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annotate m-toolbox/test/diagnostics/ltpda_arma_freq.m @ 41:6def6533cb16 database-connection-manager

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author Daniele Nicolodi <nicolodi@science.unitn.it>
date Mon, 05 Dec 2011 18:04:34 +0100
parents f0afece42f48
children
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0
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Daniele Nicolodi <nicolodi@science.unitn.it>
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1 function varargout = ltpda_arma_freq(varargin)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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2 % LTPDA_ARMA_FREQ estimates the ARMA parameters of the transfer function
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Daniele Nicolodi <nicolodi@science.unitn.it>
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3 % relating an output to an input
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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 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Daniele Nicolodi <nicolodi@science.unitn.it>
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6 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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7 % DESCRIPTION: LTPDA_ARMA_FREQ estimates the ARMA parameters of the
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Daniele Nicolodi <nicolodi@science.unitn.it>
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8 % transfer function relating an output to an input time series. The
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Daniele Nicolodi <nicolodi@science.unitn.it>
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9 % algorithm uses the IV method to find a set of initial parameters
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Daniele Nicolodi <nicolodi@science.unitn.it>
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10 % and then performs an iterative search based on the Optimization
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Daniele Nicolodi <nicolodi@science.unitn.it>
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11 % Toolbox.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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12 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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13 % CALL: b = ltpda_arma_freq(ax,ay,pl)
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14 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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15 % INPUTS: ax - analysis object containig the input time series
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Daniele Nicolodi <nicolodi@science.unitn.it>
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16 % ay - analysis object containig the output time series
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Daniele Nicolodi <nicolodi@science.unitn.it>
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17 % pl - parameters list
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Daniele Nicolodi <nicolodi@science.unitn.it>
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18 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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19 % OUTPUTS: b - cdata type analysis object containing the ARMA
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Daniele Nicolodi <nicolodi@science.unitn.it>
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20 % parameters and the residual of the fit
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21 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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22 % PARAMETERS:
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Daniele Nicolodi <nicolodi@science.unitn.it>
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23 % MaxIter - Maximum number of iterations to be performed by the
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Daniele Nicolodi <nicolodi@science.unitn.it>
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24 % iterative search (default 4e2)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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25 % MaxFunEvals - Maximum number of function evaluations (default 1e2)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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26 % TolX - Tolerance on the estimated parameter (default 1e-6)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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27 % TolFun - Tolerance on the evaluated function (default 1e-6)
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28 % UpBound - Array of parameters upper bounds for the iterative search
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29 % (default is 1 for each parameter)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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30 % LowBound - Array of parameters lower bounds for the iterative search
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Daniele Nicolodi <nicolodi@science.unitn.it>
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31 % (default is 1 for each parameter)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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32 % ARMANum - MA order of the ARMA filter (default 2)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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33 % ARMADen - AR order of the ARMA filter (default 1)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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34 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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35 % VERSION: $Id: ltpda_arma_freq.m,v 1.1 2008/03/04 12:55:05 miquel Exp $
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Daniele Nicolodi <nicolodi@science.unitn.it>
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36 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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37 % HISTORY: 25-02-2008 M Nofrarias
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Daniele Nicolodi <nicolodi@science.unitn.it>
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38 % Creation
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Daniele Nicolodi <nicolodi@science.unitn.it>
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39 %
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40 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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41 % TODO: - Add parameters errors
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Daniele Nicolodi <nicolodi@science.unitn.it>
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42 % - Pass from univariate to multivariate
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43 %
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44 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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45 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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46
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47
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48
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Daniele Nicolodi <nicolodi@science.unitn.it>
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49 %% Standard history variables
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50
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51 ALGONAME = mfilename;
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52 VERSION = '$Id: ltpda_arma_freq.m,v 1.1 2008/03/04 12:55:05 miquel Exp $';
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53 CATEGORY = 'SIGPROC';
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54
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55
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Daniele Nicolodi <nicolodi@science.unitn.it>
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56 %% Check if this is a call for parameters
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Daniele Nicolodi <nicolodi@science.unitn.it>
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57 if nargin == 1 && ischar(varargin{1})
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Daniele Nicolodi <nicolodi@science.unitn.it>
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58 in = char(varargin{1});
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Daniele Nicolodi <nicolodi@science.unitn.it>
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59 if strcmpi(in, 'Params')
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Daniele Nicolodi <nicolodi@science.unitn.it>
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60 varargout{1} = getDefaultPL();
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Daniele Nicolodi <nicolodi@science.unitn.it>
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61 return
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Daniele Nicolodi <nicolodi@science.unitn.it>
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62 elseif strcmpi(in, 'Version')
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63 varargout{1} = VERSION;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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64 return
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Daniele Nicolodi <nicolodi@science.unitn.it>
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65 elseif strcmpi(in, 'Category')
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66 varargout{1} = CATEGORY;
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67 return
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68 end
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69 end
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70
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Daniele Nicolodi <nicolodi@science.unitn.it>
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71 %% Capture input variables names
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Daniele Nicolodi <nicolodi@science.unitn.it>
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72 invars = {};
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73 as = [];
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74 ps = [];
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Daniele Nicolodi <nicolodi@science.unitn.it>
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75 for j=1:nargin
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Daniele Nicolodi <nicolodi@science.unitn.it>
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76 invars = [invars cellstr(inputname(j))];
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Daniele Nicolodi <nicolodi@science.unitn.it>
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77 if isa(varargin{j}, 'ao')
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78 as = [as varargin{j}];
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79 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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80 if isa(varargin{j}, 'plist')
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81 ps = [ps varargin{j}];
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82 end
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83 end
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84
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85
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Daniele Nicolodi <nicolodi@science.unitn.it>
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86 %% Check plist
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Daniele Nicolodi <nicolodi@science.unitn.it>
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87 if isempty(ps)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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88 pl = getDefaultPL();
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89 else
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90 pl = combine(ps, getDefaultPL);
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91 end
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92
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93
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Daniele Nicolodi <nicolodi@science.unitn.it>
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94 %% Fourier transform input varialbles
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95
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Daniele Nicolodi <nicolodi@science.unitn.it>
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96 Fs=0.65;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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97 L=length(xin)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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98 NFFT = 2^nextpow2(L); % Next power of 2 from length of y
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Daniele Nicolodi <nicolodi@science.unitn.it>
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99 NFFT=length(xin);
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100
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Daniele Nicolodi <nicolodi@science.unitn.it>
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101 x_ = fft(xin,NFFT)/L;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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102 y_ = fft(yout',NFFT)/L;
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103
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Daniele Nicolodi <nicolodi@science.unitn.it>
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104 Px = 2*abs(x_(1:NFFT/2)); % single-sided amplitude spectrum.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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105 Py = 2*abs(y_(1:NFFT/2)); % single-sided amplitude spectrum.
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106
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Daniele Nicolodi <nicolodi@science.unitn.it>
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107 f = Fs/2*linspace(0,1,NFFT/2)';
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Daniele Nicolodi <nicolodi@science.unitn.it>
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108
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109
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110
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111
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Daniele Nicolodi <nicolodi@science.unitn.it>
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112 %% Iterative search using the Optimization Toolbox
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113
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114
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Daniele Nicolodi <nicolodi@science.unitn.it>
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115 % Options for the lsqcurvefit function
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Daniele Nicolodi <nicolodi@science.unitn.it>
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116 opt = optimset(...
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117 'MaxIter',find(pl, 'MaxIter'),...
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118 'TolX',find(pl, 'TolXm'),...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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119 'TolFun',find(pl, 'TolFun'),...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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120 'MaxFunEvals',find(pl, 'MaxFunEvals'),...
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121 'Display','off');
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122
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Daniele Nicolodi <nicolodi@science.unitn.it>
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123 % Upper and Lower Bounds for the parameters
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124 ub=find(pl,'UpBound');
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125 lb=find(pl,'LowBound');
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126 if isempty(ub)
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127 ub=ones(p+q,1);
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128 pl = append(pl, param('UpBound', ub));
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129 disp('! Parameters Upper Bound set to 1')
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130 end
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131 if isempty(lb)
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132 lb=-ones(p+q,1);
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133 pl = append(pl, param('LowBound', lb));
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134 disp('! Parameters Lower Bound set to -1')
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135 end
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136
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Daniele Nicolodi <nicolodi@science.unitn.it>
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137 % Call to the Optimization Toolbox function
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Daniele Nicolodi <nicolodi@science.unitn.it>
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138 [par,res]=lsqcurvefit(@(par,xdata)filter([par(1:p)],[1 par(p+1:p+q)],xdata),...
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139 par0,x,y,lb,ub,opt);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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140
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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 %% Build output ao
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143
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Daniele Nicolodi <nicolodi@science.unitn.it>
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144 % New output history
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145 h = history(ALGONAME, VERSION, pl,[as(1).hist as(2).hist]);
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146 h = set(h,'invars', invars);
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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 % Make output analysis object
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Daniele Nicolodi <nicolodi@science.unitn.it>
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149 b = ao([par; res]);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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150
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Daniele Nicolodi <nicolodi@science.unitn.it>
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151 % Name, mfilename, description for this object
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Daniele Nicolodi <nicolodi@science.unitn.it>
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152 b = setnh(b,...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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153 'name', ['ARMA param. Input: ' sprintf('%s ', char(invars{1})) ' Output: ' char(invars{2})],...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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154 'mfilename', ALGONAME, ...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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155 'description', find(pl,'description'),...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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156 'hist', h);
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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 varargout{1} = b;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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159
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160
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Daniele Nicolodi <nicolodi@science.unitn.it>
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161 %% --- FUNCTIONS ---
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162
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163
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Daniele Nicolodi <nicolodi@science.unitn.it>
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164 % Get default parameters
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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165 function plo = getDefaultPL();
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
166 disp('* creating default plist...');
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
167 plo = plist();
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
168 plo = append(plo, param('MaxIter',4e2));
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
169 plo = append(plo, param('MaxFunEvals',1e2));
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
170 plo = append(plo, param('TolX',1e-6));
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
171 plo = append(plo, param('TolFun',1e-6));
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
172 plo = append(plo, param('ARMANum',2));
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
173 plo = append(plo, param('ARMADen',1));
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
174 plo = append(plo, param('fs', 1));
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
175 disp('* done.');
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
176
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
177
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
178
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
179 % siz=length(Px);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
180 % % siz=200;
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
181 %
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
182 % xdataf=Px(1:siz)*1e5;
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
183 % ydataf=Py(1:siz)*1e5;
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
184 % % xdataf=Px.data.y;
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
185 % % ydataf=Py.data.y;
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
186 % global freq
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
187 % % freq=Px.data.x;
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
188 % freq =f(1:siz);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
189
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
190
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
191 tic;
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
192 [x1f,resnorm1f]=...
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
193 lsqcurvefit(@myfunf,p0,xdataf,ydataf,[-1 -1 -1],[1 1 1],options);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
194 elaps=toc
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
195
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
196 % %
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
197 % %%
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
198 % % Ff = ((x1f(1)+x1f(2)*exp(-i*2*pi*f/0.65))./(1+x1f(3)*exp(-i*2*pi*f/0.65)));
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
199 % % F = ((x1(1)+x1(2)*exp(-i*2*pi*f/0.65))./(1+x1(3)*exp(-i*2*pi*f/0.65)));
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
200 % %
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
201 % % figure(1)
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
202 % % hold off
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
203 % % loglog(Px.data.x,ydataf./xdataf)
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
204 % % hold
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
205 % % loglog(Px.data.x,abs(Ff),'k')
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
206 % % loglog(Px.data.x,abs(F),'m')
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
207 % % loglog(f,abs((39.6e-3-39.5e-3*exp(-i*2*pi*f/0.65))./(1-0.996*exp(-i*2*pi*f/0.65))),'r')
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
208 % %
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
209 % %
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
210 %
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
211 % %%
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
212 %
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
213 % Fs=18;
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
214 % Lw=2;
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
215 %
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
216 % Ff = ((x1f(1)+x1f(2)*exp(-i*2*pi*f/0.65))./(1+x1f(3)*exp(-i*2*pi*f/0.65)));
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
217 % F = ((x1(1)+x1(2)*exp(-i*2*pi*f/0.65))./(1+x1(3)*exp(-i*2*pi*f/0.65)));
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
218 %
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
219 % figure(1)
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
220 % set(gca,'Fontsize',Fs)
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
221 % hold off
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
222 % loglog(f,Py./Px,'LineWidth',Lw)
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
223 % hold
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
224 % % % loglog(f,ydataf,'m')
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
225 % loglog(f,abs(Ff),'k','LineWidth',Lw)
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
226 % loglog(f,abs(F),'m','LineWidth',Lw)
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
227 %
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
228 % % loglog(f,(x1(1)+x1(2)*exp(-i*2*pi*f/1.32))./(1+x1(3)*exp(-i*2*pi*f/1.32)),'r')
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
229 % loglog(f,abs((39.6e-3-39.5e-3*exp(-i*2*pi*f/0.65))./(1-0.996*exp(-i*2*pi*f/0.65))),'r')
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
230 %
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
231 % legend('Empirical','Freq.domain','Time domain','Analytic')
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
232 %