+
−
+
−
+
−
+
−<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>
+
−
+
−<p>
+
−  <div align="center">
+
−    <IMG src="images/example_matrix_linlsqsvd_01.png" align="center" border="0">
+
−  </div>
+
−</p>
+
−<p>
+
−  <div align="center">
+
−    <IMG src="images/example_matrix_linlsqsvd_02.png" align="center" border="0">
+
−  </div>
+
−</p>
+
−