octave:2> P=magic(4) P = 16 2 3 13 5 11 10 8 9 7 6 12 4 14 15 1 octave:3> sum(P) ans = 34 34 34 34 octave:4> P=magic(4)/34 P = 0.470588 0.058824 0.088235 0.382353 0.147059 0.323529 0.294118 0.235294 0.264706 0.205882 0.176471 0.352941 0.117647 0.411765 0.441176 0.029412 octave:5> sum(P) ans = 1 1 1 1 octave:6> sum(P,2) ans = 1 1 1 1 octave:7> P=1/4*ones(4) P = 0.25000 0.25000 0.25000 0.25000 0.25000 0.25000 0.25000 0.25000 0.25000 0.25000 0.25000 0.25000 0.25000 0.25000 0.25000 0.25000 octave:8> Q=randstocsym(4) Q = 0.284091 0.269571 0.305171 0.141167 0.269571 0.119722 0.406219 0.204488 0.305171 0.406219 0.274851 0.013760 0.141167 0.204488 0.013760 0.640585 octave:9> sum(Q) ans = 1.0000 1.0000 1.0000 1.0000 octave:10> v=rand(1,4);,v=v/sum(v); octave:11> v v = 0.031852 0.376775 0.389735 0.201638 octave:12> V=repmat(v,4,1) V = 0.031852 0.376775 0.389735 0.201638 0.031852 0.376775 0.389735 0.201638 0.031852 0.376775 0.389735 0.201638 0.031852 0.376775 0.389735 0.201638 octave:13> W=V' W = 0.031852 0.031852 0.031852 0.031852 0.376775 0.376775 0.376775 0.376775 0.389735 0.389735 0.389735 0.389735 0.201638 0.201638 0.201638 0.201638 octave:14> repmat(v',1,4) ans = 0.031852 0.031852 0.031852 0.031852 0.376775 0.376775 0.376775 0.376775 0.389735 0.389735 0.389735 0.389735 0.201638 0.201638 0.201638 0.201638 octave:15> V>=W ans = 1 1 1 1 0 1 1 0 0 0 1 0 0 1 1 1 octave:16> v v = 0.031852 0.376775 0.389735 0.201638 octave:17> P=zeros(4) P = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 octave:18> P(V>=W) ans = 0 0 0 0 0 0 0 0 0 0 octave:19> P=reshape(1:16,4,4) P = 1 5 9 13 2 6 10 14 3 7 11 15 4 8 12 16 octave:20> V>=W ans = 1 1 1 1 0 1 1 0 0 0 1 0 0 1 1 1 octave:21> P(V>=W) ans = 1 5 6 8 9 10 11 12 13 16 octave:22> P(V>=W)=-1 P = -1 -1 -1 -1 2 -1 -1 14 3 7 -1 15 4 -1 -1 -1 octave:23> P=reshape(1:16,4,4) P = 1 5 9 13 2 6 10 14 3 7 11 15 4 8 12 16 octave:24> Q=-P Q = -1 -5 -9 -13 -2 -6 -10 -14 -3 -7 -11 -15 -4 -8 -12 -16 octave:25> P(V>=W)=Q(V>=W) P = -1 -5 -9 -13 2 -6 -10 14 3 7 -11 15 4 -8 -12 -16 octave:26> v=rand(1,4) v = 0.759610 0.145470 0.091835 0.833979 octave:27> P=metropolis(v) P = 0.4922197 0.0216263 0.0298737 0.4562803 0.1129273 0.6577587 0.2057563 0.0235577 0.2470987 0.3259256 0.1486770 0.2782987 0.4155924 0.0041092 0.0306454 0.5496530 octave:28> sum(P,2) ans = 1 1 1 1 octave:29> invariantPotenze(P,1e-6,100) ans = 0.414884 0.079454 0.050159 0.455503 octave:30> v/sum(v) ans = 0.414885 0.079453 0.050159 0.455503 octave:31> P=metropolis(v) P = 0.5949091 0.0224144 0.0202090 0.3624675 0.1170424 0.4694772 0.3665408 0.0469397 0.1671573 0.5806142 0.0489036 0.2033249 0.3301452 0.0081877 0.0223895 0.6392776 octave:32> invariantPotenze(P,1e-6,100) ans = 0.414884 0.079454 0.050159 0.455503 octave:33> H=[-1,1] H = -1 1 octave:34> epsilon=1e-3 epsilon = 0.0010000 octave:35> v=exp(-H/epsilon) v = Inf 0 octave:36> v=v/sum(v) v = NaN 0 octave:37> realmax ans = 1.7977e+308 octave:38> realmin ans = 2.2251e-308 octave:39> realmin/2 ans = 1.1125e-308 octave:40> realmax*2 ans = Inf octave:41> realmax ans = 1.7977e+308 octave:42> v=[3e307,4e307] v = 3.0000e+307 4.0000e+307 octave:43> sqrt(v(1)^2+v(2)^2) ans = Inf octave:44> norm(v) ans = 5.0000e+307 octave:45> octave:45> octave:45> octave:45> octave:45> 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:45> v = 1./sum(exp(-(repmat(H',1,2)-repmat(H,2,1))/epsilon)) v = 1 0 octave:46> epsilon=1e-1 epsilon = 0.10000 octave:47> exp(-H/epsilon) ans = 2.2026e+04 4.5400e-05 octave:48> v=exp(-H/epsilon) v = 2.2026e+04 4.5400e-05 octave:49> v=v/sum(v) v = 1.0000e+00 2.0612e-09 octave:50> format long e octave:51> v=v/sum(v) v = 9.99999997938846e-01 2.06115361819020e-09 octave:52> v = 1./sum(exp(-(repmat(H',1,2)-repmat(H,2,1))/epsilon)) v = 9.99999997938846e-01 2.06115361819020e-09 octave:53> H=[-1,0,1] H = -1.00000000000000e+00 0.00000000000000e+00 1.00000000000000e+00 octave:54> epsilon=1 epsilon = 1.00000000000000e+00 octave:55> 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:55> v = 1./sum(exp(-(repmat(H',1,3)-repmat(H,3,1))/epsilon)) v = 6.65240955774822e-01 2.44728471054798e-01 9.00305731703805e-02 octave:56> epsilon=1e-1 epsilon = 1.00000000000000e-01 octave:57> v = 1./sum(exp(-(repmat(H',1,3)-repmat(H,3,1))/epsilon)) v = 9.99954600070331e-01 4.53978686088667e-05 2.06106004620906e-09 octave:58> epsilon=1e-2 epsilon = 1.00000000000000e-02 octave:59> v = 1./sum(exp(-(repmat(H',1,3)-repmat(H,3,1))/epsilon)) v = 1.00000000000000e+00 3.72007597602084e-44 1.38389652673674e-87 octave:60> epsmet ans = Columns 1 through 6: 2.0219e-01 3.4034e-03 3.4880e-02 6.6813e-02 1.8213e-01 1.6508e-01 3.8503e-03 2.1600e-01 1.2666e-01 7.7553e-03 7.1312e-02 8.2581e-02 5.5589e-02 1.7843e-01 1.0325e-01 5.1160e-02 1.2737e-01 5.2845e-02 7.5585e-02 7.7553e-03 3.6316e-02 2.8124e-01 1.0094e-01 9.3843e-02 1.0526e-01 3.6429e-02 4.6189e-02 5.1565e-02 5.8806e-01 5.1741e-02 1.8675e-01 8.2581e-02 3.7512e-02 9.3843e-02 1.0128e-01 1.3667e-01 1.0685e-01 1.3688e-01 7.3181e-02 1.5469e-01 1.6099e-01 2.5610e-02 8.4671e-02 1.0807e-01 3.8926e-02 5.8980e-02 1.2566e-01 1.6284e-01 3.9893e-02 2.9439e-02 2.5506e-02 2.8308e-02 7.0042e-03 5.2357e-03 6.1480e-02 1.8406e-01 1.0920e-01 1.4570e-01 2.0899e-02 1.6258e-01 Columns 7 through 10: 3.1115e-02 7.4844e-02 1.8521e-01 5.4344e-02 4.5095e-02 1.0807e-01 1.5462e-01 1.8406e-01 3.3964e-02 5.4837e-02 1.8872e-01 1.5383e-01 5.0964e-02 5.8980e-02 1.4868e-01 1.4570e-01 2.7094e-02 6.4192e-02 1.8793e-02 1.0676e-02 8.4373e-03 1.6284e-01 2.7499e-02 1.6258e-01 8.3146e-02 1.0062e-01 1.3995e-02 1.4404e-01 3.3148e-02 1.5206e-01 1.3936e-01 9.6294e-02 8.7787e-04 2.6534e-02 8.3465e-01 2.5515e-03 4.7455e-02 9.6294e-02 1.3401e-02 1.5893e-01 guarda P(5,5) e P(9,9) ans = Columns 1 through 6: 2.7954e-01 3.0084e-03 2.1886e-02 5.9058e-02 1.8213e-01 1.4592e-01 3.8503e-03 2.8299e-01 8.9909e-02 7.7553e-03 7.1312e-02 8.2581e-02 5.5589e-02 1.7843e-01 1.2145e-01 5.1160e-02 1.2737e-01 5.2845e-02 7.5585e-02 7.7553e-03 2.5779e-02 3.2595e-01 1.0094e-01 9.3843e-02 6.0830e-02 1.8610e-02 1.6750e-02 2.6342e-02 7.8944e-01 2.6432e-02 1.8675e-01 8.2581e-02 2.6628e-02 9.3843e-02 1.0128e-01 1.5321e-01 1.0685e-01 1.3688e-01 7.3181e-02 1.5469e-01 1.6099e-01 2.5610e-02 8.4671e-02 1.0807e-01 2.7632e-02 5.8980e-02 1.2566e-01 1.6284e-01 8.5928e-03 5.6051e-03 3.4473e-03 5.3897e-03 2.6105e-03 9.9687e-04 6.1480e-02 1.8406e-01 7.7515e-02 1.4570e-01 2.0899e-02 1.6258e-01 Columns 7 through 10: 9.0610e-03 6.6157e-02 1.8521e-01 4.8037e-02 1.4857e-02 1.0807e-01 1.5462e-01 1.8406e-01 1.5763e-02 5.4837e-02 1.8872e-01 1.5383e-01 1.6790e-02 5.8980e-02 1.4868e-01 1.4570e-01 4.5600e-03 3.2792e-02 1.8793e-02 5.4539e-03 2.7797e-03 1.6284e-01 2.7499e-02 1.6258e-01 8.3146e-02 1.0062e-01 1.3995e-02 1.4404e-01 1.0921e-02 1.8558e-01 1.3936e-01 9.6294e-02 5.5066e-05 5.0519e-03 9.6776e-01 4.8579e-04 1.5634e-02 9.6294e-02 1.3401e-02 2.2244e-01 guarda P(5,5) e P(9,9) ans = Columns 1 through 6: 5.9769e-01 3.2652e-04 4.9751e-06 6.4100e-03 1.8213e-01 1.5838e-02 3.8503e-03 3.8757e-01 1.8830e-04 7.7553e-03 7.1312e-02 8.2581e-02 5.5589e-02 1.7843e-01 1.3722e-01 5.1160e-02 1.2737e-01 5.2845e-02 7.5585e-02 7.7553e-03 5.3991e-05 3.6847e-01 1.0094e-01 9.3843e-02 3.1463e-06 1.0447e-07 1.9693e-10 1.4788e-07 9.8120e-01 1.4839e-07 1.8675e-01 8.2581e-02 5.5769e-05 9.3843e-02 1.0128e-01 1.8256e-01 1.0685e-01 1.3688e-01 7.3181e-02 1.5469e-01 1.6099e-01 2.5610e-02 8.4671e-02 1.0807e-01 5.7871e-05 5.8980e-02 1.2566e-01 1.6284e-01 8.5596e-15 6.0601e-16 7.8061e-19 5.8273e-16 5.0276e-11 1.0778e-16 6.1480e-02 1.8406e-01 1.6234e-04 1.4570e-01 2.0899e-02 1.6258e-01 Columns 7 through 10: 2.0557e-12 7.1805e-03 1.8521e-01 5.2138e-03 3.1055e-11 1.0807e-01 1.5462e-01 1.8406e-01 1.5733e-08 5.4837e-02 1.8872e-01 1.5383e-01 3.5096e-11 5.8980e-02 1.4868e-01 1.4570e-01 5.3511e-17 1.8409e-07 1.8793e-02 3.0617e-08 5.8104e-12 1.6284e-01 2.7499e-02 1.6258e-01 8.3146e-02 1.0062e-01 1.3995e-02 1.4404e-01 2.2828e-11 2.2408e-01 1.3936e-01 9.6294e-02 1.2445e-26 5.4620e-16 1.0000e+00 5.2523e-17 3.2680e-11 9.6294e-02 1.3401e-02 3.1542e-01 guarda P(5,5) e P(9,9) ans = Columns 1 through 6: 6.3267e-01 7.4081e-14 1.8329e-42 1.4543e-12 1.8213e-01 3.5932e-12 3.8503e-03 3.8775e-01 3.0577e-31 7.7553e-03 7.1312e-02 8.2581e-02 5.5589e-02 1.7843e-01 1.3722e-01 5.1160e-02 1.2737e-01 5.2845e-02 7.5585e-02 7.7553e-03 8.7671e-32 3.6852e-01 1.0094e-01 9.3843e-02 4.3118e-49 3.2483e-60 9.9426e-90 4.5979e-60 9.8121e-01 4.6136e-60 1.8675e-01 8.2581e-02 9.0558e-32 9.3843e-02 1.0128e-01 1.8262e-01 1.0685e-01 1.3688e-01 7.3181e-02 1.5469e-01 1.6099e-01 2.5610e-02 8.4671e-02 1.0807e-01 9.3971e-32 5.8980e-02 1.2566e-01 1.6284e-01 8.2346e-135 1.3227e-145 2.7666e-175 1.2719e-145 3.5294e-88 2.3524e-146 6.1480e-02 1.8406e-01 2.6361e-31 1.4570e-01 2.0899e-02 1.6258e-01 Columns 7 through 10: 7.4283e-109 1.6291e-12 1.8521e-01 1.1829e-12 4.9460e-98 1.0807e-01 1.5462e-01 1.8406e-01 1.5431e-68 5.4837e-02 1.8872e-01 1.5383e-01 5.5897e-98 5.8980e-02 1.4868e-01 1.4570e-01 2.6498e-156 5.7238e-60 1.8793e-02 9.5195e-61 9.2540e-99 1.6284e-01 2.7499e-02 1.6258e-01 8.3146e-02 1.0062e-01 1.3995e-02 1.4404e-01 3.6357e-98 2.2414e-01 1.3936e-01 9.6294e-02 4.3261e-243 1.1922e-145 1.0000e+00 1.1464e-146 5.2049e-98 9.6294e-02 1.3401e-02 3.1559e-01 guarda P(5,5) e P(9,9) ans = Columns 1 through 6: 5.7892e-02 3.8503e-03 5.5589e-02 7.5585e-02 1.8213e-01 1.8675e-01 3.8503e-03 7.2446e-02 1.7843e-01 7.7553e-03 7.1312e-02 8.2581e-02 5.5589e-02 1.7843e-01 6.4034e-02 5.1160e-02 1.2737e-01 5.2845e-02 7.5585e-02 7.7553e-03 5.1160e-02 1.6267e-01 1.0094e-01 9.3843e-02 1.8213e-01 7.1312e-02 1.2737e-01 1.0094e-01 9.0623e-02 1.0128e-01 1.8675e-01 8.2581e-02 5.2845e-02 9.3843e-02 1.0128e-01 1.0416e-01 1.0685e-01 1.3688e-01 7.3181e-02 1.5469e-01 1.6099e-01 2.5610e-02 8.4671e-02 1.0807e-01 5.4837e-02 5.8980e-02 1.2566e-01 1.6284e-01 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 6.1480e-02 1.8406e-01 1.5383e-01 1.4570e-01 2.0899e-02 1.6258e-01 Columns 7 through 10: 1.0685e-01 8.4671e-02 1.8521e-01 6.1480e-02 1.3688e-01 1.0807e-01 1.5462e-01 1.8406e-01 7.3181e-02 5.4837e-02 1.8872e-01 1.5383e-01 1.5469e-01 5.8980e-02 1.4868e-01 1.4570e-01 1.6099e-01 1.2566e-01 1.8793e-02 2.0899e-02 2.5610e-02 1.6284e-01 2.7499e-02 1.6258e-01 8.3146e-02 1.0062e-01 1.3995e-02 1.4404e-01 1.0062e-01 6.8682e-02 1.3936e-01 9.6294e-02 0.0000e+00 0.0000e+00 1.0000e+00 0.0000e+00 1.4404e-01 9.6294e-02 1.3401e-02 1.7713e-02 guarda P(5,5) e P(9,9) octave:61> quit