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<h1 class="title"><a name="f3-12899" id="f3-12899"></a>Linear least squares with singular value deconposition - single experiment</h1>
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<p>
<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>
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