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Fix. Default password should be [] not an empty string
author Daniele Nicolodi <nicolodi@science.unitn.it>
date Wed, 07 Dec 2011 17:29:47 +0100
parents f0afece42f48
children
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Daniele Nicolodi <nicolodi@science.unitn.it>
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1 % Training session Topic 5 exercise 05
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Daniele Nicolodi <nicolodi@science.unitn.it>
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2 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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3 % Fitting time series with xfit
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Daniele Nicolodi <nicolodi@science.unitn.it>
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4 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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5 % ao/xfit uses a full non-linear least square algorithm to fit data. Here
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Daniele Nicolodi <nicolodi@science.unitn.it>
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6 % the main features will be described to fit an up-chirp sine.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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7 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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8 % 1) Load time series data
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Daniele Nicolodi <nicolodi@science.unitn.it>
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9 % 2) Define the model to fit
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Daniele Nicolodi <nicolodi@science.unitn.it>
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10 % 3) Inspect data in order to find an initial guess
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Daniele Nicolodi <nicolodi@science.unitn.it>
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11 % 4) Fit data with ao/xfit starting from that guess
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Daniele Nicolodi <nicolodi@science.unitn.it>
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12 % 5) Check results
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Daniele Nicolodi <nicolodi@science.unitn.it>
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13 % 6) Fit again by changing the fitting algorithm (fminunc will be used)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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14 % 7) Check results
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Daniele Nicolodi <nicolodi@science.unitn.it>
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15 % 8) Fit again by using a Monte Carlo search
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Daniele Nicolodi <nicolodi@science.unitn.it>
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16 % 9) Check results
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Daniele Nicolodi <nicolodi@science.unitn.it>
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17 % 10) Final fit with the full model (data bias included)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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18 % 11) Check results
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Daniele Nicolodi <nicolodi@science.unitn.it>
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19 % 12) Comments
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Daniele Nicolodi <nicolodi@science.unitn.it>
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20 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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21 % Trento, 01-03-2010
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Daniele Nicolodi <nicolodi@science.unitn.it>
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22 % Giuseppe Congedo
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Daniele Nicolodi <nicolodi@science.unitn.it>
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23 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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24 % $Id: TrainigSession_T5_Ex05.m,v 1.3 2011/05/13 15:13:12 ingo Exp $
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Daniele Nicolodi <nicolodi@science.unitn.it>
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25 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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26 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Daniele Nicolodi <nicolodi@science.unitn.it>
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27
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Daniele Nicolodi <nicolodi@science.unitn.it>
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28 %% 1) load tsdata
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29
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Daniele Nicolodi <nicolodi@science.unitn.it>
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30 % load test noise AO from file
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Daniele Nicolodi <nicolodi@science.unitn.it>
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31 data = ao(plist('filename', 'topic5/T5_Ex05_TestNoise.xml'));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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32 data.setName;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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33
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Daniele Nicolodi <nicolodi@science.unitn.it>
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34 % look at data
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Daniele Nicolodi <nicolodi@science.unitn.it>
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35 iplot(data)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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36 % iplot(abs(fft(data)))
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Daniele Nicolodi <nicolodi@science.unitn.it>
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37 % iplot(psd(data))
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Daniele Nicolodi <nicolodi@science.unitn.it>
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38
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Daniele Nicolodi <nicolodi@science.unitn.it>
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39 %% 2) set the model
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Daniele Nicolodi <nicolodi@science.unitn.it>
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40
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Daniele Nicolodi <nicolodi@science.unitn.it>
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41 % try a linearly chirped sine wave with a bias
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Daniele Nicolodi <nicolodi@science.unitn.it>
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42 mdl = smodel('a + P1.*sin(2.*pi.*(P2 + P3.*t).*t + P4)');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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43 mdl.setParams({'a', 'P1', 'P2', 'P3', 'P4'});
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Daniele Nicolodi <nicolodi@science.unitn.it>
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44 mdl.setXvar('t');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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45 mdl.subs('a',5); % set additional parameters - data bias
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Daniele Nicolodi <nicolodi@science.unitn.it>
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46
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Daniele Nicolodi <nicolodi@science.unitn.it>
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47 %% 3) try to find an initial guess
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Daniele Nicolodi <nicolodi@science.unitn.it>
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48
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Daniele Nicolodi <nicolodi@science.unitn.it>
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49 % plot the tentative model
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Daniele Nicolodi <nicolodi@science.unitn.it>
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50 mdlTry = mdl.setValues([4 1e-4 1e-5 0]);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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51 mdlTry.setXvals(data.x);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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52 iplot(data,mdlTry.eval)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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53
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Daniele Nicolodi <nicolodi@science.unitn.it>
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54 %% 4) xfit from an initial guess
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Daniele Nicolodi <nicolodi@science.unitn.it>
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55
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Daniele Nicolodi <nicolodi@science.unitn.it>
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56 % fit plist
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Daniele Nicolodi <nicolodi@science.unitn.it>
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57 plfit = plist('Function', mdl, ...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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58 'P0', [4 1e-4 1e-5 0], ... % set initial guess for the parameters
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Daniele Nicolodi <nicolodi@science.unitn.it>
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59 'LB', [2 1e-6 1e-6 0], ... % set lower bounds for parameters
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Daniele Nicolodi <nicolodi@science.unitn.it>
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60 'UB', [5 1e-2 1e-2 2*pi] ... % set upper bounds for parameters
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Daniele Nicolodi <nicolodi@science.unitn.it>
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61 );
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Daniele Nicolodi <nicolodi@science.unitn.it>
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62
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Daniele Nicolodi <nicolodi@science.unitn.it>
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63 % do fit
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Daniele Nicolodi <nicolodi@science.unitn.it>
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64 params = xfit(data, plfit)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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65
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Daniele Nicolodi <nicolodi@science.unitn.it>
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66 %% 5) check results
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Daniele Nicolodi <nicolodi@science.unitn.it>
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67
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Daniele Nicolodi <nicolodi@science.unitn.it>
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68 bestMdl = eval(params);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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69
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Daniele Nicolodi <nicolodi@science.unitn.it>
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70 % plotting results
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Daniele Nicolodi <nicolodi@science.unitn.it>
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71 iplot(data,bestMdl)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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72 iplot(data-bestMdl)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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73 iplot(psd(data-bestMdl))
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Daniele Nicolodi <nicolodi@science.unitn.it>
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74
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Daniele Nicolodi <nicolodi@science.unitn.it>
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75 % Comments.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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76 % Fit is not so bad, but let's now try to change the fitting algorithm.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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77
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Daniele Nicolodi <nicolodi@science.unitn.it>
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78 %% 6) xfit from an initial guess (change algorithm)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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79
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Daniele Nicolodi <nicolodi@science.unitn.it>
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80 % fit plist
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Daniele Nicolodi <nicolodi@science.unitn.it>
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81 plfit = plist('Function', mdl, ...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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82 'P0', [4 1e-4 1e-5 0], ... % set initial guess for the parameters
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Daniele Nicolodi <nicolodi@science.unitn.it>
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83 'LB', [2 1e-6 1e-6 0], ... % set lower bounds for parameters
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Daniele Nicolodi <nicolodi@science.unitn.it>
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84 'UB', [5 1e-2 1e-2 2*pi], ... % set upper bounds for parameters
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Daniele Nicolodi <nicolodi@science.unitn.it>
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85 'algorithm', 'fminunc'); % set fitting algorithm
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Daniele Nicolodi <nicolodi@science.unitn.it>
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86
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Daniele Nicolodi <nicolodi@science.unitn.it>
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87 % do fit
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Daniele Nicolodi <nicolodi@science.unitn.it>
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88 params = xfit(data, plfit)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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89
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Daniele Nicolodi <nicolodi@science.unitn.it>
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90 %% 7) check results
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Daniele Nicolodi <nicolodi@science.unitn.it>
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91
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Daniele Nicolodi <nicolodi@science.unitn.it>
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92 bestMdl = eval(params);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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93
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Daniele Nicolodi <nicolodi@science.unitn.it>
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94 % plotting results
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Daniele Nicolodi <nicolodi@science.unitn.it>
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95 iplot(data,bestMdl)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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96 iplot(data-bestMdl)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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97 iplot(psd(data-bestMdl))
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Daniele Nicolodi <nicolodi@science.unitn.it>
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98
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Daniele Nicolodi <nicolodi@science.unitn.it>
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99 % Comments.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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100 % Fit is not so bad: an improvement with respect to using fminsearch.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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101 % Let's now try to do a Monte Carlo search.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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102
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Daniele Nicolodi <nicolodi@science.unitn.it>
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103 %% 8) xfit from a Monte Carlo search (bounds are shrinked about the best-fit found above)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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104
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Daniele Nicolodi <nicolodi@science.unitn.it>
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105 % fit plist
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Daniele Nicolodi <nicolodi@science.unitn.it>
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106 plfit = plist('Function', mdl, ...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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107 'LB', [2.5 1e-5 1e-6 0], ... % set lower bounds for parameters
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Daniele Nicolodi <nicolodi@science.unitn.it>
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108 'UB', [3.5 1e-3 1e-4 2*pi], ... % set upper bounds for parameters
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Daniele Nicolodi <nicolodi@science.unitn.it>
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109 'algorithm', 'fminunc', ... % set fitting algorithm
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Daniele Nicolodi <nicolodi@science.unitn.it>
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110 'MonteCarlo', 'y', 'Npoints', 1e4); % set the number of points in the parameter space
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Daniele Nicolodi <nicolodi@science.unitn.it>
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111
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Daniele Nicolodi <nicolodi@science.unitn.it>
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112 % do fit
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Daniele Nicolodi <nicolodi@science.unitn.it>
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113 params = xfit(data, plfit)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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114
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Daniele Nicolodi <nicolodi@science.unitn.it>
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115 %% 9) check results
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Daniele Nicolodi <nicolodi@science.unitn.it>
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116
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Daniele Nicolodi <nicolodi@science.unitn.it>
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117 bestMdl = eval(params);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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118
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Daniele Nicolodi <nicolodi@science.unitn.it>
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119 % plotting results
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Daniele Nicolodi <nicolodi@science.unitn.it>
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120 iplot(data,bestMdl)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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121 iplot(data-bestMdl)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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122 iplot(psd(data-bestMdl))
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Daniele Nicolodi <nicolodi@science.unitn.it>
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123
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Daniele Nicolodi <nicolodi@science.unitn.it>
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124 % Comments.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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125 % Fit is not so bad: no further improvements with respect to the previous fit.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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126 % Let's now try to fit the full model by doing a Monte Carlo search.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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127
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Daniele Nicolodi <nicolodi@science.unitn.it>
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128 %% 10) xfit with full model
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Daniele Nicolodi <nicolodi@science.unitn.it>
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129
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Daniele Nicolodi <nicolodi@science.unitn.it>
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130 % set the full model (including the data bias)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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131 mdl = smodel('a + P1.*sin(2.*pi.*(P2 + P3.*t).*t + P4)');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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132 mdl.setParams({'a', 'P1', 'P2', 'P3', 'P4'});
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Daniele Nicolodi <nicolodi@science.unitn.it>
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133 mdl.setXvar('t');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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134
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Daniele Nicolodi <nicolodi@science.unitn.it>
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135 % fit plist
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Daniele Nicolodi <nicolodi@science.unitn.it>
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136 plfit = plist('Function', mdl, ...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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137 'P0', [5 3.01 7.27e-5 1.00e-5 0.325], ... % set initial guess for the parameters
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Daniele Nicolodi <nicolodi@science.unitn.it>
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138 'LB', [4 2.5 1e-5 1e-6 0], ... % set lower bounds for parameters
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Daniele Nicolodi <nicolodi@science.unitn.it>
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139 'UB', [6 3.5 1e-3 1e-4 2*pi], ... % set upper bounds for parameters
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Daniele Nicolodi <nicolodi@science.unitn.it>
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140 'algorithm', 'fminunc' ... % set fitting algorithm
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Daniele Nicolodi <nicolodi@science.unitn.it>
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141 );
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Daniele Nicolodi <nicolodi@science.unitn.it>
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142
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Daniele Nicolodi <nicolodi@science.unitn.it>
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143 % do fit
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Daniele Nicolodi <nicolodi@science.unitn.it>
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144 params = xfit(data, plfit)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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145
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Daniele Nicolodi <nicolodi@science.unitn.it>
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146 %% 11) check results
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Daniele Nicolodi <nicolodi@science.unitn.it>
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147
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Daniele Nicolodi <nicolodi@science.unitn.it>
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148 bestMdl = eval(params);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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149
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Daniele Nicolodi <nicolodi@science.unitn.it>
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150 % plotting results
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Daniele Nicolodi <nicolodi@science.unitn.it>
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151 iplot(data,bestMdl)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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152 iplot(data-bestMdl)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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153 iplot(psd(data-bestMdl))
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Daniele Nicolodi <nicolodi@science.unitn.it>
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154
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Daniele Nicolodi <nicolodi@science.unitn.it>
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155 % Comments.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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156 % Fit is good, even for the full model (including bias).
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Daniele Nicolodi <nicolodi@science.unitn.it>
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157
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Daniele Nicolodi <nicolodi@science.unitn.it>
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158 %% 12) Comments
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Daniele Nicolodi <nicolodi@science.unitn.it>
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159
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Daniele Nicolodi <nicolodi@science.unitn.it>
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160 % Let's compare the fit results with the real parameters.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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161 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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162 % Firstly, data were generated with the set of parameters:
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
163 % a = 5
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
164 % P1 = 3
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
165 % P2 = 1e-4
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
166 % P3 = 1e-5
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
167 % P4 = 0.3
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
168 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
169 % In the end, the fit results are
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
170 % chi2 = 1.03
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
171 % dof = 995
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
172 % a = 4.965 +/- 0.033
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
173 % P1 = 3.018 +/- 0.047
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
174 % P2 = 6.6e-5 +/- 3.1e-5
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
175 % P3 = 1.0032e-5 +/- 3.1e-8
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
176 % P4 = 0.334 +/- 0.043
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
177 % Quite in well accordance with expected values!
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
178 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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179 % Are they biased? No, they are not. Indeed:
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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180 % (p_fit - p_true)/dp = ...
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
181 % 1.1
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
182 % 0.39
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
183 % 1.1
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
184 % 1.1
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
185 % 0.80
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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186 % Very good.