octave:3> v=[1,2,3] v = 1 2 3 octave:4> V=repmat(v,3,1); octave:5> W=repmat(v',1,3); octave:6> V V = 1 2 3 1 2 3 1 2 3 octave:7> W W = 1 1 1 2 2 2 3 3 3 octave:8> V>=W ans = 1 1 1 0 1 1 0 0 1 octave:9> P=[1,2,3;4,5,6;7,8,9] P = 1 2 3 4 5 6 7 8 9 octave:10> P(V>=W) ans = 1 2 5 3 6 9 octave:11> randstocsym(3) ans = 0.050949 0.565472 0.383579 0.565472 0.298680 0.135848 0.383579 0.135848 0.480573 octave:12> sum(ans,2) ans = 1 1 1 octave:13> v=[1,2,3] v = 1 2 3 octave:14> P=metropolis(v) P = 0.29273 0.40701 0.30026 0.20350 0.50542 0.29108 0.10009 0.19405 0.70586 octave:15> sum(P,2) ans = 1 1 1 octave:16> invariantPotenze(P,1e-6,100) ans = 0.16667 0.33333 0.50000 octave:17> v/sum(v) ans = 0.16667 0.33333 0.50000 octave:18> P=metropolis(v,ones(3)/3) P = 0.33333 0.33333 0.33333 0.16667 0.50000 0.33333 0.11111 0.22222 0.66667 octave:19> invariantPotenze(P) error: 'tol' undefined near line 17 column 15 error: called from: error: /home/accounts/personale/clrmrc90/aa1516/sistemi_stocastici/invariantPotenze.m at line 17, column 13 octave:19> invariantPotenze(P,1e-6,100) ans = 0.16667 0.33333 0.50000 octave:20> eps=1/100; octave:21> Hi=1; octave:22> exp(-Hi/eps) ans = 3.7201e-44 octave:23> Hi=-1 Hi = -1 octave:24> exp(-Hi/eps) ans = 2.6881e+43 octave:25> Hi=-2 Hi = -2 octave:26> exp(-Hi/eps) ans = 7.2260e+86 octave:27> Hi=-10 Hi = -10 octave:28> exp(-Hi/eps) ans = Inf octave:29> H(1)=-1 H = -1 octave:30> H(2)=1 H = -1 1 octave:31> eps=1e-3; octave:32> v=exp(-H/eps); octave:33> vhat = v/sum(v) vhat = NaN 0 octave:34> v v = Inf 0 octave:35> v = 1./sum(exp(-(repmat(H’,1,2)-repmat(H,2,1))/epsilon)) error: invalid character 'â' (ASCII 226) near line 1, column 27 parse error: syntax error >>> v = 1./sum(exp(-(repmat(H’,1,2)-repmat(H,2,1))/epsilon)) ^ octave:35> v = 1./sum(exp(-(repmat(H',1,2)-repmat(H,2,1))/epsilon)) error: 'epsilon' undefined near line 1 column 47 error: evaluating argument list element number 1 error: evaluating argument list element number 1 octave:35> epsilon=1e-3 epsilon = 0.0010000 octave:36> v = 1./sum(exp(-(repmat(H',1,2)-repmat(H,2,1))/epsilon)) v = 1 0 octave:37> H H = -1 1 octave:38> H=[1,-1] H = 1 -1 octave:39> v = 1./sum(exp(-(repmat(H',1,2)-repmat(H,2,1))/epsilon)) v = 0 1 octave:40> sum(exp(-(repmat(H',1,2)-repmat(H,2,1))/epsilon)) ans = Inf 1 octave:41> H=[1,-1,0] H = 1 -1 0 octave:42> epsilon=1 epsilon = 1 octave:43> v = 1./sum(exp(-(repmat(H',1,2)-repmat(H,2,1))/epsilon)) error: operator -: nonconformant arguments (op1 is 3x2, op2 is 2x3) error: evaluating argument list element number 1 error: evaluating argument list element number 1 octave:43> v = 1./sum(exp(-(repmat(H',1,3)-repmat(H,3,1))/epsilon)) v = 0.090031 0.665241 0.244728 octave:44> epsilon=1e-1 epsilon = 0.10000 octave:45> v = 1./sum(exp(-(repmat(H',1,3)-repmat(H,3,1))/epsilon)) v = 2.0611e-09 9.9995e-01 4.5398e-05 octave:46> epsilon=1e-2 epsilon = 0.010000 octave:47> v = 1./sum(exp(-(repmat(H',1,3)-repmat(H,3,1))/epsilon)) v = 1.3839e-87 1.0000e+00 3.7201e-44 octave:48> epsmet ans = Columns 1 through 6: 1.9228e-01 1.1932e-01 4.7554e-02 6.6749e-02 9.4786e-02 1.2125e-01 1.3498e-01 1.6223e-01 5.7967e-02 1.2216e-01 8.5571e-02 1.1532e-01 7.5788e-02 8.1661e-02 1.4064e-01 1.1364e-01 9.9122e-02 1.3633e-01 7.5513e-02 1.2216e-01 8.0670e-02 2.0487e-01 1.6789e-01 5.1736e-02 5.4779e-02 4.3714e-02 3.5944e-02 8.5765e-02 5.1806e-01 7.0394e-02 1.3717e-01 1.1532e-01 9.6777e-02 5.1736e-02 1.3780e-01 1.8285e-01 5.2378e-02 7.4709e-02 1.2447e-01 1.0310e-01 1.1302e-01 5.2853e-02 9.3850e-02 7.0729e-02 8.3881e-02 5.4670e-02 6.1101e-02 9.2094e-02 3.2331e-02 2.7276e-02 8.2815e-03 1.2087e-02 4.0055e-02 1.7363e-02 1.2416e-01 8.3166e-02 8.2064e-02 1.4504e-01 6.5843e-02 7.7655e-02 Columns 7 through 10: 1.5253e-02 8.2958e-02 1.5010e-01 1.0975e-01 2.4613e-02 7.0729e-02 1.4326e-01 8.3166e-02 5.7767e-02 1.1817e-01 6.1274e-02 1.1561e-01 3.3966e-02 5.4670e-02 6.3483e-02 1.4504e-01 1.9020e-02 3.1214e-02 1.0747e-01 3.3636e-02 1.7413e-02 9.2094e-02 9.1192e-02 7.7655e-02 8.9714e-02 1.1252e-01 1.2340e-01 1.5384e-01 3.7069e-02 2.3481e-01 1.9286e-01 7.8937e-02 7.7406e-03 3.6720e-02 8.1024e-01 7.9070e-03 5.0683e-02 7.8937e-02 4.1529e-02 2.5092e-01 guarda P(5,5) e P(9,9) octave:48> epsmet epsilon = 2.0000e+01 ans = Columns 1 through 6: 2.0837e-01 1.8477e-02 8.4085e-02 8.2581e-02 2.1152e-01 2.0880e-04 2.0904e-02 2.7874e-01 3.5601e-02 3.3978e-02 9.8549e-02 1.2319e-01 1.3401e-01 5.0153e-02 1.1408e-01 3.7005e-02 1.5484e-01 1.0883e-01 9.3424e-02 3.3978e-02 2.6268e-02 2.3682e-01 2.1586e-01 6.0337e-02 1.2225e-01 5.0343e-02 5.6150e-02 1.1027e-01 5.1071e-01 7.0292e-03 2.3622e-04 1.2319e-01 7.7254e-02 6.0337e-02 1.3760e-02 1.9292e-01 6.3974e-02 1.6785e-01 1.3964e-01 1.6414e-01 3.9963e-02 1.3967e-01 2.2690e-01 1.5960e-01 9.8705e-02 5.3408e-02 7.0646e-02 2.1105e-01 7.2528e-03 3.5358e-02 1.4939e-02 1.5409e-02 2.4558e-02 2.7075e-02 1.6052e-01 8.4415e-03 6.1541e-02 1.4489e-01 6.7622e-02 1.3303e-01 Columns 7 through 10: 1.8630e-02 2.0056e-01 3.3672e-02 1.4189e-01 5.5297e-02 1.5960e-01 1.8570e-01 8.4415e-03 6.4809e-02 1.3905e-01 1.1053e-01 8.6695e-02 5.4077e-02 5.3408e-02 8.0932e-02 1.4489e-01 6.7257e-03 3.6089e-02 6.5890e-02 3.4545e-02 4.6013e-02 2.1105e-01 1.4221e-01 1.3303e-01 6.8578e-02 3.2499e-02 6.0491e-02 1.2320e-01 1.0707e-02 1.2008e-01 9.8359e-04 4.7919e-02 3.7944e-03 1.8727e-04 8.3648e-01 3.4945e-02 4.0587e-02 4.7919e-02 1.8354e-01 1.5191e-01 guarda P(5,5) e P(9,9) epsilon = 1.0000e+01 ans = Columns 1 through 6: 4.7473e-01 1.6636e-02 5.7521e-02 5.5773e-03 6.6131e-02 9.1223e-03 2.1291e-02 3.2821e-01 7.8132e-02 1.5399e-01 1.0248e-01 4.5604e-02 1.4610e-01 1.5506e-01 1.0667e-01 8.8264e-02 6.1854e-02 1.1215e-01 7.1380e-03 1.5399e-01 4.4476e-02 1.8745e-01 1.5566e-01 8.0932e-02 2.2088e-02 2.6744e-02 8.1338e-03 4.0623e-02 7.6694e-01 3.0082e-02 1.1675e-02 4.5604e-02 5.6510e-02 8.0932e-02 1.1527e-01 4.5017e-01 1.5190e-01 1.6414e-01 7.7571e-02 3.0962e-02 1.9027e-01 1.4811e-01 1.8118e-01 4.2352e-02 4.7007e-02 1.1729e-01 2.9013e-02 3.3829e-02 9.9655e-03 4.3983e-03 1.3233e-03 4.9194e-03 8.6484e-03 5.7077e-03 1.3319e-03 8.8793e-02 7.4310e-02 1.1399e-01 1.1561e-01 3.2490e-02 Columns 7 through 10: 1.2882e-02 1.4156e-01 2.1479e-01 1.0407e-03 1.7815e-02 4.2352e-02 1.2133e-01 8.8793e-02 1.6709e-02 9.3287e-02 7.2442e-02 1.4747e-01 3.3606e-03 1.1729e-01 1.3570e-01 1.1399e-01 5.3893e-03 7.5714e-03 6.2258e-02 3.0170e-02 1.6076e-02 3.3829e-02 1.5745e-01 3.2490e-02 1.2437e-02 1.0428e-01 5.5121e-02 6.5198e-02 1.1319e-02 1.6831e-01 1.6616e-01 2.0353e-01 2.1688e-04 6.0235e-03 9.5867e-01 1.3047e-04 7.0764e-03 2.0353e-01 3.5990e-03 3.5927e-01 guarda P(5,5) e P(9,9) epsilon = 1.0000e+00 ans = Columns 1 through 6: 7.6611e-01 8.7510e-03 7.7724e-06 8.1296e-03 8.9907e-02 9.2651e-03 1.0319e-01 2.9945e-01 1.1689e-04 8.8309e-02 9.0733e-02 1.0194e-01 8.6844e-02 1.1076e-01 1.9491e-01 9.2897e-02 1.1782e-01 8.9351e-02 9.5862e-02 8.8309e-02 9.8038e-05 3.0443e-01 8.9432e-02 1.1669e-01 1.5532e-06 1.3293e-07 1.8216e-10 1.3102e-07 8.9241e-01 1.4720e-07 1.0925e-01 1.0194e-01 9.4295e-05 1.1669e-01 1.0048e-01 2.6796e-01 9.7959e-02 9.5341e-02 1.0625e-01 8.3436e-02 1.1012e-01 8.8809e-02 1.1224e-01 1.1190e-01 9.2282e-05 1.0313e-01 9.3445e-02 1.1806e-01 4.5712e-15 3.5815e-16 5.4235e-19 3.1449e-16 2.8784e-10 3.3716e-16 1.1086e-01 1.1299e-01 9.3773e-05 1.2182e-01 9.0404e-02 9.9503e-02 Columns 7 through 10: 1.8848e-12 9.5181e-03 9.8907e-02 9.4012e-03 2.1631e-11 1.1190e-01 9.1378e-02 1.1299e-01 2.2841e-08 8.7443e-02 1.3112e-01 8.8856e-02 1.8930e-11 1.0313e-01 8.0238e-02 1.2182e-01 3.6603e-17 1.3690e-07 1.0759e-01 1.3245e-07 2.0149e-11 1.1806e-01 8.6024e-02 9.9503e-02 1.1818e-01 9.5158e-02 8.4089e-02 1.2066e-01 2.1589e-11 2.7191e-01 9.2782e-02 9.6454e-02 7.4774e-26 3.6365e-16 1.0000e+00 4.6470e-16 2.7374e-11 9.6454e-02 1.1856e-01 2.4932e-01 guarda P(5,5) e P(9,9) epsilon = 1.0000e-01 ans = Columns 1 through 6: 7.6171e-01 8.3172e-13 3.2127e-42 9.6947e-13 1.1854e-01 2.9287e-12 4.3228e-02 3.1048e-01 2.3970e-31 1.0654e-01 9.8921e-02 1.2532e-01 9.7438e-02 1.3988e-01 2.6930e-01 1.2140e-01 2.9749e-02 1.8089e-01 5.0387e-02 1.0654e-01 2.0804e-31 3.4613e-01 1.4978e-01 3.3405e-02 2.8063e-49 4.5059e-60 2.3222e-90 6.8226e-60 8.6850e-01 4.1821e-60 1.5221e-01 1.2532e-01 3.0999e-31 3.3405e-02 9.1813e-02 3.3480e-01 1.1536e-01 2.9644e-02 8.8473e-02 1.0853e-01 5.2115e-02 5.2324e-02 3.0731e-02 1.2290e-01 1.4473e-31 1.5476e-01 1.0247e-01 9.2996e-02 5.3247e-135 1.2379e-145 6.6576e-176 3.2098e-146 2.4696e-87 6.8588e-146 1.5137e-01 4.7907e-02 5.3929e-32 1.2148e-01 1.6879e-01 8.9268e-02 Columns 7 through 10: 8.0204e-109 5.9128e-13 1.1976e-01 2.9125e-12 1.0712e-98 1.2290e-01 1.4470e-01 4.7907e-02 1.8655e-68 8.4459e-02 4.5414e-02 3.1470e-02 3.9215e-98 1.5476e-01 3.7522e-02 1.2148e-01 8.5778e-157 4.6677e-60 1.3150e-01 7.6885e-60 1.8907e-98 9.2996e-02 8.0177e-02 8.9268e-02 1.3521e-01 8.7980e-02 1.0774e-01 2.2263e-01 3.1791e-98 2.7448e-01 1.7977e-01 4.1891e-02 3.3303e-242 1.5379e-145 1.0000e+00 9.5932e-146 8.0444e-98 4.1891e-02 1.1214e-01 2.6715e-01 guarda P(5,5) e P(9,9) epsilon = 1.0000e-03 ans = Columns 1 through 6: 1.4881e-01 5.2973e-02 1.7141e-01 2.2113e-01 2.9248e-02 2.6166e-02 5.2973e-02 1.5627e-01 3.9560e-02 8.4458e-02 1.8741e-01 1.4696e-01 1.7141e-01 3.9560e-02 7.1923e-02 1.3177e-01 5.2937e-02 9.7432e-02 2.2113e-01 8.4458e-02 1.3177e-01 2.4132e-02 3.5550e-02 8.0696e-02 2.9248e-02 1.8741e-01 5.2937e-02 3.5550e-02 1.2509e-01 3.2668e-02 2.6166e-02 1.4696e-01 9.7432e-02 8.0696e-02 3.2668e-02 1.7291e-01 1.4289e-02 2.0842e-01 1.2105e-01 3.6265e-02 6.1534e-02 1.6777e-01 2.1069e-01 7.9380e-02 8.0733e-02 1.0609e-01 1.6797e-01 9.2359e-02 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 8.2043e-02 3.5661e-02 9.1261e-02 1.8843e-01 1.3743e-01 8.3526e-02 Columns 7 through 10: 1.4289e-02 2.1069e-01 4.3245e-02 8.2043e-02 2.0842e-01 7.9380e-02 8.9067e-03 3.5661e-02 1.2105e-01 8.0733e-02 1.4192e-01 9.1261e-02 3.6265e-02 1.0609e-01 9.1476e-02 1.8843e-01 6.1534e-02 1.6797e-01 1.7016e-01 1.3743e-01 1.6777e-01 9.2359e-02 9.9516e-02 8.3526e-02 5.7339e-02 1.0129e-01 1.1400e-01 1.1804e-01 1.0129e-01 4.3260e-02 4.9229e-02 6.9002e-02 0.0000e+00 0.0000e+00 1.0000e+00 0.0000e+00 1.1804e-01 6.9002e-02 1.0891e-01 8.5700e-02 guarda P(5,5) e P(9,9) octave:49> diary off