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annotate m-toolbox/classes/+utils/@math/fisher_2x2.m @ 0:f0afece42f48

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Import.
author Daniele Nicolodi <nicolodi@science.unitn.it>
date Wed, 23 Nov 2011 19:22:13 +0100
parents
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Daniele Nicolodi <nicolodi@science.unitn.it>
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1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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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 % Compute Fisher matrix
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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 % Parameters are:
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Daniele Nicolodi <nicolodi@science.unitn.it>
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6 % i1 - input 1st channel (ao)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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7 % i2 - input 2nd channel (ao)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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8 % n - noise both channels (matrix 2x1)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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9 % mdl - model (matrix or ssm)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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10 % params - parameters
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Daniele Nicolodi <nicolodi@science.unitn.it>
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11 % numparams - numerical value of parameters
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Daniele Nicolodi <nicolodi@science.unitn.it>
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12 % freqs - frequnecies being evaluated
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Daniele Nicolodi <nicolodi@science.unitn.it>
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13 % N - number of fft frequencies
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Daniele Nicolodi <nicolodi@science.unitn.it>
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14 % pl - plist
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Daniele Nicolodi <nicolodi@science.unitn.it>
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15 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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16 % M Nofrarias 15-06-09
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Daniele Nicolodi <nicolodi@science.unitn.it>
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17 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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18 % $Id: fisher_2x2.m,v 1.3 2011/09/19 06:19:13 miquel Exp $
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Daniele Nicolodi <nicolodi@science.unitn.it>
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19 %
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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 function FisMat = fisher_2x2(i1,i2,n,mdl,params,numparams,freqs,N,pl,inNames,outNames)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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22
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Daniele Nicolodi <nicolodi@science.unitn.it>
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23 import utils.const.*
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Daniele Nicolodi <nicolodi@science.unitn.it>
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24
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Daniele Nicolodi <nicolodi@science.unitn.it>
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25 % Compute psd
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Daniele Nicolodi <nicolodi@science.unitn.it>
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26 n1 = psd(n.getObjectAtIndex(1,1), pl);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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27 n2 = psd(n.getObjectAtIndex(2,1), pl);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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28 n12 = cpsd(n.getObjectAtIndex(1,1),n.getObjectAtIndex(2,1), pl);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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29
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Daniele Nicolodi <nicolodi@science.unitn.it>
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30 % interpolate to given frequencies
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Daniele Nicolodi <nicolodi@science.unitn.it>
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31 % noise
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Daniele Nicolodi <nicolodi@science.unitn.it>
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32 S11 = interp(n1,plist('vertices',freqs));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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33 S12 = interp(n12,plist('vertices',freqs));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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34 S22 = interp(n2,plist('vertices',freqs));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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35 S21 = conj(S12);
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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 % get some parameters used below
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Daniele Nicolodi <nicolodi@science.unitn.it>
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38 fs = S11.fs;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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39
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Daniele Nicolodi <nicolodi@science.unitn.it>
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40 if ~isempty(mdl) && all(strcmp(class(mdl),'matrix'))
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Daniele Nicolodi <nicolodi@science.unitn.it>
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41 % compute built-in matrix
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Daniele Nicolodi <nicolodi@science.unitn.it>
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42 for i = 1:numel(mdl.objs)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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43 % set Xvals
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Daniele Nicolodi <nicolodi@science.unitn.it>
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44 h(i) = mdl.getObjectAtIndex(i).setXvals(freqs);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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45 % set alias
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Daniele Nicolodi <nicolodi@science.unitn.it>
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46 h(i).assignalias(mdl.objs(i),plist('xvals',freqs));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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47 % set paramaters
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Daniele Nicolodi <nicolodi@science.unitn.it>
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48 h(i).setParams(params,numparams);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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49 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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50 % differentiate and eval
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Daniele Nicolodi <nicolodi@science.unitn.it>
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51 for i = 1:length(params)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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52 utils.helper.msg(msg.IMPORTANT, sprintf('computing symbolic differentiation with respect %s',params{i}), mfilename('class'), mfilename);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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53 % differentiate symbolically
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Daniele Nicolodi <nicolodi@science.unitn.it>
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54 dH11 = diff(h(1),params{i});
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Daniele Nicolodi <nicolodi@science.unitn.it>
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55 dH12 = diff(h(3),params{i}); % taking into account matrix index convention h(2) > H(2,1)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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56 dH21 = diff(h(2),params{i});
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Daniele Nicolodi <nicolodi@science.unitn.it>
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57 dH22 = diff(h(4),params{i});
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Daniele Nicolodi <nicolodi@science.unitn.it>
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58 % evaluate
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Daniele Nicolodi <nicolodi@science.unitn.it>
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59 d11(i) = eval(dH11);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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60 d12(i) = eval(dH12);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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61 d21(i) = eval(dH21);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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62 d22(i) = eval(dH22);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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63 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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64
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Daniele Nicolodi <nicolodi@science.unitn.it>
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65 elseif ~isempty(mdl) && all(strcmp(class(mdl),'ssm'))
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Daniele Nicolodi <nicolodi@science.unitn.it>
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66
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Daniele Nicolodi <nicolodi@science.unitn.it>
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67 meval = copy(mdl,1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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68 % set parameter values
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Daniele Nicolodi <nicolodi@science.unitn.it>
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69 meval.doSetParameters(params, numparams);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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70 % get the differentiation step
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Daniele Nicolodi <nicolodi@science.unitn.it>
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71 step = find(pl,'step');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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72 % case no diff. step introduced
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Daniele Nicolodi <nicolodi@science.unitn.it>
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73 if isempty(step)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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74 utils.helper.msg(msg.IMPORTANT, ...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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75 sprintf('computing optimal differentiation steps'), mfilename('class'), mfilename);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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76 ranges = find(pl,'stepRanges');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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77 if isempty(ranges)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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78 error('### Please input upper and lower ranges for the parameters: ''ranges''')
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Daniele Nicolodi <nicolodi@science.unitn.it>
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79 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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80 ngrid = find(pl,'ngrid');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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81 if isempty(ngrid)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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82 error('### Please input a number of points for the grid to compute the diff. step : ''ngrid''')
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Daniele Nicolodi <nicolodi@science.unitn.it>
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83 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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84 % look for numerical differentiation step
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Daniele Nicolodi <nicolodi@science.unitn.it>
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85 step = utils.math.diffStepFish(i1,i2,S11,S12,S21,S22,N,meval,params,ngrid,ranges,freqs,inNames,outNames);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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86 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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87
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Daniele Nicolodi <nicolodi@science.unitn.it>
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88 % differentiate and eval
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Daniele Nicolodi <nicolodi@science.unitn.it>
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89 for i = 1:length(params)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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90 utils.helper.msg(msg.IMPORTANT, ...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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91 sprintf('computing numerical differentiation with respect %s, Step:%4.2d ',params{i},step(i)), mfilename('class'), mfilename);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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92 % differentiate numerically
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Daniele Nicolodi <nicolodi@science.unitn.it>
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93 dH = meval.parameterDiff(plist('names', params(i),'values',step(i)));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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94 % create plist with correct outNames (since parameterDiff change them)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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95 out1 = strrep(outNames{1},'.', sprintf('_DIFF_%s.',params{i})); % 2x2 case
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Daniele Nicolodi <nicolodi@science.unitn.it>
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96 out2 =strrep(outNames{2},'.', sprintf('_DIFF_%s.',params{i}));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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97 spl = plist('set', 'for bode', ...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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98 'outputs', {out1,out2}, ...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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99 'inputs', inNames, ...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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100 'reorganize', true,...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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101 'f', freqs);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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102 % do bode
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Daniele Nicolodi <nicolodi@science.unitn.it>
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103 d = bode(dH, spl);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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104 % assign according matlab's matrix notation: H(1,1)->h(1) H(2,1)->h(2) H(1,2)->h(3) H(2,2)->h(4)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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105 d11(i) = d.objs(1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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106 d21(i) = d.objs(2);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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107 d12(i) = d.objs(3);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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108 d22(i) = d.objs(4);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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109 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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110
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Daniele Nicolodi <nicolodi@science.unitn.it>
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111 else
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Daniele Nicolodi <nicolodi@science.unitn.it>
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112 error('### please introduce models for the transfer functions')
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Daniele Nicolodi <nicolodi@science.unitn.it>
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113 end
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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 % scaling of PSD
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Daniele Nicolodi <nicolodi@science.unitn.it>
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116 % PSD = 2/(N*fs) * FFT *conj(FFT)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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117 C11 = N*fs/2.*S11.y;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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118 C22 = N*fs/2.*S22.y;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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119 C12 = N*fs/2.*S12.y;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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120 C21 = N*fs/2.*S21.y;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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121
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Daniele Nicolodi <nicolodi@science.unitn.it>
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122 % compute elements of inverse cross-spectrum matrix
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Daniele Nicolodi <nicolodi@science.unitn.it>
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123 InvS11 = (C22./(C11.*C22 - C12.*C21));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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124 InvS22 = (C11./(C11.*C22 - C12.*C21));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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125 InvS12 = (C21./(C11.*C22 - C12.*C21));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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126 InvS21 = (C12./(C11.*C22 - C12.*C21));
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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 % compute Fisher Matrix
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Daniele Nicolodi <nicolodi@science.unitn.it>
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129 for i =1:length(params)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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130 for j =1:length(params)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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131
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Daniele Nicolodi <nicolodi@science.unitn.it>
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132 v1v1 = conj(d11(i).y.*i1.y + d12(i).y.*i2.y).*(d11(j).y.*i1.y + d12(j).y.*i2.y);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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133 v2v2 = conj(d21(i).y.*i1.y + d22(i).y.*i2.y).*(d21(j).y.*i1.y + d22(j).y.*i2.y);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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134 v1v2 = conj(d11(i).y.*i1.y + d12(i).y.*i2.y).*(d21(j).y.*i1.y + d22(j).y.*i2.y);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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135 v2v1 = conj(d21(i).y.*i1.y + d22(i).y.*i2.y).*(d11(j).y.*i1.y + d12(j).y.*i2.y);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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136
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Daniele Nicolodi <nicolodi@science.unitn.it>
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137 FisMat(i,j) = sum(real(InvS11.*v1v1 + InvS22.*v2v2 - InvS12.*v1v2 - InvS21.*v2v1));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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138 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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139 end
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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 end