| 1 | function ildp
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| 2 |
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| 3 | tic
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| 4 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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| 5 | %pocatecni konstanty
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| 6 |
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| 7 | % [b=1, yr=1] - to jsme zkouseli spolu sigma = 0.1; rho = 0.5;
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| 8 | % [b=-1, yr=1] sigma = 0.1; rho = 0.5; !aprior
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| 9 | % [b=10, yr=5] sigma = 0.5; rho = 2.0;
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| 10 | % [b=0.6, yr=10] sigma = 0.1; rho = 1.0;
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| 11 |
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| 12 | Iterace = 10; %iterace
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| 13 | K = 5; %casy
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| 14 | N = 100; %vzorky
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| 15 |
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| 16 | sigma = 0.1;
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| 17 | Sigmas = [[sigma^2 0 0]; [0 0 0]; [0 0 0]];
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| 18 |
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| 19 | h = 0;
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| 20 | hdx = [0; 0; 0];
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| 21 | hdxdx = [[0 0 0]; [0 0 0]; [0 0 0]];
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| 22 |
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| 23 | Rk = 1*ones(1, K);
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| 24 | x0 = [0; 1; 1];
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| 25 |
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| 26 | %velikost okoli pro lokalni metodu
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| 27 | rho = 0.5;
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| 28 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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| 29 | %globalni promenne
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| 30 |
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| 31 | Kpi = ones(4, K);
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| 32 | Kpi(4, :) = zeros(1, K);
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| 33 | % Kpi(3, :) = zeros(1, K);
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| 34 |
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| 35 | Wv = zeros(9, K);
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| 36 |
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| 37 | Xkn = zeros(3, K, N);
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| 38 | Xstripe = zeros(3, K);
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| 39 |
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| 40 | gka = 0;
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| 41 | gnu = 0;
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| 42 |
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| 43 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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| 44 | %iteracni smycka
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| 45 |
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| 46 | for i = 1:Iterace,
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| 47 | %generovani stavu
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| 48 | for n = 1:N,
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| 49 | Xkn(:, 1, n) = x0 + [sigma*randn(); 0; 0];
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| 50 | for k = 1:K-1,
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| 51 | Uk = uPi(k, Xkn(:, k, n));
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| 52 | Kk = Uk*Xkn(3, k, n)/(Uk^2*Xkn(3, k, n) + sigma^2);
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| 53 | Xkn(1, k+1, n) = Xkn(1, k, n) + Xkn(2, k, n)*Uk + sigma*randn();
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| 54 | Xkn(2, k+1, n) = Xkn(2, k, n) + Kk*(Xkn(1, k+1, n) - Xkn(1, k, n) - Xkn(2, k, n)*Uk);
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| 55 | Xkn(3, k+1, n) = (1 - Kk*Uk)*Xkn(3, k, n);
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| 56 | end
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| 57 | end
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| 58 | Xstripe = mean(Xkn, 3);
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| 59 |
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| 60 | for k = K-1:-1:1,
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| 61 | gka = k;
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| 62 | % 1]
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| 63 | for n = 1:N,
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| 64 | %krive okoli
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| 65 | Xkn(1, k, n) = Xstripe(1, k) + rho*randn();
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| 66 | Xkn(2, k, n) = Xstripe(2, k) + rho*randn();
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| 67 | Xkn(3, k, n) = Xstripe(3, k)*exp(rho*randn());
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| 68 | end
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| 69 | % 2]
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| 70 | for n = 1:N,
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| 71 | gnu = n;
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| 72 | [Uopt(n), Hmin(n)] = fminunc(@Hamilt, uPi(k, Xkn(:, k, n)), optimset('GradObj','on','Display','notify'));
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| 73 | end
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| 74 | % 3]
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| 75 | for n = 1:N,
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| 76 | Vn(n) = Hmin(n) + Vtilde(k+1, Xkn(:, k, n));
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| 77 | end
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| 78 | % 4]
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| 79 | Epsilon = zeros(3, N);
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| 80 | for n = 1:N,
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| 81 | Epsilon(1, n) = Xkn(1, k, n) - Xstripe(1, k);
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| 82 | Epsilon(2, n) = Xkn(2, k, n) - Xstripe(2, k);
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| 83 | Epsilon(3, n) = Xkn(3, k, n)/Xstripe(3, k);
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| 84 | end
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| 85 | mFi = matrixFi(Epsilon);
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| 86 | FiFiTInvFi = (mFi*mFi')\mFi;
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| 87 | Wv(:,k) = FiFiTInvFi * Vn';
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| 88 | for n = 1:N,
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| 89 | yt(n) = Xkn(1, k, n);
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| 90 | bt(n) = Xkn(2, k, n);
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| 91 | pt(n) = Xkn(3, k, n);
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| 92 | end
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| 93 | mPsi = [yt',...
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| 94 | bt'.*Uopt',...
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| 95 | pt'.*Uopt',...
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| 96 | Uopt'];
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| 97 | PsiPsiTInvPsi = (mPsi'*mPsi)\mPsi';
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| 98 | Kpi(:,k) = PsiPsiTInvPsi * (Rk(k)*ones(N,1));
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| 99 | end
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| 100 | end
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| 101 | %%%%%%%%%%%
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| 102 | toc
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| 103 |
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| 104 | Kpi
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| 105 |
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| 106 | for n = 1:N,
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| 107 | Xkn(:, 1, n) = x0 + [sigma*randn(); 0; 0];
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| 108 | for k = 1:K-1,
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| 109 | Uk = uPi(k, Xkn(:, k, n));
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| 110 | UU(k,n) = Uk;
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| 111 | Kk = Uk*Xkn(3, k, n)/(Uk^2*Xkn(3, k, n) + sigma^2);
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| 112 | Xkn(1, k+1, n) = Xkn(1, k, n) + Xkn(2, k, n)*Uk + sigma*randn();
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| 113 | Xkn(2, k+1, n) = Xkn(2, k, n) + Kk*(Xkn(1, k+1, n) - Xkn(1, k, n) - Xkn(2, k, n)*Uk);
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| 114 | Xkn(3, k+1, n) = (1 - Kk*Uk)*Xkn(3, k, n);
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| 115 | end
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| 116 | hold all
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| 117 | subplot(4,1,1);
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| 118 | plot(1:K,Xkn(1,:,n))
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| 119 | hold all
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| 120 | subplot(4,1,2);
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| 121 | plot(1:K,Xkn(2,:,n))
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| 122 | hold all
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| 123 | subplot(4,1,3);
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| 124 | plot(1:K,Xkn(3,:,n))
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| 125 | hold all
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| 126 | subplot(4,1,4);
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| 127 | plot(1:K-1,UU(:,n))
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| 128 |
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| 129 | end
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| 130 | title('iLDP')
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| 131 | figure
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| 132 | for n = 1:N,
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| 133 | Xkn(:, 1, n) = x0 + [sigma*randn(); 0; 0];
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| 134 | for k = 1:K-1,
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| 135 | Uk = (Rk(k) - Xkn(1, k, n))/(Xkn(2, k, n) + Xkn(3, k, n));
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| 136 | UU(k,n) = Uk;
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| 137 | Kk = Uk*Xkn(3, k, n)/(Uk^2*Xkn(3, k, n) + sigma^2);
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| 138 | Xkn(1, k+1, n) = Xkn(1, k, n) + Xkn(2, k, n)*Uk + sigma*randn();
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| 139 | Xkn(2, k+1, n) = Xkn(2, k, n) + Kk*(Xkn(1, k+1, n) - Xkn(1, k, n) - Xkn(2, k, n)*Uk);
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| 140 | Xkn(3, k+1, n) = (1 - Kk*Uk)*Xkn(3, k, n);
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| 141 | end
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| 142 | hold all
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| 143 | subplot(4,1,1);
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| 144 | plot(1:K,Xkn(1,:,n))
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| 145 | hold all
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| 146 | subplot(4,1,2);
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| 147 | plot(1:K,Xkn(2,:,n))
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| 148 | hold all
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| 149 | subplot(4,1,3);
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| 150 | plot(1:K,Xkn(3,:,n))
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| 151 | hold all
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| 152 | subplot(4,1,4);
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| 153 | plot(1:K-1,UU(:,n))
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| 154 |
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| 155 | end
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| 156 | title('CE')
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| 157 |
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| 158 | for vzorek = 1:100,
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| 159 | loss(vzorek) = 0;
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| 160 | bb = randn() + x0(2);
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| 161 | yy(1) = x0(1);
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| 162 | for k=1:K-1,
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| 163 | yy(k+1)=yy(k)+bb*uPi(k,[yy(k); bb; 0]);
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| 164 | loss(vzorek) = loss(vzorek) + (yy(k+1) - Rk(k+1))^2;
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| 165 | end
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| 166 | end
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| 167 | figure
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| 168 | hist(log(loss))
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| 169 |
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| 170 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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| 171 | %pomocne funkce
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| 172 |
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| 173 | function [val_uPi] = uPi(k_uPi, x_uPi)
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| 174 | val_uPi = (Rk(k_uPi) - Kpi(1, k_uPi)*x_uPi(1))/(Kpi(2, k_uPi)*x_uPi(2) + Kpi(3, k_uPi)*x_uPi(3) + Kpi(4, k_uPi));
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| 175 |
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| 176 | end
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| 177 |
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| 178 | function [val_ham, val_grad] = Hamilt(u_ham)
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| 179 | % Vtddx = Vtilde_dx(gka+1, Xkn(:, gka, gnu));
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| 180 | val_ham = (Xkn(1, gka, gnu) + Xkn(2, gka, gnu)*u_ham - Rk(gka+1))^2 + Xkn(3, gka, gnu)*u_ham^2 ... + sigma^2 ... %ztrata l
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| 181 | + [Xkn(2, gka, gnu)*u_ham; ...
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| 182 | Xkn(3, gka, gnu)*u_ham*(Xkn(1, gka+1, gnu) - Xkn(1, gka, gnu) - Xkn(2, gka, gnu)*u_ham)/(Xkn(3, gka, gnu)*u_ham^2 + sigma^2); ...
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| 183 | -Xkn(3, gka, gnu)^2*u_ham^2/(Xkn(3, gka, gnu)*u_ham^2 + sigma^2)]' ... %fce f
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| 184 | *Vtilde_dx(gka+1, Xkn(:, gka, gnu)) ...
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| 185 | + Wv(5, gka+1)*sigma;%+ Wv(4, gka+1)*sigma;
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| 186 |
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| 187 | val_grad = 2*(Xkn(1, gka, gnu) + Xkn(2, gka, gnu)*u_ham - Rk(gka+1))*Xkn(2, gka, gnu) + 2*Xkn(3, gka, gnu)*u_ham ... %ztrata du
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| 188 | + [Xkn(2, gka, gnu);...
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| 189 | (2*u_ham^2*Xkn(3, gka, gnu)^2*(Xkn(1, gka, gnu) - Xkn(1, gka+1, gnu) + u_ham*Xkn(2, gka, gnu)))/(sigma^2 + u_ham^2*Xkn(3, gka, gnu))^2 - (u_ham*Xkn(2, gka, gnu)*Xkn(3, gka, gnu))/(sigma^2 + u_ham^2*Xkn(3, gka, gnu)) - (Xkn(3, gka, gnu)*(Xkn(1, gka, gnu) - Xkn(1, gka+1, gnu) + u_ham*Xkn(2, gka, gnu)))/(sigma^2 + u_ham^2*Xkn(3, gka, gnu));...
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| 190 | (2*u_ham^3*Xkn(3, gka, gnu)^3)/(sigma^2 + u_ham^2*Xkn(3, gka, gnu))^2 - (2*u_ham*Xkn(3, gka, gnu)^2)/(sigma^2 + u_ham^2*Xkn(3, gka, gnu))]' ... %fce f du
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| 191 | * Vtilde_dx(gka+1, Xkn(:, gka, gnu)); %derivace Bellman fce
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| 192 | end
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| 193 |
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| 194 | function [val_Vt] = Vtilde(k_Vt, x_Vt)
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| 195 | if(k_Vt == K)
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| 196 | val_Vt = h;
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| 197 | else
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| 198 | Epsl = zeros(3, 1);
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| 199 | Epsl(1) = x_Vt(1) - Xstripe(1, k_Vt);
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| 200 | Epsl(2) = x_Vt(2) - Xstripe(2, k_Vt);
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| 201 | Epsl(3) = x_Vt(3)/Xstripe(3, k_Vt);
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| 202 |
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| 203 | val_Vt = vectFi(Epsl)' * Wv(:,k_Vt);
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| 204 | end
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| 205 | end
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| 206 |
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| 207 | function [val_Vt] = Vtilde_dx(k_Vt, x_Vt)
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| 208 | if(k_Vt == K)
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| 209 | val_Vt = hdx;
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| 210 | else
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| 211 | Epsl = zeros(3, 1);
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| 212 | Epsl(1) = x_Vt(1) - Xstripe(1, k_Vt);
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| 213 | Epsl(2) = x_Vt(2) - Xstripe(2, k_Vt);
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| 214 | Epsl(3) = x_Vt(3)/Xstripe(3, k_Vt);
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| 215 |
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| 216 | val_Vt = difFi(Epsl)' * Wv(:,k_Vt);
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| 217 | end
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| 218 | end
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| 219 |
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| 220 | function [val_Fi] = vectFi(x_Fi)
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| 221 | val_Fi = [ ...
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| 222 | 1; ...
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| 223 | x_Fi(1); ...
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| 224 | x_Fi(2); ...
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| 225 | log(x_Fi(3)); ...
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| 226 | x_Fi(1)^2; ...
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| 227 | x_Fi(1)*x_Fi(2); ...
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| 228 | x_Fi(1)*log(x_Fi(3)); ...
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| 229 | x_Fi(2)^2; ...
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| 230 | x_Fi(2)*log(x_Fi(3)); ...
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| 231 | % 2*ln(x_Fi(3)); ...
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| 232 | ];
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| 233 | end
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| 234 |
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| 235 | function [val_Fi] = matrixFi(x_Fi)
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| 236 | val_Fi = [ ...
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| 237 | ones(1, N); ...
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| 238 | x_Fi(1, :); ...
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| 239 | x_Fi(2, :); ...
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| 240 | log(x_Fi(3, :)); ...
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| 241 | x_Fi(1, :).^2; ...
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| 242 | x_Fi(1, :).*x_Fi(2, :); ...
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| 243 | x_Fi(1, :).*log(x_Fi(3, :)); ...
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| 244 | x_Fi(2, :).^2; ...
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| 245 | x_Fi(2, :).*log(x_Fi(3, :)); ...
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| 246 | ];
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| 247 |
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| 248 | end
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| 249 |
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| 250 | function [val_Fi] = difFi(x_Fi)
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| 251 | val_Fi = [ ...
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| 252 | 0 0 0; ...
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| 253 | 1 0 0; ...
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| 254 | 0 1 0; ...
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| 255 | 0 0 1/(x_Fi(3)); ...
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| 256 | 2*x_Fi(1) 0 0; ...
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| 257 | x_Fi(2) x_Fi(1) 0; ...
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| 258 | log(x_Fi(3)) 0 x_Fi(1)/(x_Fi(3)); ...
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| 259 | 0 2*x_Fi(2) 0; ...
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| 260 | 0 log(x_Fi(3)) x_Fi(2)/(x_Fi(3)); ...
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| 261 | ];
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| 262 | end
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| 263 | end |
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