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annotate m-toolbox/classes/+utils/@math/diffStepFish_1x1.m @ 0:f0afece42f48

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Import.
author Daniele Nicolodi <nicolodi@science.unitn.it>
date Wed, 23 Nov 2011 19:22:13 +0100
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Daniele Nicolodi <nicolodi@science.unitn.it>
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1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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2 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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3 % Look for differentiation step for a given parameter and
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4 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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5 % Parameters are:
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6
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7 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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8 % $Id: diffStepFish_1x1.m,v 1.1 2011/10/07 08:17:52 miquel Exp $
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9 %
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10 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Daniele Nicolodi <nicolodi@science.unitn.it>
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11 function best = diffStepFish_1x1(i1,S11,N,meval,params,numparams,ngrid,ranges,freqs,inNames,outNames)
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12
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13 import utils.const.*
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14
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15 % remove aux file if existing
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16 if exist('diffStepFish.txt') == 2
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Daniele Nicolodi <nicolodi@science.unitn.it>
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17 ! rm diffStepFish.txt
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18 end
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19
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20 step = ones(ngrid,numel(params));
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21
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22 % initialize matrix of steps
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Daniele Nicolodi <nicolodi@science.unitn.it>
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23 for ii = 1:numel(params)
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24 step(:,ii) = ranges(1)*numparams(ii);
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25 end
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26
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27 % step(:,1) = logspace(ranges(1,1),ranges(2,1),ngrid);
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28
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29 for kk = 1:length(params)
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30 step(:,kk) = numparams(kk)*logspace(log10(ranges(1)),log10(ranges(2)),ngrid);
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31 Rmat = [];
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32 for jj = 1:ngrid
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33 for ii = 1:length(params)
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34 % differentiate numerically
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Daniele Nicolodi <nicolodi@science.unitn.it>
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35 dH = meval.parameterDiff(plist('names', params(ii),'values',step(jj,ii)));
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36 % create plist with correct outNames (since parameterDiff change them)
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37 out1 = strrep(outNames{1},'.', sprintf('_DIFF_%s.',params{ii})); % 2x2 case
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38 spl = plist('set', 'for bode', ...
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39 'outputs', {out1}, ...
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40 'inputs', inNames, ...
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41 'reorganize', true,...
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42 'f', freqs);
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43 % do bode
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44 d = bode(dH, spl);
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45 % assign according matlab's matrix notation:
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46 % H(1,1)->h(1) H(2,1)->h(2) H(1,2)->h(3) H(2,2)->h(4)
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47 d11(ii) = d.objs(1);
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48 end
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49
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50 fs = S11.fs;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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51 % scaling of PSD
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Daniele Nicolodi <nicolodi@science.unitn.it>
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52 % PSD = 2/(N*fs) * FFT *conj(FFT)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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53 C11 = N*fs/2.*S11.y;
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54
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55 % compute elements of inverse cross-spectrum matrix
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Daniele Nicolodi <nicolodi@science.unitn.it>
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56 InvS11 = 1./C11;
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57
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58 % compute Fisher Matrix
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59 for i =1:length(params)
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60 for j =1:length(params)
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61
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62 v1v1 = conj(d11(i).y.*i1.y).*(d11(j).y.*i1.y);
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63 FisMat(i,j) = sum(real(InvS11.*v1v1));
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64 end
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65 end
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66
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67 detFisMat = det(FisMat);
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68 R = [step(jj,:) detFisMat];
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Daniele Nicolodi <nicolodi@science.unitn.it>
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69 % only file diffStepFish.txt stores all iterations. Rmat is
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Daniele Nicolodi <nicolodi@science.unitn.it>
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70 % initialized for each loop
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71 save('diffStepFish.txt','R','-ascii','-append');
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72 Rmat = [Rmat; R];
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73 end
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74
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75 % look for the stable step: compute diff and
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76 % look for the smallest one in absolute value
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77 % The smallest slope marks the plateau
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78 diffDetFisMat = abs(diff(Rmat(:,end)));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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79 lowdet = diffDetFisMat(1);
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80 ind = 2;
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81 for k = 1:numel(diffDetFisMat)
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82 if diffDetFisMat(k) < lowdet
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Daniele Nicolodi <nicolodi@science.unitn.it>
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83 lowdet = diffDetFisMat(k);
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84 ind = k+1; % index give by diff = x(2) - x(1). We take the step corresponding to x(2)
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85 end
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86 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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87 % display message
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Daniele Nicolodi <nicolodi@science.unitn.it>
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88 utils.helper.msg(msg.IMPORTANT, ...
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89 sprintf('Best numerical diff. step with respect %s: %d',params{kk}, step(ind,kk)), mfilename('class'), mfilename);
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90 % reassing all current column to the best step
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91 step(:,kk) = step(ind,kk)*ones(ngrid,1);
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92
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93 figure
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94 diffDetFisMat(diffDetFisMat == 0) = 1e-20; % to avoid zeros in loglog plot
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95 loglog(Rmat(1:end-1,kk)/numparams(kk),diffDetFisMat,'--ks','LineWidth',2,'MarkerSize',10)
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96 title(sprintf('Parameter: %s',params{kk}))
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97 ylabel('\Delta FisMat / \Delta\theta')
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98 xlabel('Normalised \Delta\theta')
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99
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100 end
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101 best = step(1,:);
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102 end
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103