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Import.
author Daniele Nicolodi <nicolodi@science.unitn.it>
date Wed, 23 Nov 2011 19:22:13 +0100
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1
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4 <p>Determine the coefficients of a linear combination of noises</p>
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6 <h2>Contents</h2>
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7 <div><ul><li><a href="#1">Make data</a></li>
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8 <li><a href="#2">Do fit</a></li></ul></div>
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10 <h2>Make data<a name="1"></a></h2>
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12 <div class="fragment"><pre>
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13
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14 fs = 10;
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15 nsecs = 10;
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17 <span class="comment">% fit basis for 2 experiments case</span>
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18 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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19 B1.setName;
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20 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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21 B2.setName;
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22 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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23 B3.setName;
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24 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>));
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25 B4.setName;
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26
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27 C1 = matrix(B1,B2,plist(<span class="string">'shape'</span>,[2,1]));
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28 C1.setName;
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29 C2 = matrix(B3,B4,plist(<span class="string">'shape'</span>,[2,1]));
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30 C2.setName;
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31
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32 <span class="comment">% make additive noise</span>
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33 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>));
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34 n1.setName;
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35 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>));
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36 n2.setName;
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37
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38 <span class="comment">% coefficients of the linear combination</span>
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39 a1 = ao(1,plist(<span class="string">'yunits'</span>,<span class="string">'m/T'</span>));
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40 a1.setName;
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41 a2 = ao(2,plist(<span class="string">'yunits'</span>,<span class="string">'m/T'</span>));
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42 a2.setName;
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43
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44 <span class="comment">% assign output values</span>
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45 <span class="comment">% y is a matrix containing the outputs of two experiments:</span>
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46 y1 = a1*B1 + a2*B3 + n1;
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47 y2 = a1*B2 + a2*B4 + n2;
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48 y = matrix(y1,y2,plist(<span class="string">'shape'</span>,[2,1]));
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49
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50 </pre></div>
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51
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52
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53 </pre><h2>Do fit<a name="2"></a></h2>
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54
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55 <div class="fragment"><pre>
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56
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57 <span class="comment">% Get a fit with linlsqsvd</span>
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58 pobj = linlsqsvd(C1, C2, y)
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59
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60 </pre></div>
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62 <div class="fragment"><pre>
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63
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64 ---- pest 1 ----
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65 name: a1*C1+a2*C2
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66 param names: {'a1', 'a2'}
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67 y: [0.97312642877028477;2.0892132651873916]
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68 dy: [0.06611444020240001;0.065007088662104057]
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69 yunits: [T^(-1) m][T^(-1) m]
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70 pdf: []
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71 cov: [2x2], ([0.00437111920327673 -0.000390118937121542;-0.000390118937121542 0.00422592157632266])
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72 corr: []
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73 chain: []
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74 chi2: 0.85210029717685576
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75 dof: 198
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76 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)
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77 description:
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78 UUID: 545c9699-e749-40d5-bbe1-1322599c9c5d
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79 ----------------
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80
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81 </pre></div>
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82
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83 <div class="fragment"><pre>
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84
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85 <span class="comment">% do linear combination: using eval</span>
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86 yfit = pobj.eval;
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87
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88 <span class="comment">% extract objects</span>
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89 yfit1 = getObjectAtIndex(yfit,1);
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90 yfit2 = getObjectAtIndex(yfit,2);
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91
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92 <span class="comment">% Plot - compare data with fit</span>
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93 iplot(y1, yfit1)
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94 iplot(y2, yfit2)
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95
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96 </pre></div>
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97
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98 <p>
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99 <div align="center">
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100 <IMG src="images/example_matrix_linlsqsvd_01.png" align="center" border="0">
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101 </div>
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102 </p>
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103 <p>
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104 <div align="center">
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105 <IMG src="images/example_matrix_linlsqsvd_02.png" align="center" border="0">
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106 </div>
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107 </p>
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108