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Update utils.jquery * * * Update utils.jmysql.getsinfo
author Daniele Nicolodi <nicolodi@science.unitn.it>
date Mon, 05 Dec 2011 16:20:06 +0100
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1
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2
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3
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4 <p>Determine the coefficients of a linear combination of noises and comapre with lscov</p>
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5 <h2>Contents</h2>
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6 <div>
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7 <ul>
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8 <li><a href="#1">Make data</a></li>
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9 <li><a href="#2">Do fit and check results</a></li>
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10 </ul>
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11 </div>
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13 <h2>Make data<a name="1"></a></h2>
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15 <div class="fragment"><pre>
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16
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17 fs = 10;
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18 nsecs = 10;
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19
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20 <span class="comment">% Elements of the fit basis</span>
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21 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>));
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22 B1.setName;
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23 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>));
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24 B2.setName;
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25 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>));
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26 B3.setName;
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27
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28 <span class="comment">% random additive noise</span>
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29 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>));
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30
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31 <span class="comment">% coefficients of the linear combination</span>
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32 c1 = ao(1,plist(<span class="string">'yunits'</span>,<span class="string">'m/T'</span>));
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33 c1.setName;
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34
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35 c2 = ao(2,plist(<span class="string">'yunits'</span>,<span class="string">'m/T'</span>));
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36 c2.setName;
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37
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38 c3 = ao(3,plist(<span class="string">'yunits'</span>,<span class="string">'m T^-1'</span>));
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39 c3.setName;
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40
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41 <span class="comment">% build output of linear system</span>
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42 y = c1*B1 + c2*B2 + c3*B3 + n;
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43 y.simplifyYunits;
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44
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45 </pre></div>
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48 <h2>Do fit and check results<a name="2"></a></h2>
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49
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50 <div class="fragment"><pre>
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51
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52 <span class="comment">% Get a fit with linlsqsvd</span>
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53 pobj1 = linlsqsvd(B1, B2, B3, y)
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54
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55 </pre></div>
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56
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57 <div class="fragment"><pre>
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58
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59 ---- pest 1 ----
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60 name: a1*B1+a2*B2+a3*B3
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61 param names: {'a1', 'a2', 'a3'}
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62 y: [0.81162366736073077;1.8907151217948008;3.0098623857384701]
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63 dy: [0.091943725803872112;0.089863977231447567;0.097910574305897308]
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64 yunits: [m T^(-1)][m T^(-1)][m T^(-1)]
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65 pdf: []
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66 cov: [3x3], ([0.00845364871469762 0.000268768332741779 0.000180072770333592;0.000268768332741779 0.00807553440385413 0.00125972375325089;0.000180072770333592 0.00125972375325089 0.00958648056091064])
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67 corr: [3x3], ([1 0.0325289738130578 0.020003055941376;0.0325289738130578 1 0.143172656986983;0.020003055941376 0.143172656986983 1])
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68 chain: []
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69 chi2: 0.87276552675043451
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70 dof: 97
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71 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
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72 description:
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73 UUID: b8628843-a1e8-4815-b69b-90efdadc16c2
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74 ----------------
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75
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76 </pre></div>
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77
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78 <div class="fragment"><pre>
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79
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80 <span class="comment">% do linear combination: using eval</span>
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81 yfit = pobj1.eval(B1, B2, B3);
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82
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83 <span class="comment">% Plot - compare data with fit result</span>
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84 iplot(y, yfit)
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85
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86 </pre></div>
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87
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88 <p>
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89 <div align="center">
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90 <IMG src="images/example_ao_linlsqsvd_01.png" align="center" border="0">
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91 </div>
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92 </p>
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94