Mercurial > hg > ltpda

annotate m-toolbox/classes/@ao/ngsetup.m @ 33:5e7477b94d94 database-connection-manager

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author Daniele Nicolodi <nicolodi@science.unitn.it>
date Mon, 05 Dec 2011 16:20:06 +0100
parents f0afece42f48
children
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0
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Daniele Nicolodi <nicolodi@science.unitn.it>
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1 % NGSETUP is called by the function fromPzmodel
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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 % Inputs calculated by ...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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4 % ... NGCONV:
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Daniele Nicolodi <nicolodi@science.unitn.it>
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5 % - den: denominator coefficients
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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 % ... USER
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Daniele Nicolodi <nicolodi@science.unitn.it>
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8 % - fs: sampling frequency given as input to LTPDA_NOISEGEN
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Daniele Nicolodi <nicolodi@science.unitn.it>
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9 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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10 % Outputs:
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Daniele Nicolodi <nicolodi@science.unitn.it>
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11 % - Tinit: matrix to calculate initial state vector
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Daniele Nicolodi <nicolodi@science.unitn.it>
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12 % - Tprop: matrix to calculate propagation vector
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Daniele Nicolodi <nicolodi@science.unitn.it>
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13 % - E: matrix to calculate propagation vector
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Daniele Nicolodi <nicolodi@science.unitn.it>
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14 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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15 % A Monsky 24-07-07
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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 % $Id: ngsetup.m,v 1.3 2008/10/20 08:38:29 anneke Exp $
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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 function [Tinit,Tprop,E] = ngsetup(den,fs)
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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 den=den';
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Daniele Nicolodi <nicolodi@science.unitn.it>
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22 dt = 1/fs;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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23 length(den);
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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 n = length(den)-1;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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26
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Daniele Nicolodi <nicolodi@science.unitn.it>
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27 %% setting up matrix Aij
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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 m_a = zeros(n,n);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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30 for i = 1:n
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Daniele Nicolodi <nicolodi@science.unitn.it>
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31 for j = 1:n
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Daniele Nicolodi <nicolodi@science.unitn.it>
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32 if j == i+1
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Daniele Nicolodi <nicolodi@science.unitn.it>
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33 m_a(i,j) = 1;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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34 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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35 if i == n
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Daniele Nicolodi <nicolodi@science.unitn.it>
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36 m_a(i,j) = -den(j);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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37 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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38 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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39 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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40
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Daniele Nicolodi <nicolodi@science.unitn.it>
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41 %% Matrix exponential E
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Daniele Nicolodi <nicolodi@science.unitn.it>
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42 E = expm(m_a*dt);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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43
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Daniele Nicolodi <nicolodi@science.unitn.it>
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44 %% setting up matrix Bij
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Daniele Nicolodi <nicolodi@science.unitn.it>
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45 B = zeros(n,n);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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46 for i=1:n
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Daniele Nicolodi <nicolodi@science.unitn.it>
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47 if rem(i,2) ~= 0
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Daniele Nicolodi <nicolodi@science.unitn.it>
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48 j0 = (i+1)/2;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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49 s = (-1)^(j0+1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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50 j = j0;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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51 for k=1:2:(n+1)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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52 B(i,j) = s*den(k);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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53 s = -s;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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54 j = j+1;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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55 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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56 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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57 if rem(i,2) == 0
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Daniele Nicolodi <nicolodi@science.unitn.it>
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58 j0 = i/2+1;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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59 s = (-1)^j0;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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60 j = j0;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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61 for k=2:2:(n+1)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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62 B(i,j) = s * den(k);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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63 s = -s;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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64 j = j+1;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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65 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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66 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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67 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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68
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Daniele Nicolodi <nicolodi@science.unitn.it>
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69 %% solve B * m = k
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Daniele Nicolodi <nicolodi@science.unitn.it>
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70 m_k = zeros(n,1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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71 m_k(n) = 0.5;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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72 m_m = B\m_k;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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73
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Daniele Nicolodi <nicolodi@science.unitn.it>
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74 %% filling covariance matrix Cinit
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Daniele Nicolodi <nicolodi@science.unitn.it>
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75 Cinit = zeros(n,n);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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76 for i=1:n
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Daniele Nicolodi <nicolodi@science.unitn.it>
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77 for j=1:n
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Daniele Nicolodi <nicolodi@science.unitn.it>
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78 if rem((i+j),2) == 0 % even
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Daniele Nicolodi <nicolodi@science.unitn.it>
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79 Cinit(i,j) = (-1)^((i-j)/2) * m_m((i+j)/2);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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80 else
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Daniele Nicolodi <nicolodi@science.unitn.it>
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81 Cinit(i,j) = 0;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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82 end
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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 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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85
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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 %cholesky decomposition
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Daniele Nicolodi <nicolodi@science.unitn.it>
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88
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Daniele Nicolodi <nicolodi@science.unitn.it>
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89 Tinit = chol(Cinit,'lower'); %lower triangular matrix
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Daniele Nicolodi <nicolodi@science.unitn.it>
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90
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Daniele Nicolodi <nicolodi@science.unitn.it>
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91 %% setting up matrix D
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Daniele Nicolodi <nicolodi@science.unitn.it>
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92 N = n*(n+1)/2;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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93
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Daniele Nicolodi <nicolodi@science.unitn.it>
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94 m_d = zeros(N);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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95 g = zeros(n);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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96 for i=1:n
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Daniele Nicolodi <nicolodi@science.unitn.it>
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97 for j=1:n
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Daniele Nicolodi <nicolodi@science.unitn.it>
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98 if i>=j
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Daniele Nicolodi <nicolodi@science.unitn.it>
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99 g(i,j) = (i*i-i)/2+(j);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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100 else
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Daniele Nicolodi <nicolodi@science.unitn.it>
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101 g(i,j) = (j*j-j)/2+(i);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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102 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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103 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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104 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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105
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Daniele Nicolodi <nicolodi@science.unitn.it>
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106 for i=1:n
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Daniele Nicolodi <nicolodi@science.unitn.it>
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107 for j=i:n
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Daniele Nicolodi <nicolodi@science.unitn.it>
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108 for k=1:n
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Daniele Nicolodi <nicolodi@science.unitn.it>
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109 m_d(g(i,j),g(j,k)) = m_d(g(i,j),g(j,k)) + m_a(i,k);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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110 m_d(g(i,j),g(i,k)) = m_d(g(i,j),g(i,k)) + m_a(j,k);
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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 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
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Daniele Nicolodi <nicolodi@science.unitn.it>
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116 %% setting up q from D * p = q
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Daniele Nicolodi <nicolodi@science.unitn.it>
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117 m_q = zeros(1,g(n,n));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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118 for i=1:n
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Daniele Nicolodi <nicolodi@science.unitn.it>
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119 for j=i:n
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Daniele Nicolodi <nicolodi@science.unitn.it>
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120 if i==n
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Daniele Nicolodi <nicolodi@science.unitn.it>
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121 m_q(g(i,j)) = (E(n,n))*(E(n,n))-1;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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122 else
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Daniele Nicolodi <nicolodi@science.unitn.it>
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123 m_q(g(i,j)) = (E(i,n)*E(j,n));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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124 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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125 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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126 end
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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 m_p = m_d\m_q';
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Daniele Nicolodi <nicolodi@science.unitn.it>
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129
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Daniele Nicolodi <nicolodi@science.unitn.it>
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130 Cprop = zeros(n);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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131 for i=1:n
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Daniele Nicolodi <nicolodi@science.unitn.it>
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132 for j=1:n
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Daniele Nicolodi <nicolodi@science.unitn.it>
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133 Cprop(i,j) = m_p(g(i,j));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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134 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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135 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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136 Tprop = chol(Cprop,'lower');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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137
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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138 % %% writing the generator
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Daniele Nicolodi <nicolodi@science.unitn.it>
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139 % r = randn(n,1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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140 % y = Tinit * r;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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141 % x = zeros(Nfft,1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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142 % for i=1:Nfft
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Daniele Nicolodi <nicolodi@science.unitn.it>
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143 % r = randn(n,1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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144 % y = E * y + Tprop * r;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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145 % x(i) = a*y;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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146 % end
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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 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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149