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author Daniele Nicolodi <nicolodi@science.unitn.it>
date Mon, 05 Dec 2011 16:20:06 +0100
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  <title>Linear least squares with singular value deconposition - multiple experiments (LTPDA Toolbox)</title>
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      <td valign="baseline"><b>LTPDA Toolbox</b></td><td><a href="../helptoc.html">contents</a></td>

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  <h1 class="title"><a name="f3-12899" id="f3-12899"></a>Linear least squares with singular value deconposition - multiple experiments</h1>
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<p>Determine the coefficients of a linear combination of noises</p>

<h2>Contents</h2>
<div><ul><li><a href="#1">Make data</a></li>
<li><a href="#2">Do fit</a></li></ul></div>

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

<div class="fragment"><pre>

  fs    = 10;
  nsecs = 10;

  <span class="comment">% fit basis for 2 experiments case</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;
  B4 = 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>));
  B4.setName;

  C1 = matrix(B1,B2,plist(<span class="string">'shape'</span>,[2,1]));
  C1.setName;
  C2 = matrix(B3,B4,plist(<span class="string">'shape'</span>,[2,1]));
  C2.setName;

  <span class="comment">% make additive noise</span>
  n1  = 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>));
  n1.setName;
  n2  = 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>));
  n2.setName;

  <span class="comment">% coefficients of the linear combination</span>
  a1 = ao(1,plist(<span class="string">'yunits'</span>,<span class="string">'m/T'</span>));
  a1.setName;
  a2 = ao(2,plist(<span class="string">'yunits'</span>,<span class="string">'m/T'</span>));
  a2.setName;

  <span class="comment">% assign output values</span>
  <span class="comment">% y is a matrix containing the outputs of two experiments:</span>
  y1 = a1*B1 + a2*B3 + n1;
  y2 = a1*B2 + a2*B4 + n2;
  y = matrix(y1,y2,plist(<span class="string">'shape'</span>,[2,1]));

</pre></div>


</pre><h2>Do fit<a name="2"></a></h2>

  <div class="fragment"><pre>

  <span class="comment">% Get a fit with linlsqsvd</span>
  pobj = linlsqsvd(C1, C2, y)

</pre></div>

<div class="fragment"><pre>

  ---- pest 1 ----
         name: a1*C1+a2*C2
  param names: {'a1', 'a2'}
            y: [0.97312642877028477;2.0892132651873916]
           dy: [0.06611444020240001;0.065007088662104057]
       yunits: [T^(-1) m][T^(-1) m]
          pdf: []
          cov: [2x2], ([0.00437111920327673 -0.000390118937121542;-0.000390118937121542 0.00422592157632266])
         corr: []
        chain: []
         chi2: 0.85210029717685576
          dof: 198
       models: matrix(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), matrix(B3/tsdata Ndata=[100x1], fs=10, nsecs=10, t0=1970-01-01 00:00:00.000 UTC, B4/tsdata Ndata=[100x1], fs=10, nsecs=10, t0=1970-01-01 00:00:00.000 UTC)
  description: 
         UUID: 545c9699-e749-40d5-bbe1-1322599c9c5d
  ----------------

</pre></div>

<div class="fragment"><pre>

  <span class="comment">% do linear combination: using eval</span>
  yfit = pobj.eval;

  <span class="comment">% extract objects</span>
  yfit1 = getObjectAtIndex(yfit,1);
  yfit2 = getObjectAtIndex(yfit,2);

  <span class="comment">% Plot - compare data with fit</span>
  iplot(y1, yfit1)
  iplot(y2, yfit2)

</pre></div>

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      "Linear least squares with singular value deconposition - single experiment"></a>&nbsp;</td>

      <td align="left">Linear least squares with singular value deconposition - single experiment</td>

      <td>&nbsp;</td>

      <td align="right">Iterative linear parameter estimation for multichannel systems - symbolic system model in frequency domain</td>

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