Mercurial > hg > ltpda

annotate m-toolbox/classes/@ao/ngsetup_vpa.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
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
0
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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1 function [Tinit,Tprop,E] = ngsetup_vpa(den,fs, ndigits)
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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2
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Daniele Nicolodi <nicolodi@science.unitn.it>
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3 % ALGONAME = mfilename;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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4 % VERSION = '$Id: ngsetup_vpa.m,v 1.2 2008/08/01 13:19:42 ingo Exp $';
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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5 digits(ndigits)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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6 fs = sym(fs);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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7 den = sym(den,'d');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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8 den=den';
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Daniele Nicolodi <nicolodi@science.unitn.it>
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9 dt = vpa(1/fs);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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10
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Daniele Nicolodi <nicolodi@science.unitn.it>
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11 n = length(den)-1;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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12 % digits(d);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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13
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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14 %% setting up matrix Aij
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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15 m_a = vpa(zeros(n,n));
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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16 for i = 1:n
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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17 for j = 1:n
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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18 if j == i+1
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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19 m_a(i,j) = 1;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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20 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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21 if i == n
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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22 m_a(i,j) = -den(j);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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23 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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24 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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25 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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26
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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27 %% Matrix exponential E
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Daniele Nicolodi <nicolodi@science.unitn.it>
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28 a = m_a*dt;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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29 E = expm(a);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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30
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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31
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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32 %% setting up matrix Bij
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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33 B = vpa(zeros(n,n));
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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34 for i=1:n
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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35 if rem(i,2) ~= 0
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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36 j0 = (i+1)/2;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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37 s = (-1)^(j0+1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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38 j = j0;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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39 for k=1:2:(n+1)
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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40 d1 = den(k);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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41 d2 = s*d1;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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42 B(i,j) = d2;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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43 s = -s;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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44 j = j+1;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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45 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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46 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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47 if rem(i,2) == 0
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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48 j0 = i/2+1;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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49 s = (-1)^j0;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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50 j = j0;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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51 for k=2:2:(n+1)
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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52 d1 = den(k);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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53 d2 = s*d1;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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54 B(i,j) = d2;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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55 s = -s;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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56 j = j+1;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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57 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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58 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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59 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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60
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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61 %% solve B * m = k
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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62 m_k = vpa(zeros(n,1));
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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63 m_k(n) = 0.5;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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64 m_m = vpa(B\m_k);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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65
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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66 %% filling covariance matrix Cinit
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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67 % Cinit = vpa(zeros(n,n));
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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68 % for i=1:n
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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69 % for j=1:n
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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70 % if rem((i+j),2) == 0 % even
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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71 % d1 = (-1)^((i-j)/2);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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72 % d1 = subs(d1)
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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73 % d2 = vpa('m_m((i+j)/2)');
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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74 % d2 = subs(d2)
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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75 % d3 = vpa(ctranspose(d2));
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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76 % d3 = subs(d3)
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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77 % d4 = vpa('d1 * d3');
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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78 % d4 = subs(d4)
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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79 % Cinit(i,j) = d4;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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80 % else
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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81 % Cinit(i,j) = 0;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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82 % end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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83 % end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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84 % end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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85
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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86 Cinit = vpa(zeros(n,n));
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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87 for i=1:n
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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88 for j=1:n
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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89 if rem((i+j),2) == 0 % even
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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90 d1 = (-1)^((i-j)/2);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
91 d2 = (i+j)/2;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
92 Cinit(i,j) = d1 * m_m(d2);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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93 % else
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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94 % Cinit(i,j) = 0;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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95 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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96 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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97 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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98 %cholesky decomposition
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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99
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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100 % Tinit = chol(double(Cinit),'lower'); %lower triangular matrix
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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101 Tinit = ao.mchol(Cinit);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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102
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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103 %% setting up matrix D
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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104 N = n*(n+1)/2;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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105
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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106 m_d = vpa(zeros(N));
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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107 g = zeros(n);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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108 for i=1:n
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
109 for j=1:n
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
110 if i>=j
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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111 g(i,j) = (i*i-i)/2+(j);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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112 else
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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113 g(i,j) = (j*j-j)/2+(i);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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114 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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115 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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116 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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117
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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118 for i=1:n
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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119 for j=i:n
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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120 for k=1:n
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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121 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>
parents:
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122 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>
parents:
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123 end
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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 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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126
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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127
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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128 %% setting up q from D * p = q
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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129 m_q = vpa(zeros(1,g(n,n)));
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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130 for i=1:n
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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131 for j=i:n
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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132 if i==n
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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133 m_q(g(i,j)) = (E(n,n))*(E(n,n))-1;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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134 else
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
135 m_q(g(i,j)) = (E(i,n)*E(j,n));
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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136 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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137 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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138 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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139
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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140 m_p = m_d\m_q';
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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141
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
142 Cprop = vpa(zeros(n));
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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143 for i=1:n
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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144 for j=1:n
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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145 Cprop(i,j) = m_p(g(i,j));
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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146 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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147 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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148
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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149 Tprop = ao.mchol(Cprop);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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150 Tprop = double(Tprop);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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151 E = double(E);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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152 Tinit = double(Tinit);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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153
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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154 % Tprop = chol(Cprop,'lower');
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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155
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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156 % Tprop = chol(double((Cprop)),'lower');
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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157 % Tprop = mchol(Cprop);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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158
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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159 % %% writing the generator
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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160 % r = randn(n,1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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161 % y = Tinit * r;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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162 % x = zeros(Nfft,1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
163 % for i=1:Nfft
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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164 % r = randn(n,1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
165 % y = E * y + Tprop * r;
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
166 % x(i) = a*y;
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
167 % end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
168
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
169 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
170