v=[1,2,3,4] v = 1 2 3 4 repmat(v,4,1) ans = 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 repmat(v',1,4) ans = 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 V>=W ??? Undefined function or variable 'V'. V=repmat(v,4,1) V = 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 W=repmat(v',1,4) W = 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 V>=W ans = 1 1 1 1 0 1 1 1 0 0 1 1 0 0 0 1 P=rand(4) P = 0.1576 0.8003 0.7922 0.8491 0.9706 0.1419 0.9595 0.9340 0.9572 0.4218 0.6557 0.6787 0.4854 0.9157 0.0357 0.7577 P(V>=W) ans = 0.1576 0.8003 0.1419 0.7922 0.9595 0.6557 0.8491 0.9340 0.6787 0.7577 P(P>1/2) ans = 0.9706 0.9572 0.8003 0.9157 0.7922 0.9595 0.6557 0.8491 0.9340 0.6787 0.7577 v=rand(1,4) v = 0.7431 0.3922 0.6555 0.1712 P=metropolis(v,ones(4)/4) P = 0.5899 0.1320 0.2205 0.0576 0.2500 0.3909 0.2500 0.1091 0.2500 0.1496 0.5351 0.0653 0.2500 0.2500 0.2500 0.2500 sum(P,2) ans = 1.0000 1.0000 1.0000 1.0000 help invariantPotenze [v,iter,stimaerrore] = invariantPotenze(P,tol,maxit) Calcola la probabilita' invariante mediante il metodo delle potenze (dunque calcola la probabilita' limite) invariantPotenze(P,1e-6,100) ans = 0.3788 0.1999 0.3341 0.0873 v v = 0.7431 0.3922 0.6555 0.1712 v/sum(v) ans = 0.3788 0.1999 0.3341 0.0873 w=rand(1,4) w = 0.0971 0.8235 0.6948 0.3171 w=w/(sum(w)) w = 0.0503 0.4261 0.3595 0.1641 w=w*P w = 0.2671 0.2680 0.3510 0.1139 w=w*P w = 0.3408 0.2210 0.3422 0.0960 w=w*P w = 0.3659 0.2065 0.3375 0.0901 w=w*P w = 0.3744 0.2020 0.3354 0.0882 w=w*P w = 0.3773 0.2006 0.3346 0.0875 w=w*P w = 0.3783 0.2001 0.3343 0.0873 w=w*P w = 0.3786 0.2000 0.3342 0.0873 w=w*P w = 0.3787 0.1999 0.3341 0.0873 w=w*P w = 0.3787 0.1999 0.3341 0.0873 w=w*P w = 0.3788 0.1999 0.3341 0.0873 w=w*P w = 0.3788 0.1999 0.3341 0.0873 w=w*P w = 0.3788 0.1999 0.3341 0.0873 w=w*P w = 0.3788 0.1999 0.3341 0.0873 w=w*P w = 0.3788 0.1999 0.3341 0.0873 w=w*P w = 0.3788 0.1999 0.3341 0.0873 v/sum(v) ans = 0.3788 0.1999 0.3341 0.0873 H=[-1,1] H = -1 1 epsilon=1e-1 epsilon = 0.1000 exp(-H/epsilon) ans = 1.0e+04 * 2.2026 0.0000 format long e exp(-H/epsilon) ans = 2.202646579480672e+04 4.539992976248485e-05 format e ??? Error using ==> format Unknown command option. format short e exp(-H/epsilon) ans = 2.2026e+04 4.5400e-05 epsilon=1e-2 epsilon = 1.0000e-02 exp(-H/epsilon) ans = 2.6881e+43 3.7201e-44 epsilon=1e-3 epsilon = 1.0000e-03 exp(-H/epsilon) ans = Inf 0 exp(-(H(2)-H(1))/epsilon) ans = 0 exp(-H/epsilon) ans = Inf 0 exp(-H/epsilon)/Inf ans = NaN 0 v = 1./sum(exp(-(repmat(H’,1,2)-repmat(H,2,1))/epsilo ??? v = 1./sum(exp(-(repmat(H’,1,2)-repmat(H,2,1))/epsilo | Error: The input character is not valid in MATLAB statements or expressions. v = 1./sum(exp(-(repmat(H',1,2)-repmat(H,2,1))/epsilo ??? v = 1./sum(exp(-(repmat(H',1,2)-repmat(H,2,1))/epsilo | Error: Expression or statement is incorrect--possibly unbalanced (, {, or [. v = 1./sum(exp(-(repmat(H',1,2)-repmat(H,2,1))/epsilon ??? v = 1./sum(exp(-(repmat(H',1,2)-repmat(H,2,1))/epsilon | Error: Expression or statement is incorrect--possibly unbalanced (, {, or [. v = 1./sum(exp(-(repmat(H',1,2)-repmat(H,2,1))/epsilon)) v = 1 0 epsilon=1e-1 epsilon = 1.0000e-01 v = 1./sum(exp(-(repmat(H',1,2)-repmat(H,2,1))/epsilon)) v = 1.0000e+00 2.0612e-09 1/Inf ans = 0 epsilon=1e-1 epsilon = 1.0000e-01 v = 1./sum(exp(-(repmat(H',1,2)-repmat(H,2,1))/epsilon)) v = 1.0000e+00 2.0612e-09 epsilon=1 epsilon = 1 v = 1./sum(exp(-(repmat(H',1,2)-repmat(H,2,1))/epsilon)) v = 8.8080e-01 1.1920e-01 epsilon=0.01 epsilon = 1.0000e-02 v = 1./sum(exp(-(repmat(H',1,2)-repmat(H,2,1))/epsilon)) v = 1.0000e+00 1.3839e-87 uiopen('/home/accounts/personale/clrmrc90/aa1415/sistemi_stocastici/epsmet.m', true); epsmet ans = Columns 1 through 4 2.7953e-01 5.1177e-02 5.8628e-02 7.8148e-02 5.7897e-02 2.0417e-01 8.8829e-02 8.0569e-02 9.3436e-02 1.2514e-01 1.2270e-01 1.0201e-01 8.8409e-02 8.0569e-02 7.2414e-02 2.3738e-01 7.0599e-02 6.0360e-02 2.6434e-02 5.8670e-02 1.2477e-01 1.1586e-01 8.1905e-02 7.0063e-02 7.1295e-02 7.0010e-02 7.5417e-02 7.1233e-02 9.7920e-02 6.5949e-02 6.7879e-02 8.3094e-02 2.0255e-02 1.9282e-02 1.5026e-02 2.7992e-02 1.1168e-01 1.4423e-01 8.9889e-02 8.2740e-02 Columns 5 through 8 1.2216e-01 1.1029e-01 2.0762e-02 8.6555e-02 1.1816e-01 1.1586e-01 2.3065e-02 6.5949e-02 7.2897e-02 1.1538e-01 3.5002e-02 9.5623e-02 1.1485e-01 7.0063e-02 2.3468e-02 8.3094e-02 5.6737e-01 3.8873e-02 2.2866e-02 4.3614e-02 7.6095e-02 1.9815e-01 3.0273e-02 8.2376e-02 1.3587e-01 9.1889e-02 1.1287e-01 1.5164e-01 8.5375e-02 8.2376e-02 4.9957e-02 2.6109e-01 2.6837e-02 2.2820e-02 5.3334e-03 1.7828e-02 7.6754e-02 1.0065e-01 4.4396e-02 1.1273e-01 Columns 9 through 10 9.4037e-02 9.8719e-02 1.0127e-01 1.4423e-01 1.1118e-01 1.2663e-01 1.4702e-01 8.2740e-02 7.2005e-02 3.9210e-02 1.1986e-01 1.0065e-01 8.5026e-02 1.3476e-01 9.3633e-02 1.1273e-01 8.2894e-01 1.5688e-02 8.2399e-02 1.5454e-01 guarda P(5,5) e P(9,9) ans = Columns 1 through 4 3.5977e-01 1.0429e-01 3.0666e-02 8.4563e-02 1.3347e-01 2.3664e-01 3.9636e-02 1.0435e-01 7.7888e-02 7.8660e-02 1.6855e-01 1.3281e-01 1.0823e-01 1.0435e-01 6.6924e-02 2.3419e-01 3.3852e-02 2.2023e-02 1.0463e-02 2.9932e-02 6.9731e-02 1.0741e-01 6.3839e-02 6.9129e-02 9.2211e-02 1.0948e-01 1.0658e-01 1.0580e-01 8.0119e-02 1.1295e-01 6.9844e-02 1.0781e-01 5.7444e-03 3.4595e-03 1.3587e-03 3.9971e-03 9.0421e-02 7.3843e-02 5.0330e-02 7.2928e-02 Columns 5 through 8 1.0135e-01 5.4484e-02 7.8200e-03 6.2601e-02 8.4389e-02 1.0741e-01 1.1883e-02 1.1295e-01 7.9571e-02 1.2669e-01 2.2956e-02 1.3861e-01 1.1470e-01 6.9129e-02 1.1483e-02 1.0781e-01 6.9854e-01 2.2677e-02 3.5205e-03 2.5776e-02 8.6898e-02 2.3179e-01 9.0284e-03 8.2253e-02 1.2429e-01 8.3182e-02 9.4965e-02 7.5778e-02 9.8773e-02 8.2253e-02 8.2247e-03 2.3211e-01 1.8329e-02 5.5885e-03 4.3018e-04 3.9233e-03 8.1497e-02 1.2576e-01 1.0679e-02 9.9688e-02 Columns 9 through 10 1.2381e-01 7.0650e-02 9.5430e-02 7.3843e-02 7.4379e-02 9.9883e-02 1.1026e-01 7.2928e-02 1.3195e-01 2.1268e-02 1.5416e-01 1.2576e-01 1.0933e-01 9.8386e-02 1.0822e-01 9.9688e-02 9.5592e-01 1.2490e-03 3.4454e-02 3.6040e-01 guarda P(5,5) e P(9,9) ans = Columns 1 through 4 7.3878e-01 6.9214e-03 8.4456e-06 5.7610e-03 8.1616e-02 2.7952e-01 7.9405e-05 1.4069e-01 9.4366e-02 7.5241e-02 2.6378e-01 1.2369e-01 6.7932e-02 1.4069e-01 1.3054e-04 3.0308e-01 2.2332e-06 1.5015e-07 1.0904e-10 1.5343e-07 1.3230e-01 8.8006e-02 9.3481e-05 1.0987e-01 9.9658e-02 1.0388e-01 1.0079e-01 1.0464e-01 9.9542e-02 7.3798e-02 1.5732e-04 9.2404e-02 4.0969e-15 3.0286e-16 2.7279e-19 3.8559e-16 1.2908e-01 1.5652e-01 7.2607e-05 8.2789e-02 Columns 5 through 8 1.2927e-01 1.1220e-02 1.9175e-12 8.4417e-03 1.0249e-01 8.8006e-02 2.3567e-11 7.3798e-02 7.0528e-02 8.8579e-02 2.1668e-08 1.4907e-01 1.0473e-01 1.0987e-01 2.3741e-11 9.2404e-02 9.0840e-01 1.1475e-07 3.8265e-17 1.1416e-07 7.8328e-02 2.6830e-01 1.5694e-11 1.1949e-01 1.1512e-01 6.9174e-02 1.0269e-01 1.0365e-01 7.7926e-02 1.1949e-01 2.3517e-11 3.3882e-01 2.4505e-10 4.3261e-16 8.1190e-26 3.8966e-16 1.1060e-01 9.3238e-02 2.4749e-11 9.8440e-02 Columns 9 through 10 8.8646e-02 1.0947e-02 7.7273e-02 1.5652e-01 6.5951e-02 6.8800e-02 9.8379e-02 8.2789e-02 9.1597e-02 1.6204e-07 1.1038e-01 9.3238e-02 9.1304e-02 1.0908e-01 9.9417e-02 9.8440e-02 1.0000e+00 4.6744e-16 1.1926e-01 2.0999e-01 guarda P(5,5) e P(9,9) ans = Columns 1 through 4 8.0650e-01 1.8218e-12 3.6558e-42 2.0999e-12 9.4686e-02 3.0627e-01 2.0256e-31 9.2684e-02 1.1088e-01 1.1820e-01 1.9127e-01 8.9541e-02 1.0914e-01 9.2684e-02 1.5344e-31 3.1237e-01 2.3716e-49 4.2776e-60 8.3606e-90 4.3558e-60 1.0217e-01 9.1739e-02 1.8667e-31 1.0939e-01 1.0119e-01 9.3977e-02 9.5738e-02 1.1377e-01 9.0750e-02 1.0215e-01 1.5036e-31 9.3991e-02 4.1493e-135 8.3198e-146 1.3388e-175 7.6800e-146 9.7994e-02 1.2131e-01 1.6280e-31 9.7018e-02 Columns 5 through 8 1.0017e-01 1.9657e-12 7.0351e-109 1.7461e-12 9.3908e-02 9.1739e-02 3.3958e-98 1.0215e-01 1.0711e-01 1.0893e-01 2.0187e-68 8.7743e-02 9.5626e-02 1.0939e-01 4.1109e-98 9.3991e-02 9.0480e-01 4.6219e-60 1.7235e-156 4.0242e-60 1.0147e-01 3.0026e-01 3.8173e-98 1.0124e-01 1.0471e-01 1.0564e-01 8.9856e-02 9.4360e-02 8.8346e-02 1.0124e-01 3.4096e-98 3.0337e-01 1.7880e-87 8.2017e-146 3.2336e-242 8.6516e-146 1.1607e-01 9.7870e-02 3.4742e-98 1.1902e-01 Columns 9 through 10 9.3324e-02 1.8854e-12 9.7255e-02 1.2131e-01 9.1327e-02 9.5003e-02 8.9776e-02 9.7018e-02 9.5203e-02 5.2871e-60 9.5874e-02 9.7870e-02 1.0461e-01 9.6148e-02 1.0113e-01 1.1902e-01 1.0000e+00 1.0013e-145 1.1705e-01 2.3367e-01 guarda P(5,5) e P(9,9) ans = Columns 1 through 4 6.8507e-02 1.8421e-01 7.0363e-03 1.6504e-01 1.8421e-01 2.0625e-02 1.0893e-01 1.6125e-02 7.0363e-03 1.0893e-01 7.5941e-02 1.5879e-01 1.6504e-01 1.6125e-02 1.5879e-01 1.0343e-01 1.7028e-01 9.8743e-02 4.4954e-02 1.0475e-01 1.4845e-01 7.4640e-02 6.9406e-03 1.4575e-01 1.8405e-02 1.1767e-01 1.6910e-01 1.3660e-01 4.8825e-02 1.0800e-01 1.1363e-01 9.7805e-02 0 0 0 0 1.2673e-01 1.3456e-01 2.0560e-01 4.0690e-02 Columns 5 through 8 1.7028e-01 1.4845e-01 1.8405e-02 4.8825e-02 9.8743e-02 7.4640e-02 1.1767e-01 1.0800e-01 4.4954e-02 6.9406e-03 1.6910e-01 1.1363e-01 1.0475e-01 1.4575e-01 1.3660e-01 9.7805e-02 1.5786e-01 5.1059e-03 8.7235e-02 2.9902e-02 5.1059e-03 1.7649e-01 1.6613e-01 2.1025e-02 8.7235e-02 1.6613e-01 1.4444e-02 1.0546e-01 2.9902e-02 2.1025e-02 1.0546e-01 2.2997e-01 0 0 0 0 1.2691e-01 1.4964e-02 1.6540e-01 4.2157e-02 Columns 9 through 10 6.2526e-02 1.2673e-01 1.3650e-01 1.3456e-01 1.0907e-01 2.0560e-01 3.1021e-02 4.0690e-02 1.7427e-01 1.2691e-01 2.4050e-01 1.4964e-02 1.9556e-02 1.6540e-01 2.0322e-01 4.2157e-02 1.0000e+00 0 1.0275e-02 1.3270e-01 guarda P(5,5) e P(9,9) diary off