Mercurial > hg > ltpda

annotate m-toolbox/classes/+utils/@math/getinitstate.m @ 52:daf4eab1a51e database-connection-manager tip

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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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rev   line source
0
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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1 % GETINITSTATE
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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 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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4 % DESCRIPTION:
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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 % Initialize filters for noise generation
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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 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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9 % CALL:
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Daniele Nicolodi <nicolodi@science.unitn.it>
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10 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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11 % INPUT:
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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 % - res
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Daniele Nicolodi <nicolodi@science.unitn.it>
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14 % - poles
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Daniele Nicolodi <nicolodi@science.unitn.it>
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15 % - S0
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Daniele Nicolodi <nicolodi@science.unitn.it>
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16 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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17 % OUTPUT:
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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 % Zi
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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 % REFERENCES:
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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 %
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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 % HISTORY: 23-04-2009 L Ferraioli
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Daniele Nicolodi <nicolodi@science.unitn.it>
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26 % Creation
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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 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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29 % VERSION: $Id: ndeigcsd.m,v 1.2 2009/06/10 16:15:32 luigi Exp $
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Daniele Nicolodi <nicolodi@science.unitn.it>
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30 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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31 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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32 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Daniele Nicolodi <nicolodi@science.unitn.it>
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33 function Zi = getinitstate(res,poles,S0,varargin)
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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 % default value for the method used
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Daniele Nicolodi <nicolodi@science.unitn.it>
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36 mtd = 'svd';
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Daniele Nicolodi <nicolodi@science.unitn.it>
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37
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Daniele Nicolodi <nicolodi@science.unitn.it>
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38 if ~isempty(varargin)
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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39 for j=1:length(varargin)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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40 if strcmpi(varargin{j},'mtd')
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Daniele Nicolodi <nicolodi@science.unitn.it>
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41 mtd = lower(varargin{j+1});
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Daniele Nicolodi <nicolodi@science.unitn.it>
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42 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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43 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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44 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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45
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Daniele Nicolodi <nicolodi@science.unitn.it>
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46 % get problem dimesionality, it is assumed that res for a given filter are
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Daniele Nicolodi <nicolodi@science.unitn.it>
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47 % input as columns and that each different filter has the same number of
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Daniele Nicolodi <nicolodi@science.unitn.it>
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48 % residues and poles
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Daniele Nicolodi <nicolodi@science.unitn.it>
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49 [rw,cl] = size(res);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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50
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Daniele Nicolodi <nicolodi@science.unitn.it>
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51 N = numel(res(:,1));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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52
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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 % check size
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Daniele Nicolodi <nicolodi@science.unitn.it>
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55 if cl == 1 % one dimensional
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Daniele Nicolodi <nicolodi@science.unitn.it>
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56 A = res(:);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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57 p = poles(:);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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58
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Daniele Nicolodi <nicolodi@science.unitn.it>
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59 % Marking complex and real poles
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Daniele Nicolodi <nicolodi@science.unitn.it>
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60 % cindex = 1; pole is complex, next conjugate pole is marked with cindex
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Daniele Nicolodi <nicolodi@science.unitn.it>
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61 % = 2. cindex = 0; pole is real
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Daniele Nicolodi <nicolodi@science.unitn.it>
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62 cindex=zeros(numel(p),1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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63 for mm=1:numel(p)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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64 if imag(p(mm))~=0
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Daniele Nicolodi <nicolodi@science.unitn.it>
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65 if mm==1
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Daniele Nicolodi <nicolodi@science.unitn.it>
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66 cindex(mm)=1;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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67 else
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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68 if cindex(mm-1)==0 || cindex(mm-1)==2
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Daniele Nicolodi <nicolodi@science.unitn.it>
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69 cindex(mm)=1; cindex(mm+1)=2;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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70 else
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Daniele Nicolodi <nicolodi@science.unitn.it>
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71 cindex(mm)=2;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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72 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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73 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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74 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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75 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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76
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Daniele Nicolodi <nicolodi@science.unitn.it>
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77 NA = numel(A);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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78
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Daniele Nicolodi <nicolodi@science.unitn.it>
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79 % Build covariance matrix for filter states
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Daniele Nicolodi <nicolodi@science.unitn.it>
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80 H = zeros(NA);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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81 for aa = 1:NA
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Daniele Nicolodi <nicolodi@science.unitn.it>
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82 for bb = 1:NA
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Daniele Nicolodi <nicolodi@science.unitn.it>
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83 H(aa,bb) = (p(aa)*conj(p(bb))*A(aa)*conj(A(bb))*S0)/(1-p(aa)*conj(p(bb)));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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84 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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85 end
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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 % avoiding problems caused by roundoff errors
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Daniele Nicolodi <nicolodi@science.unitn.it>
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88 HH = triu(H,0); % get upper triangular part of H
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Daniele Nicolodi <nicolodi@science.unitn.it>
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89 HH1 = triu(H,1); % get upper triangular part of H above principal diagonal
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Daniele Nicolodi <nicolodi@science.unitn.it>
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90 HH2 = HH1'; % do transpose conjugate
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Daniele Nicolodi <nicolodi@science.unitn.it>
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91 H = HH + HH2; % reconstruct H in order to be really hermitian
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Daniele Nicolodi <nicolodi@science.unitn.it>
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92
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Daniele Nicolodi <nicolodi@science.unitn.it>
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93 % switch between methods
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Daniele Nicolodi <nicolodi@science.unitn.it>
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94 switch mtd
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Daniele Nicolodi <nicolodi@science.unitn.it>
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95 case 'svd'
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Daniele Nicolodi <nicolodi@science.unitn.it>
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96 % get decomposition of Hr
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Daniele Nicolodi <nicolodi@science.unitn.it>
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97 [U,S,V] = svd(H,0);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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98 % output initial states for gaussian data series
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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99 ZZ = V*(sqrt(diag(S)).*randn(N,1));
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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100
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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101 % cleaning up results for numerical approximations
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Daniele Nicolodi <nicolodi@science.unitn.it>
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102 idx = imag(poles(:,1))==0;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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103 ZZ(idx) = real(ZZ(idx));
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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104
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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105 % cleaning up results for numerical roundoff errors
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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106 % states associated to complex conjugate poles must be complex
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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107 % conjugate
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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108 for jj = 1:numel(ZZ)
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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109 if cindex(jj)==1
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Daniele Nicolodi <nicolodi@science.unitn.it>
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110 ZZ(jj+1) = conj(ZZ(jj));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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111 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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112 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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113
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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114 case 'mvnorm'
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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115
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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116 ZZ = mvnrnd(zeros(N,1),H,1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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117 % willing to work with columns
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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118 if size(ZZ,2)>1
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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119 ZZ = ZZ.';
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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120 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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121 if imag(ZZ(1))~=0 && imag(p(1))==0
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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122 % flip
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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123 ZZ = flipud(ZZ);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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124 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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125
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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126 % cleaning up results for numerical roundoff errors
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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127 % states associated to complex conjugate poles must be complex
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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128 % conjugate
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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129 for jj = 1:numel(ZZ)
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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130 if cindex(jj)==1
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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131 ZZ(jj+1) = conj(ZZ(jj));
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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132 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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133 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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134
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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135 end
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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>
parents:
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137
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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138
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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139 else % cl dmensional
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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140
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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141 % join residues and poles
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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142 A = [];
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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143 p = [];
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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144 pdim = [];
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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145
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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146 for ii=1:cl
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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147 % Join poles and residues as a single column
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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148 A = [A; res(:,ii)];
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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149 p = [p; poles(:,ii)];
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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150 pdim = [pdim; numel(poles(:,ii))];
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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151 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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152
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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153 % Marking complex and real poles
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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154 % cindex = 1; pole is complex, next conjugate pole is marked with cindex
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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155 % = 2. cindex = 0; pole is real
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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156 cindex=zeros(numel(p),1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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157 for mm=1:numel(p)
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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158 if imag(p(mm))~=0
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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159 if mm==1
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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160 cindex(mm)=1;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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161 else
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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162 if cindex(mm-1)==0 || cindex(mm-1)==2
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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163 cindex(mm)=1; cindex(mm+1)=2;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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164 else
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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165 cindex(mm)=2;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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166 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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167 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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168 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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169 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
170
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
171 % sanity check, search if poles are equals
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
172 eqpoles = false;
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
173 if ~all(logical(diff(pdim))) % is executed if the elements of pdim are equal
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
174 % compare poles series
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
175 for ii=2:cl
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
176 if all((poles(:,ii)-poles(:,ii-1))<eps)
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
177 eqpoles = true;
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
178 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
179 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
180 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
181
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
182 if ~eqpoles % poles are different
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
183
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
184 NA = numel(A);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
185
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
186 % Build covariance matrix for filter states
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
187 H = zeros(NA);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
188 for aa = 1:NA
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
189 for bb = 1:NA
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
190 H(aa,bb) = (p(aa)*conj(p(bb))*A(aa)*conj(A(bb))*S0)/(1-p(aa)*conj(p(bb)));
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
191 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
192 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
193
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
194 % avoiding problems caused by roundoff errors
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
195 HH = triu(H,0); % get upper triangular part of H
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
196 HH1 = triu(H,1); % get upper triangular part of H above principal diagonal
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
197 HH2 = HH1'; % do transpose conjugate
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
198 H = HH + HH2; % reconstruct H in order to be really hermitian
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
199
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
200 % get full rank H
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
201 [U,S,V] = svd(H,0);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
202
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
203 % reducing size
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
204 Ur = U(1:N,1:N);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
205 Sr = S(1:N,1:N);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
206 Vr = V(1:N,1:N);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
207
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
208 % New full rank covariance
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
209 Hr = Vr*Sr*Vr';
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
210
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
211 % avoiding problems caused by roundoff errors
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
212 HH = triu(Hr,0); % get upper triangular part of H
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
213 HH1 = triu(Hr,1); % get upper triangular part of H above principal diagonal
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
214 HH2 = HH1'; % do transpose conjugate
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
215 Hr = HH + HH2; % reconstruct H in order to be really hermitian
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
216
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
217 % switch between methods
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
218 switch mtd
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
219 case 'svd'
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
220 % get decomposition of Hr
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
221 [UU,SS,VV] = svd(Hr,0);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
222 % output initial states for gaussian data series
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
223 ZZ = VV*(sqrt(diag(SS)).*randn(N,1));
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
224
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
225 % cleaning up results for numerical roundoff errors
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
226 idx = imag(p)==0;
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
227 ZZ(idx) = real(ZZ(idx));
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
228
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
229 % cleaning up results for numerical roundoff errors
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
230 % states associated to complex conjugate poles must be complex
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
231 % conjugate
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
232 for jj = 1:numel(ZZ)
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
233 if cindex(jj)==1
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
234 ZZ(jj+1) = conj(ZZ(jj));
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
235 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
236 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
237
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
238
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
239 case 'mvnorm'
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
240
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
241 ZZ = mvnrnd(zeros(N,1),Hr,1);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
242 % willing to work with columns
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
243 if size(ZZ,2)>1
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
244 ZZ = ZZ.';
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
245 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
246 if imag(ZZ(1))~=0 && imag(p(1))==0
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
247 % flip
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
248 ZZ = flipud(ZZ);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
249 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
250
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
251 % cleaning up results for numerical roundoff errors
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
252 % states associated to complex conjugate poles must be complex
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
253 % conjugate
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
254 for jj = 1:numel(ZZ)
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
255 if cindex(jj)==1
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
256 ZZ(jj+1) = conj(ZZ(jj));
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
257 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
258 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
259
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
260 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
261
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
262 else % poles are in common
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
263
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
264 NA = numel(A);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
265
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
266 % Build block diagonal covariance matrix for filter states
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
267 H = zeros(NA);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
268 for ii = 1:numel(pdim)
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
269 for aa = 1+(ii-1)*pdim(ii):(ii-1)*pdim(ii)+pdim(ii)
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
270 for bb = 1+(ii-1)*pdim(ii):(ii-1)*pdim(ii)+pdim(ii)
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
271 H(aa,bb) = (p(aa)*conj(p(bb))*A(aa)*conj(A(bb))*S0)/(1-p(aa)*conj(p(bb)));
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
272 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
273 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
274 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
275
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
276 % avoiding problems caused by roundoff errors
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
277 HH = triu(H,0); % get upper triangular part of H
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
278 HH1 = triu(H,1); % get upper triangular part of H above principal diagonal
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
279 HH2 = HH1'; % do transpose conjugate
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
280 H = HH + HH2; % reconstruct H in order to be really hermitian
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
281
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
282 % switch between methods
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
283 switch mtd
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
284 case 'svd'
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
285 % get decomposition of Hr
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
286 [UU,SS,VV] = svd(H,0);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
287 % output initial states for gaussian data series
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
288 rd = randn(N,1);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
289 rdv = [];
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
290 for jj = 1:numel(pdim);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
291 rdv = [rdv; rd];
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
292 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
293 ZZ = VV*(sqrt(diag(SS)).*rdv);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
294
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
295 % cleaning up results for numerical roundoff errors
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
296 idx = imag(p)==0;
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
297 ZZ(idx) = real(ZZ(idx));
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
298
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
299 % cleaning up results for numerical roundoff errors
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
300 % states associated to complex conjugate poles must be complex
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
301 % conjugate
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
302 for jj = 1:numel(ZZ)
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
303 if cindex(jj)==1
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
304 ZZ(jj+1) = conj(ZZ(jj));
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
305 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
306 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
307
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
308
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
309 case 'mvnorm'
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
310
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
311 ZZ = mvnrnd(zeros(N,1),H,1);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
312 % willing to work with columns
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
313 if size(ZZ,2)>1
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
314 ZZ = ZZ.';
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
315 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
316 if imag(ZZ(1))~=0 && imag(p(1))==0
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
317 % flip
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
318 ZZ = flipud(ZZ);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
319 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
320
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
321 % cleaning up results for numerical roundoff errors
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
322 % states associated to complex conjugate poles must be complex
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
323 % conjugate
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
324 for jj = 1:numel(ZZ)
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
325 if cindex(jj)==1
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
326 ZZ(jj+1) = conj(ZZ(jj));
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
327 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
328 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
329
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
330 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
331
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
332 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
333
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
334 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
335
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
336 Zi = ZZ;
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
337
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
338 end