pwd ans = /home/accounts/personale/clrmrc90/aa1415/sistemi_stocastici A=spdiags([1;2;3;4],0,4,4) A = (1,1) 1 (2,2) 2 (3,3) 3 (4,4) 4 A=spdiags([[1;2;3;4],[5;6;7;8],[9;10;11;12]],[-1,0,1],4,4) A = (1,1) 5 (2,1) 1 (1,2) 10 (2,2) 6 (3,2) 2 (2,3) 11 (3,3) 7 (4,3) 3 (3,4) 12 (4,4) 8 full(A) ans = 5 10 0 0 1 6 11 0 0 2 7 12 0 0 3 8 P=rand(4) P = 0.8147 0.6324 0.9575 0.9572 0.9058 0.0975 0.9649 0.4854 0.1270 0.2785 0.1576 0.8003 0.9134 0.5469 0.9706 0.1419 [V,D]=eig(P') V = -0.5308 -0.6543 -0.3872 -0.0825 -0.3371 0.1107 -0.1442 -0.6424 -0.5902 0.6246 -0.3503 -0.0637 -0.5062 0.4117 0.8406 0.7593 D = 2.4021 0 0 0 0 -0.0346 0 0 0 0 -0.7158 0 0 0 0 -0.4400 norm(V(:,1)) ans = 1 P'*V ans = -1.2751 0.0226 0.2772 0.0363 -0.8097 -0.0038 0.1032 0.2826 -1.4178 -0.0216 0.2507 0.0280 -1.2159 -0.0142 -0.6017 -0.3341 V*D ans = -1.2751 0.0226 0.2772 0.0363 -0.8097 -0.0038 0.1032 0.2826 -1.4178 -0.0216 0.2507 0.0280 -1.2159 -0.0142 -0.6017 -0.3341 uiopen('/home/accounts/personale/clrmrc90/aa1415/sistemi_stocastici/randstoc.m', true); P=randstoc(4) P = 0.1749 0.2719 0.2814 0.2718 0.4870 0.0190 0.4030 0.0910 0.2563 0.2748 0.2405 0.2285 0.4140 0.4030 0.1692 0.0137 sum(P,2) ans = 1.0000 1.0000 1.0000 1.0000 [V,D]=eig(P') V = Columns 1 through 2 0.6117 0.6170 0.4614 0.0539 0.5467 -0.7778 0.3378 0.1069 Columns 3 through 4 0.6102 0.6102 -0.1227 + 0.4750i -0.1227 - 0.4750i 0.0200 - 0.3277i 0.0200 + 0.3277i -0.5074 - 0.1473i -0.5074 + 0.1473i D = Columns 1 through 2 1.0000 0 0 -0.0340 0 0 0 0 Columns 3 through 4 0 0 0 0 -0.2590 + 0.1415i 0 0 -0.2590 - 0.1415i v=V(:,1)' v = 0.6117 0.4614 0.5467 0.3378 v=v/sum(v) v = 0.3125 0.2357 0.2793 0.1726 sum(v) ans = 1 v*P ans = 0.3125 0.2357 0.2793 0.1726 v v = 0.3125 0.2357 0.2793 0.1726 uiopen('/home/accounts/personale/clrmrc90/aa1415/sistemi_stocastici/invariantPotenze.m', true); [w,iter,stima]=invariantPotenze(P,1e-6,100) w = 0.3125 0.2357 0.2793 0.1726 iter = 13 stima = 6.9054e-07 P P = 0.1749 0.2719 0.2814 0.2718 0.4870 0.0190 0.4030 0.0910 0.2563 0.2748 0.2405 0.2285 0.4140 0.4030 0.1692 0.0137 A=P'-eye(4) A = -0.8251 0.4870 0.2563 0.4140 0.2719 -0.9810 0.2748 0.4030 0.2814 0.4030 -0.7595 0.1692 0.2718 0.0910 0.2285 -0.9863 A=[A;ones(1,4)] A = -0.8251 0.4870 0.2563 0.4140 0.2719 -0.9810 0.2748 0.4030 0.2814 0.4030 -0.7595 0.1692 0.2718 0.0910 0.2285 -0.9863 1.0000 1.0000 1.0000 1.0000 A\[zeros(4,1);1] ans = 0.3125 0.2357 0.2793 0.1726 B=[P-eye(4),ones(4,1)] B = -0.8251 0.2719 0.2814 0.2718 1.0000 0.4870 -0.9810 0.4030 0.0910 1.0000 0.2563 0.2748 -0.7595 0.2285 1.0000 0.4140 0.4030 0.1692 -0.9863 1.0000 [zeros(1,4),1]/B ans = 0.3125 0.2357 0.2793 0.1726 diary off