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comparison m-toolbox/test/test_ao_mcmc_td.m @ 0:f0afece42f48

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author Daniele Nicolodi <nicolodi@science.unitn.it>
date Wed, 23 Nov 2011 19:22:13 +0100
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1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2 % Test loglikehood_ssm_td
3 %
4 % Test with an harmonic hoscillator and simplex parameters search
5 %
6 % L Ferraioli 11-10-2010
7 %
8 % $Id: test_ao_mcmc_td.m,v 1.1 2010/11/26 13:52:21 luigi Exp $
9 %
10 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
11 %% set parameters
12
13 m = 2; % kg
14 k = 0.1; % kg s^-2
15 damp = 0.05; % kg s^-1
16
17 fAmp = 3;
18 NAmp = 1;
19 fs = 1;
20
21 cutbefore = 100*fs;
22 cutafter = 500*fs;
23
24 f = logspace(-5+log10(fs),log10(fs/2),300);
25
26 %% Load model
27
28 sys = ssm(plist('built-in', 'HARMONIC_OSC_1D', 'SYMBOLIC PARAMS',{'M', 'K', 'VBETA'}));
29 sys = sys.setParameters(plist('names',{'M', 'K', 'VBETA'},'values',[m k damp]));
30 sys.keepParameters();
31 sys.modifyTimeStep(plist('newtimestep',1/fs));
32
33 pl = plist('inputs', 'COMMAND.Force', 'HARMONIC_OSC_1D.outputs', 'Position', 'f', f);
34 h = bode(sys,pl);
35
36 iplot(h)
37
38 %% input force and readout noise
39
40 % input force
41 fc = ao(plist('waveform','sine wave','A',fAmp,'f',1e-1,'phi',0,'toff',cutbefore/fs,'nsecs',6e2,'fs',fs));
42 in = zeropad(fc,plist('Position','post','N',cutafter));
43
44
45 rn = ao(plist('tsfcn', 'randn(size(t))', 'fs', fs, 'nsecs', in.nsecs));
46 rn = rn.*NAmp;
47
48
49
50 %% Simulate the system
51
52
53 plsym = plist('AOS VARIABLE NAMES',{'COMMAND.Force','noise.readout'},...
54 'RETURN OUTPUTS','HARMONIC_OSC_1D.position',...
55 'AOS',[in,rn]);
56 out = simulate(sys,plsym);
57
58 iplot(out)
59
60
61 %% test parameters search with simplex only
62
63
64 mod = ssm(plist('built-in', 'HARMONIC_OSC_1D',...
65 'SYMBOLIC PARAMS',{'M', 'K', 'VBETA'}));
66 inNames = {'COMMAND.Force'};
67 outNames = {'HARMONIC_OSC_1D.position'};
68 inNoise = rn;
69 parnames = {'M', 'K', 'VBETA'};
70
71
72 % x0 = xp2;
73 x0 = [2.5 0.08 0.1];
74
75 % loglk =
76 % loglikehood_ssm_td(xp,in,out,parnames,model,inNames,outNames,varargin)
77
78 xp = fminsearch(@(x)utils.math.loglikehood_ssm_td(x,in,out,parnames,mod,inNames,outNames,inNoise,'cutbefore',cutbefore,'cutafter',cutafter),x0,optimset('Display','iter'));
79
80
81 sys = copy(mod,1);
82 sys = sys.setParameters(plist('names',{'M', 'K', 'VBETA'},'values',xp));
83 sys.keepParameters();
84 sys.modifyTimeStep(plist('newtimestep',1/fs));
85
86 plsym = plist('AOS VARIABLE NAMES',{'COMMAND.Force'},...
87 'RETURN OUTPUTS','HARMONIC_OSC_1D.position',...
88 'AOS',[in]);
89 outfit = simulate(sys,plsym);
90
91 iplot(out,outfit)
92 iplot(out-outfit)
93 iplot(out-outfit-rn)
94
95 %% Optimal covariance (taken from smodel)
96
97 smod = smodel('1./(M.*((2.*i.*pi.*f).^2)+VBETA.*(2.*i.*pi.*f)+K)');
98 smod.setParams({'M','VBETA','K'},{m,k,damp});
99 %smod.setParams({'M','VBETA','K'},{2.5, 0.08, 0.1});
100 smod.setXvar('f');
101 smod.setXvals(f);
102 smod.setYunits('kg^-1 s^-2');
103
104 % get derivatives
105 dsmod_M = diff(smod,plist('var','M'));
106 dsmod_K = diff(smod,plist('var','K'));
107 dsmod_VBETA = diff(smod,plist('var','VBETA'));
108
109 % eval first order term
110 eM = fftfilt(in,dsmod_M);
111 eK = fftfilt(in,dsmod_K);
112 eVBETA = fftfilt(in,dsmod_VBETA);
113
114 % information matrix
115 bm = [eM.y eK.y eVBETA.y];
116 Im = bm'*bm;
117
118 % covariance matrix
119 Cm = inv(Im);
120
121 %% test mcmc_td
122
123 mod = ssm(plist('built-in', 'HARMONIC_OSC_1D',...
124 'SYMBOLIC PARAMS',{'M', 'K', 'VBETA'}));
125 inNames = {'COMMAND.Force'};
126 outNames = {'HARMONIC_OSC_1D.position'};
127 inNoise = rn;
128 outNoiseNames = {'HARMONIC_OSC_1D.position'};
129 parnames = {'M', 'K', 'VBETA'};
130
131 % c = (1/sqrt(9))^2;
132 c=0.8;
133
134 ranges = {[1 3],[0 2],[0 1]};
135
136 x0 = [2.5 0.08 0.1];
137
138
139
140 pl = plist('N',6000,...
141 'Input',in,...
142 'cov',c*Cm,...
143 'range',ranges,...
144 'parnames',parnames,...
145 'noise',inNoise,...
146 'model',mod,...
147 'inNames',inNames,...
148 'outNames',outNames,...
149 'search',true,...
150 'Tc',[2000 4000],...
151 'heat',4,...
152 'jumps',[2e0 1e2 1e3 1e4],...
153 'x0',x0,...
154 'simplex',true,...
155 'plot',[1 2 3],...
156 'debug',true);
157
158 % metropolis(measurement,noise,model,plist)
159 b = mcmc_td(out,pl);
160 % save(b,'stoc6_mcmc_all_9p_23061300_ssm.mat');
161
162