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author Daniele Nicolodi <nicolodi@science.unitn.it>
date Mon, 05 Dec 2011 16:20:06 +0100
parents f0afece42f48
children
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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 - multiple experiments (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_example_ao_linlsqsvd.html"><img src="b_prev.gif" border="0" align=
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30 "bottom" alt="Linear least squares with singular value deconposition - single experiment"></a>&nbsp;&nbsp;&nbsp;<a href=
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31 "sigproc_example_matrix_linfitsvd.html"><img src="b_next.gif" border="0" align=
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32 "bottom" alt="Iterative linear parameter estimation for multichannel systems - symbolic system model in frequency domain"></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 - multiple experiments</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</p>
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44
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45 <h2>Contents</h2>
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46 <div><ul><li><a href="#1">Make data</a></li>
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47 <li><a href="#2">Do fit</a></li></ul></div>
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48
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49 <h2>Make data<a name="1"></a></h2>
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50
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51 <div class="fragment"><pre>
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52
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53 fs = 10;
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54 nsecs = 10;
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55
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56 <span class="comment">% fit basis for 2 experiments case</span>
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57 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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58 B1.setName;
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59 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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60 B2.setName;
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61 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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62 B3.setName;
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63 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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64 B4.setName;
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65
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66 C1 = matrix(B1,B2,plist(<span class="string">'shape'</span>,[2,1]));
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67 C1.setName;
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68 C2 = matrix(B3,B4,plist(<span class="string">'shape'</span>,[2,1]));
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69 C2.setName;
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70
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71 <span class="comment">% make additive noise</span>
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72 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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73 n1.setName;
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74 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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75 n2.setName;
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76
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77 <span class="comment">% coefficients of the linear combination</span>
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78 a1 = ao(1,plist(<span class="string">'yunits'</span>,<span class="string">'m/T'</span>));
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79 a1.setName;
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80 a2 = ao(2,plist(<span class="string">'yunits'</span>,<span class="string">'m/T'</span>));
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81 a2.setName;
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82
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83 <span class="comment">% assign output values</span>
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84 <span class="comment">% y is a matrix containing the outputs of two experiments:</span>
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85 y1 = a1*B1 + a2*B3 + n1;
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86 y2 = a1*B2 + a2*B4 + n2;
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87 y = matrix(y1,y2,plist(<span class="string">'shape'</span>,[2,1]));
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88
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89 </pre></div>
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90
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91
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92 </pre><h2>Do fit<a name="2"></a></h2>
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93
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94 <div class="fragment"><pre>
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95
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96 <span class="comment">% Get a fit with linlsqsvd</span>
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97 pobj = linlsqsvd(C1, C2, y)
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98
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99 </pre></div>
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100
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101 <div class="fragment"><pre>
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102
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103 ---- pest 1 ----
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104 name: a1*C1+a2*C2
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105 param names: {'a1', 'a2'}
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106 y: [0.97312642877028477;2.0892132651873916]
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107 dy: [0.06611444020240001;0.065007088662104057]
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108 yunits: [T^(-1) m][T^(-1) m]
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109 pdf: []
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110 cov: [2x2], ([0.00437111920327673 -0.000390118937121542;-0.000390118937121542 0.00422592157632266])
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111 corr: []
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112 chain: []
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113 chi2: 0.85210029717685576
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114 dof: 198
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115 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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116 description:
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117 UUID: 545c9699-e749-40d5-bbe1-1322599c9c5d
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118 ----------------
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119
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120 </pre></div>
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121
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122 <div class="fragment"><pre>
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123
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124 <span class="comment">% do linear combination: using eval</span>
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125 yfit = pobj.eval;
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126
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127 <span class="comment">% extract objects</span>
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128 yfit1 = getObjectAtIndex(yfit,1);
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129 yfit2 = getObjectAtIndex(yfit,2);
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130
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131 <span class="comment">% Plot - compare data with fit</span>
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132 iplot(y1, yfit1)
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133 iplot(y2, yfit2)
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134
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135 </pre></div>
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136
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137 <p>
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138 <div align="center">
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139 <IMG src="images/example_matrix_linlsqsvd_01.png" align="center" border="0">
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140 </div>
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141 </p>
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142 <p>
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143 <div align="center">
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144 <IMG src="images/example_matrix_linlsqsvd_02.png" align="center" border="0">
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145 </div>
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146 </p>
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149 </p>
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151 <br>
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152 <br>
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153 <table class="nav" summary="Navigation aid" border="0" width=
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154 "100%" cellpadding="0" cellspacing="0">
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155 <tr valign="top">
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156 <td align="left" width="20"><a href="sigproc_example_ao_linlsqsvd.html"><img src=
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157 "b_prev.gif" border="0" align="bottom" alt=
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158 "Linear least squares with singular value deconposition - single experiment"></a>&nbsp;</td>
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159
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160 <td align="left">Linear least squares with singular value deconposition - single experiment</td>
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161
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162 <td>&nbsp;</td>
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163
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164 <td align="right">Iterative linear parameter estimation for multichannel systems - symbolic system model in frequency domain</td>
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165
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167 "sigproc_example_matrix_linfitsvd.html"><img src="b_next.gif" border="0" align=
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168 "bottom" alt="Iterative linear parameter estimation for multichannel systems - symbolic system model in frequency domain"></a></td>
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169 </tr>
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170 </table><br>
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171
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172 <p class="copy">&copy;LTP Team</p>
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173 </body>
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174 </html>