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author Daniele Nicolodi <nicolodi@science.unitn.it>
date Mon, 05 Dec 2011 16:20:06 +0100
parents f0afece42f48
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1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
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2 "http://www.w3.org/TR/1999/REC-html401-19991224/loose.dtd">
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3
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4 <html lang="en">
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5 <head>
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6 <meta name="generator" content=
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7 "HTML Tidy for Mac OS X (vers 1st December 2004), see www.w3.org">
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8 <meta http-equiv="Content-Type" content=
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9 "text/html; charset=us-ascii">
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10
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11 <title>Linear least squares with singular value deconposition - single experiment (LTPDA Toolbox)</title>
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12 <link rel="stylesheet" href="docstyle.css" type="text/css">
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13 <meta name="generator" content="DocBook XSL Stylesheets V1.52.2">
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14 <meta name="description" content=
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15 "Presents an overview of the features, system requirements, and starting the toolbox.">
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16 </head>
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17
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18 <body>
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19 <a name="top_of_page" id="top_of_page"></a>
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20
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21 <p style="font-size:1px;">&nbsp;</p>
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22
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23 <table class="nav" summary="Navigation aid" border="0" width=
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24 "100%" cellpadding="0" cellspacing="0">
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25 <tr>
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26 <td valign="baseline"><b>LTPDA Toolbox</b></td><td><a href="../helptoc.html">contents</a></td>
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27
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28 <td valign="baseline" align="right"><a href=
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29 "sigproc_linear_param_estimation_svd.html"><img src="b_prev.gif" border="0" align=
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30 "bottom" alt="Linear Parameter Estimation with Singular Value Decomposition"></a>&nbsp;&nbsp;&nbsp;<a href=
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31 "sigproc_example_matrix_linlsqsvd.html"><img src="b_next.gif" border="0" align=
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32 "bottom" alt="Linear least squares with singular value deconposition - multiple experiments"></a></td>
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33 </tr>
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34 </table>
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35
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36 <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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37 <hr>
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38
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39 <p>
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40
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41
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42
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43 <p>Determine the coefficients of a linear combination of noises and comapre with lscov</p>
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44 <h2>Contents</h2>
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45 <div>
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46 <ul>
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47 <li><a href="#1">Make data</a></li>
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48 <li><a href="#2">Do fit and check results</a></li>
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49 </ul>
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50 </div>
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51
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52 <h2>Make data<a name="1"></a></h2>
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53
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54 <div class="fragment"><pre>
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55
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56 fs = 10;
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57 nsecs = 10;
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58
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59 <span class="comment">% Elements of the fit basis</span>
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60 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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61 B1.setName;
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62 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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63 B2.setName;
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64 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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65 B3.setName;
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66
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67 <span class="comment">% random additive noise</span>
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68 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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69
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70 <span class="comment">% coefficients of the linear combination</span>
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71 c1 = ao(1,plist(<span class="string">'yunits'</span>,<span class="string">'m/T'</span>));
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72 c1.setName;
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73
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74 c2 = ao(2,plist(<span class="string">'yunits'</span>,<span class="string">'m/T'</span>));
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75 c2.setName;
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76
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77 c3 = ao(3,plist(<span class="string">'yunits'</span>,<span class="string">'m T^-1'</span>));
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78 c3.setName;
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79
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80 <span class="comment">% build output of linear system</span>
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81 y = c1*B1 + c2*B2 + c3*B3 + n;
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82 y.simplifyYunits;
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83
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84 </pre></div>
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85
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86
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87 <h2>Do fit and check results<a name="2"></a></h2>
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88
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89 <div class="fragment"><pre>
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90
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91 <span class="comment">% Get a fit with linlsqsvd</span>
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92 pobj1 = linlsqsvd(B1, B2, B3, y)
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93
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94 </pre></div>
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95
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96 <div class="fragment"><pre>
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97
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98 ---- pest 1 ----
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99 name: a1*B1+a2*B2+a3*B3
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100 param names: {'a1', 'a2', 'a3'}
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101 y: [0.81162366736073077;1.8907151217948008;3.0098623857384701]
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102 dy: [0.091943725803872112;0.089863977231447567;0.097910574305897308]
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103 yunits: [m T^(-1)][m T^(-1)][m T^(-1)]
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104 pdf: []
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105 cov: [3x3], ([0.00845364871469762 0.000268768332741779 0.000180072770333592;0.000268768332741779 0.00807553440385413 0.00125972375325089;0.000180072770333592 0.00125972375325089 0.00958648056091064])
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106 corr: [3x3], ([1 0.0325289738130578 0.020003055941376;0.0325289738130578 1 0.143172656986983;0.020003055941376 0.143172656986983 1])
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107 chain: []
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108 chi2: 0.87276552675043451
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109 dof: 97
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110 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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111 description:
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112 UUID: b8628843-a1e8-4815-b69b-90efdadc16c2
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113 ----------------
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114
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115 </pre></div>
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116
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117 <div class="fragment"><pre>
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118
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119 <span class="comment">% do linear combination: using eval</span>
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120 yfit = pobj1.eval(B1, B2, B3);
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121
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122 <span class="comment">% Plot - compare data with fit result</span>
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123 iplot(y, yfit)
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124
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125 </pre></div>
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126
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127 <p>
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128 <div align="center">
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129 <IMG src="images/example_ao_linlsqsvd_01.png" align="center" border="0">
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130 </div>
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131 </p>
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132
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133
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134
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135 </p>
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136
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137 <br>
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138 <br>
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139 <table class="nav" summary="Navigation aid" border="0" width=
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140 "100%" cellpadding="0" cellspacing="0">
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141 <tr valign="top">
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142 <td align="left" width="20"><a href="sigproc_linear_param_estimation_svd.html"><img src=
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143 "b_prev.gif" border="0" align="bottom" alt=
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144 "Linear Parameter Estimation with Singular Value Decomposition"></a>&nbsp;</td>
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145
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146 <td align="left">Linear Parameter Estimation with Singular Value Decomposition</td>
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148 <td>&nbsp;</td>
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149
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150 <td align="right">Linear least squares with singular value deconposition - multiple experiments</td>
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152 <td align="right" width="20"><a href=
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153 "sigproc_example_matrix_linlsqsvd.html"><img src="b_next.gif" border="0" align=
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154 "bottom" alt="Linear least squares with singular value deconposition - multiple experiments"></a></td>
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155 </tr>
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156 </table><br>
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157
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158 <p class="copy">&copy;LTP Team</p>
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159 </body>
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160 </html>