nsecs, <span class="string">'yunits'</span>, <span class="string">'T'</span>));
  B3.setName;

  <span class="comment">% random additive noise</span>
  n  = ao(plist(<span class="string">'tsfcn'</span>, <span class="string">'randn(size(t))'</span>, <span class="string">'fs'</span>, fs, <span class="string">'nsecs'</span>, nsecs, <span class="string">'yunits'</span>, <span class="string">'m'</span>));

  <span class="comment">% coefficients of the linear combination</span>
  c1 = ao(1,plist(<span class="string">'yunits'</span>,<span class="string">'m/T'</span>));
  c1.setName;

  c2 = ao(2,plist(<span class="string">'yunits'</span>,<span class="string">'m/T'</span>));
  c2.setName;

  c3 = ao(3,plist(<span class="string">'yunits'</span>,<span class="string">'m T^-1'</span>));
  c3.setName;

  <span class="comment">% build output of linear system</span>
  y = c1*B1 + c2*B2 + c3*B3 + n;
  y.simplifyYunits;

</pre></div>


<h2>Do fit and check results<a name="2"></a></h2>

<div class="fragment"><pre>
  
  <span class="comment">% Get a fit with linlsqsvd</span>
  pobj1 = linlsqsvd(B1, B2, B3, y)

</pre></div>

<div class="fragment"><pre>

  ---- pest 1 ----
         name: a1*B1+a2*B2+a3*B3
  param names: {'a1', 'a2', 'a3'}
            y: [0.81162366736073077;1.8907151217948008;3.0098623857384701]
           dy: [0.091943725803872112;0.089863977231447567;0.097910574305897308]
       yunits: [m T^(-1)][m T^(-1)][m T^(-1)]
          pdf: []
          cov: [3x3], ([0.00845364871469762 0.000268768332741779 0.000180072770333592;0.000268768332741779 0.00807553440385413 0.00125972375325089;0.000180072770333592 0.00125972375325089 0.00958648056091064])
         corr: [3x3], ([1 0.0325289738130578 0.020003055941376;0.0325289738130578 1 0.143172656986983;0.020003055941376 0.143172656986983 1])
        chain: []
         chi2: 0.87276552675043451
          dof: 97
       models: B1/tsdata Ndata=[100x1], fs=10, nsecs=10, t0=1970-01-01 00:00:00.000 UTC, B2/tsdata Ndata=[100x1], fs=10, nsecs=10, t0=1970-01-01 00:00:00.000 UTC, B3/tsdata Ndata=[100x1], fs=10, nsecs=10, t0=1970-01-01 00:00:00.000 UTC
  description: 
         UUID: b8628843-a1e8-4815-b69b-90efdadc16c2
  ----------------

</pre></div>

<div class="fragment"><pre>

  <span class="comment">% do linear combination: using eval</span>
  yfit = pobj1.eval(B1, B2, B3);

  <span class="comment">% Plot - compare data with fit result</span>
  iplot(y, yfit)

</pre></div>

<p>
  <div align="center">
    <IMG src="images/example_ao_linlsqsvd_01.png" align="center" border="0">
  </div>
</p>