ltpda: m-toolbox/html_help/help/ug/ltpda_training_topic_5

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Cleanup

author	Daniele Nicolodi <nicolodi@science.unitn.it>
date	Mon, 05 Dec 2011 18:04:34 +0100
parents	f0afece42f48
children

rev	line source
0 f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2 "http://www.w3.org/TR/1999/REC-html401-19991224/loose.dtd">
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	4 <html lang="en">
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	5 <head>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	6 <meta name="generator" content=
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	7 "HTML Tidy for Mac OS X (vers 1st December 2004), see www.w3.org">
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	8 <meta http-equiv="Content-Type" content=
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	9 "text/html; charset=us-ascii">
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	10
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	11 <title>Non-linear least squares fitting of time series (LTPDA Toolbox)</title>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	12 <link rel="stylesheet" href="docstyle.css" type="text/css">
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	13 <meta name="generator" content="DocBook XSL Stylesheets V1.52.2">
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	14 <meta name="description" content=
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	15 "Presents an overview of the features, system requirements, and starting the toolbox.">
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	16 </head>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	17
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	18 <body>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	19 <a name="top_of_page" id="top_of_page"></a>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	20
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	21 <p style="font-size:1px;"> </p>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	22
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	23 <table class="nav" summary="Navigation aid" border="0" width=
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	24 "100%" cellpadding="0" cellspacing="0">
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	25 <tr>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	26 <td valign="baseline"><b>LTPDA Toolbox</b></td><td><a href="../helptoc.html">contents</a></td>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	27
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	28 <td valign="baseline" align="right"><a href=
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	29 "ltpda_training_topic_5_3.html"><img src="b_prev.gif" border="0" align=
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	30 "bottom" alt="Fitting time series with polynomials"></a>   <a href=
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	31 "ltpda_training_topic_5_5.html"><img src="b_next.gif" border="0" align=
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	32 "bottom" alt="IFO/Temperature Example - signal subtraction"></a></td>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	33 </tr>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	34 </table>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	35
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	36 <h1 class="title"><a name="f3-12899" id="f3-12899"></a>Non-linear least squares fitting of time series</h1>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	37 <hr>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	38
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	39 <p>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	40
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	41 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	42 "http://www.w3.org/TR/1999/REC-html401-19991224/loose.dtd">
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	43
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	44 <html lang="en">
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	45 <head>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	46 <meta name="generator" content=
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	47 "HTML Tidy for Mac OS X (vers 1st December 2004), see www.w3.org">
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	48 <meta http-equiv="Content-Type" content=
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	49 "text/html; charset=us-ascii">
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	50
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	51 <title>Non-linear least squares fitting of time series (LTPDA Toolbox)</title>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	52 <link rel="stylesheet" href="docstyle.css" type="text/css">
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	53 <meta name="generator" content="DocBook XSL Stylesheets V1.52.2">
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	54 <meta name="description" content=
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	55 "Presents an overview of the features, system requirements, and starting the toolbox.">
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	56
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	57 </head>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	58
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	59 <body>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	60 <a name="top_of_page" id="top_of_page"></a>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	61
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	62 <p style="font-size:1px;"> </p>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	63
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	64 <table class="nav" summary="Navigation aid" border="0" width=
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	65 "100%" cellpadding="0" cellspacing="0">
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	66 <tr>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	67 <td valign="baseline"><b>LTPDA Toolbox</b></td><td><a href="../helptoc.html">contents</a></td>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	68
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	69 <td valign="baseline" align="right"><a href=
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	70 "ltpda_training_topic_5_3.html"><img src="b_prev.gif" border="0" align=
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	71 "bottom" alt="Fitting time series with polynomials"></a>   <a href=
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	72 "ltpda_training_topic_5_5.html"><img src="b_next.gif" border="0" align=
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	73 "bottom" alt="IFO/Temperature Example - signal subtraction"></a></td>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	74 </tr>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	75 </table>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	76
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	77 <h1 class="title"><a name="f3-12899" id="f3-12899"></a>Non-linear least squares fitting of time series</h1>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	78 <hr>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	79
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	80 <p>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	81
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	82
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	83 <p>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	84
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	85 Non-linear least square fitting of time-series exploits the function <tt>ao/xfit</tt>.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	86 </p>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	87
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	88 <h2> Non-linear least square fitting of time series </h2>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	89
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	90 <p>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	91 During this exercise we will:
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	92 <ol>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	93 <li> Load time series data
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	94 <li> Fit data with <tt>ao/xfit</tt>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	95 <li> Check results
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	96 <li> Refine the fit with a Monte Carlo search
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	97 </ol>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	98 </p>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	99
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	100 <p>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	101 Let us open a new editor window and load test data.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	102 </p>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	103
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	104 <div class="fragment"><pre>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	105 a = ao(plist(<span class="string">'filename'</span>, <span class="string">'topic5/T5_Ex05_TestNoise.xml'</span>));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	106 a.setName(<span class="string">'data'</span>);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	107 iplot(a)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	108
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	109 </pre></div>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	110
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	111 <p>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	112 As can be seen this is a chirped sine wave with some noise.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	113 <div align="center">
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	114 <IMG src="images/ltpda_training_1/topic5/ltpda_training_5_4_1.png" align="center" border="0">
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	115 </div>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	116 We could now try the fit. The first parameter to pass to <tt>xfit</tt>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	117 is a fit model. In this case we assume that we are dealing with a linearly
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	118 chirped sine wave according to the equation: <br/>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	119
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	120 <br/>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	121 <div align="center">
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	122 <IMG src="images/ltpda_training_1/topic5/ex4_chirpsine.gif" align="center" border="0">
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	123 </div>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	124 <br/>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	125 The previous function can be stored within a <tt>smodel</tt> analysis object to pass to the fitting machinery:
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	126 <div class="fragment"><pre>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	127 mdl = smodel(plist(<span class="string">'Name'</span>, <span class="string">'chirp'</span>, ...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	128 <span class="string">'expression'</span>, <span class="string">'A.sin(2pi(f + f0.t).*t + p) + c'</span>, ...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	129 <span class="string">'params'</span>, <span class="string">{'A','f','f0','p','c'}</span>, ...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	130 <span class="string">'xvar'</span>, <span class="string">'t'</span>, ...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	131 <span class="string">'xunits'</span>, <span class="string">'s'</span>, <span class="string">'yunits'</span>, <span class="string">'m'</span>));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	132
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	133 </pre></div>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	134
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	135 We need to specify a starting guess for the model parameters.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	136 The output of <tt>ao/xfit</tt> is a <tt>pest</tt> analysis objects containing fit parameters.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	137
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	138 </p>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	139
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	140 <div class="fragment"><pre>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	141 plfit1 = plist(<span class="string">'Function'</span>, <span class="string">mdl</span>, ...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	142 <span class="string">'P0'</span>, [5,9e-5,9e-6,0,5]);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	143
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	144 params1 = xfit(a, plfit1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	145
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	146 </pre></div>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	147
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	148 <p>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	149 Once the fit is done. We can evaluate our model to check fit results.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	150 </p>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	151
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	152 <div class="fragment"><pre>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	153 b = eval(params1, plist(<span class="string">'xdata'</span>, a, <span class="string">'xfield'</span>, <span class="string">'x'</span>));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	154 b.setName;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	155 iplot(a,b)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	156
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	157 </pre></div>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	158
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	159 <p>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	160 As you can see, the fit is not accurate. One of the great problems of
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	161 non-linear least square methods is that they easily find a local minimum of
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	162 the chi square function and stop there without finding the global minimum.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	163 There are two possibile solutions to such kind of problems: the first one is
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	164 to refine step by step the fit by looking at the data; the second one is to
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	165 perform a Monte Carlo search in the parameter space. This way, the fitting machinery
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	166 extracts the number of points you define in the <tt>'Npoints'</tt>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	167 key, evaluates the chi square at those points, reoders by ascending chi square, selects
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	168 the first guesses and fit starting from them.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	169 </p>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	170
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	171 <div class="fragment"><pre>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	172 plfit2 = plist(<span class="string">'Function'</span>, <span class="string">mdl</span>, ...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	173 <span class="string">'MonteCarlo'</span>, <span class="string">'yes'</span>, ...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	174 <span class="string">'Npoints'</span>, 1000, ...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	175 <span class="string">'LB'</span>, [1,5e-5,5e-6,0,2], ...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	176 <span class="string">'UB'</span>, [10,5e-4,5e-5,2*pi,7]);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	177
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	178 params2 = xfit(a, plfit2);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	179
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	180 c = eval(params2, plist(<span class="string">'xdata'</span>, a, <span class="string">'xfield'</span>, <span class="string">'x'</span>));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	181 c.setName;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	182 iplot(a,c)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	183
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	184 </pre></div>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	185
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	186 <p>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	187 The fit now looks like better...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	188 <div align="center">
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	189 <IMG src="images/ltpda_training_1/topic5/ltpda_training_5_4_3.png" align="center" border="0">
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	190 </div>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	191
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	192 Let us compare fit results with nominal parameters. <br/>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	193 Data were generated with the following set of parameters:
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	194 </p>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	195
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	196 <div class="fragment"><pre>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	197 A = 3
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	198 f = 1e-4
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	199 f0 = 1e-5
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	200 p = 0.3
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	201 c = 5
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	202 </pre></div>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	203
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	204 <p>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	205
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	206 Fitted parameters are instead:
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	207 </p>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	208
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	209 <div class="fragment"><pre>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	210 A = 3.02 +/- 0.05
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	211 f = (7 +/- 3)e-5
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	212 f0 = (1.003 +/- 0.003)e-5
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	213 p = 0.33 +/- 0.04
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	214 c = 4.97 +/- 0.03
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	215 </pre></div>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	216 <p>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	217 The correlation matrix of the parameters, the chi square, the degree of freedom, the covariance matrix are
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	218 store in the output <tt>pest</tt>. Other useful information are stored in the <tt>procinfo</tt> (processing information)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	219 field. This field is a <tt>plist</tt> and is used to additional information that can be
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	220 returned from algorithms. For example, to extract the chi square, we write:
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	221 </p>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	222
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	223 <div class="fragment"><pre>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	224 params2.chi2
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	225 1.0253740840052
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	226 </pre></div>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	227 <p>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	228 And to know the correlation matrix:
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	229 </p>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	230
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	231 <div class="fragment"><pre>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	232 params2.corr
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	233 Columns 1 through 3
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	234
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	235 1 0.120986348157139 -0.0970894969803509
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	236 0.120986348157139 1 -0.966114904879414
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	237 -0.0970894969803509 -0.966114904879414 1
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	238 -0.156801230958825 -0.848296014553159 0.717376893765734
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	239 -0.0994358284166703 0.187645552903433 -0.169496082635319
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	240
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	241 Columns 4 through 5
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	242
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	243 -0.156801230958825 -0.0994358284166703
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	244 -0.848296014553159 0.187645552903433
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	245 0.717376893765734 -0.169496082635319
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	246 1 -0.199286767157984
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	247 -0.199286767157984 1
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	248 </pre></div>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	249
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	250 <p>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	251 Not so bad!
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	252 </p>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	253
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	254
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	255
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	256
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	257
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	258
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	259
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	260
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	261
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	262
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	263
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	264
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	265
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	266
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	267
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	268
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	269
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	270
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	271
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	272 </p>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	273
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	274 <br>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	275 <br>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	276 <table class="nav" summary="Navigation aid" border="0" width=
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	277 "100%" cellpadding="0" cellspacing="0">
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	278 <tr valign="top">
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	279
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	280 <td align="left" width="20"><a href="ltpda_training_topic_5_3.html"><img src=
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	281 "b_prev.gif" border="0" align="bottom" alt=
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	282 "Fitting time series with polynomials"></a> </td>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	283
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	284 <td align="left">Fitting time series with polynomials</td>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	285
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	286 <td> </td>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	287
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	288 <td align="right">IFO/Temperature Example - signal subtraction</td>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	289
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	290 <td align="right" width="20"><a href=
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	291 "ltpda_training_topic_5_5.html"><img src="b_next.gif" border="0" align=
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	292 "bottom" alt="IFO/Temperature Example - signal subtraction"></a></td>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	293 </tr>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	294
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	295 </table><br>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	296
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	297 <p class="copy">©LTP Team</p>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	298 </body>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	299 </html>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	300
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	301 </p>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	302
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	303 <br>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	304 <br>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	305 <table class="nav" summary="Navigation aid" border="0" width=
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	306 "100%" cellpadding="0" cellspacing="0">
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	307 <tr valign="top">
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	308 <td align="left" width="20"><a href="ltpda_training_topic_5_3.html"><img src=
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	309 "b_prev.gif" border="0" align="bottom" alt=
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	310 "Fitting time series with polynomials"></a> </td>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	311
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	312 <td align="left">Fitting time series with polynomials</td>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	313
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	314 <td> </td>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	315
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	316 <td align="right">IFO/Temperature Example - signal subtraction</td>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	317
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	318 <td align="right" width="20"><a href=
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	319 "ltpda_training_topic_5_5.html"><img src="b_next.gif" border="0" align=
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	320 "bottom" alt="IFO/Temperature Example - signal subtraction"></a></td>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	321 </tr>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	322 </table><br>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	323
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	324 <p class="copy">©LTP Team</p>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	325 </body>
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	326 </html>

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