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| author | Daniele Nicolodi <nicolodi@science.unitn.it> |
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| date | Wed, 23 Nov 2011 19:22:13 +0100 |
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<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/1999/REC-html401-19991224/loose.dtd"> <html lang="en"> <head> <meta name="generator" content= "HTML Tidy for Mac OS X (vers 1st December 2004), see www.w3.org"> <meta http-equiv="Content-Type" content= "text/html; charset=us-ascii"> <title>Linear least squares with singular value deconposition - single experiment (LTPDA Toolbox)</title> <link rel="stylesheet" href="docstyle.css" type="text/css"> <meta name="generator" content="DocBook XSL Stylesheets V1.52.2"> <meta name="description" content= "Presents an overview of the features, system requirements, and starting the toolbox."> </head> <body> <a name="top_of_page" id="top_of_page"></a> <p style="font-size:1px;"> </p> <table class="nav" summary="Navigation aid" border="0" width= "100%" cellpadding="0" cellspacing="0"> <tr> <td valign="baseline"><b>LTPDA Toolbox</b></td><td><a href="../helptoc.html">contents</a></td> <td valign="baseline" align="right"><a href= "sigproc_linear_param_estimation_svd.html"><img src="b_prev.gif" border="0" align= "bottom" alt="Linear Parameter Estimation with Singular Value Decomposition"></a> <a href= "sigproc_example_matrix_linlsqsvd.html"><img src="b_next.gif" border="0" align= "bottom" alt="Linear least squares with singular value deconposition - multiple experiments"></a></td> </tr> </table> <h1 class="title"><a name="f3-12899" id="f3-12899"></a>Linear least squares with singular value deconposition - single experiment</h1> <hr> <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> <p> <div align="center"> <IMG src="images/example_ao_linlsqsvd_01.png" align="center" border="0"> </div> </p> </p> <br> <br> <table class="nav" summary="Navigation aid" border="0" width= "100%" cellpadding="0" cellspacing="0"> <tr valign="top"> <td align="left" width="20"><a href="sigproc_linear_param_estimation_svd.html"><img src= "b_prev.gif" border="0" align="bottom" alt= "Linear Parameter Estimation with Singular Value Decomposition"></a> </td> <td align="left">Linear Parameter Estimation with Singular Value Decomposition</td> <td> </td> <td align="right">Linear least squares with singular value deconposition - multiple experiments</td> <td align="right" width="20"><a href= "sigproc_example_matrix_linlsqsvd.html"><img src="b_next.gif" border="0" align= "bottom" alt="Linear least squares with singular value deconposition - multiple experiments"></a></td> </tr> </table><br> <p class="copy">©LTP Team</p> </body> </html>