Testes

Testes/Práticos/Exercicios.m

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+%% Miniteste Prático 2015/2016
+% Ex2
+% a)
+fprintf("2.a)\n")
+H = [0   0   1/2 0   1/2 1/5;
+     1/4 1/3 1/2 1/2 1/2 1/5;
+     1/4 0   0   0   0   1/5;
+     1/4 1/3 0   0   0   1/5;
+     1/4 0   0   1/2 0   1/5;
+     0   1/3 0   0   0   0];
+
+ x0 = ones(6,1)/6;
+ x3 = H^3*x0;
+ prA = x3(1)
+ prB = x3(2)
+ prC = x3(3)
+ prD = x3(4)
+ prE = x3(5)
+ prF = x3(6)
+
+ % b)
+ fprintf("2.b)\n")
+ x_atual = x0;
+ N = 100;
+ resultado = zeros(length(H),N);
+ for k=1:100
+     x_atual = H*x_atual;
+     resultado(:,k) = x_atual;
+ end
+ figure;
+ stem(1:N,resultado)
+
+ %c)
+ fprintf("2.c)\n")
+ [max_pr, pag_max_pr] = max(x_atual);
+
+%% Miniteste Prático 2018/2019
+% Ex2
+% a)
+fprintf("2.a)\n")
+T = [0.7 0.1 0	 0	 0	 0;
+     0.2 0	 0	 0.3 0	 0;
+     0.1 0.3 0.1 0.4 0	 0;
+     0   0.6 0   0.1 0   0;
+     0   0   0.4 0.2 1   0;
+     0   0   0.5 0   0   1]
+
+ v = [0 1/2 0 1/2 0 0]'
+
+ %b)
+ fprintf("2.b)\n")
+ Q = T(1:4,1:4);
+ I = eye(size(Q));
+ F = inv(I-Q);
+ S = sum(F);
+ media = S(1)
+
+ %c)
+  fprintf("2.c)\n")
+  v0 = [1 0 0 0 0 0]';
+  v5 = T^5*v0;
+  prob_Iraque_EUA = v5(5)
+  v0 = [0 0 1 0 0 0]';
+  v50 = T^50*v0;
+  prob_Brasil_Israel = v50(6)

Testes/Práticos/Miniteste Prático 15 out 2015/Resolucao.m

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+%% Ex2
+% a)
+fprintf("2.a)\n")
+T = [0.84	0.1	0	0.5;
+     0.1	0.7	0	0.1;
+     0.05	0.1	0.8	0.1;
+     0.01   0.1 0.2 0.3];
+
+ TA_i = 1;
+ TB_i = 2;
+ TC_i = 10;
+ TD_i = 5;
+ TT = TA_i + TB_i + TC_i + TD_i;
+
+ x0 = [TA_i/TT TB_i/TT TC_i/TT TD_i/TT]';
+ x7 = T^7*x0;
+
+ TA_f = x7(1)*TT
+ TB_f = x7(2)*TT
+ TC_f = x7(3)*TT
+ TD_f = x7(4)*TT
+
+ TT_f = TB_f + TC_f + TA_f + TD_f; % verificação, tem de dar 18
+
+ % b)
+ fprintf("2.b)\n")
+
+ TA_max = 0;
+ i = 0;
+ while 1
+     xi = T^i*x0;
+     TA_em_i = xi(1)*TT;     
+     if TA_em_i >= TA_max
+         TA_max = TA_em_i;
+     else
+         break;
+     end
+     i = i+1;
+ end
+ TA_max
+
+ TB_max = 0;
+ i = 0;
+ while 1
+     xi = T^i*x0;
+     TB_em_i = xi(2)*TT;     
+     if TB_em_i >= TB_max
+         TB_max = TB_em_i;
+     else
+         break;
+     end
+     i = i+1;
+ end
+ TB_max
+
+ TC_max = 0;
+ i = 0;
+ while 1
+     xi = T^i*x0;
+     TC_em_i = xi(3)*TT;     
+     if TC_em_i >= TC_max
+         TC_max = TC_em_i;
+     else
+         break;
+     end
+     i = i+1;
+ end
+ TC_max
+
+ TD_max = 0;
+ i = 0;
+ while 1
+     xi = T^i*x0;
+     TD_em_i = xi(4)*TT;     
+     if TD_em_i >= TD_max
+         TD_max = TD_em_i;
+     else
+         break;
+     end
+     i = i+1;
+ end
+ TD_max
+
+ % c)
+ fprintf("2.c)\n")
+
+ mes = 1;
+ while 1
+     xi = T^mes*x0;
+     if xi(4)*TT < 2
+         break;
+     end
+     mes = mes+1;
+ end
+ mes
+

Testes/Práticos/Miniteste Prático 18 jan 2017/Resolução matlab.m

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+%% Ex1
+% a)
+fprintf("1.a)\n")
+T = [0.9 0.5 0.5; 0.09 0.4 0.4; 0.01 0.1 0.1]
+v = [0 0 1]'
+
+% b)
+fprintf("1.b)\n")
+v3 = T^3*v;
+prob_0erros = v3(1)
+prob_1erro = v3(2)
+prob_2ouMaisErros = v3(3)
+fprintf("Pacote recebido sem erros: %d\n", v3(1));
+fprintf("Pacote recebido com 1 erro: %d\n", v3(2));
+fprintf("Pacote recebido com 2 ou mais erros: %d\n", v3(3));
+
+%% Ex2
+%a)
+fprintf("2.a)\n")
+H = [0 1/2 1/3 1/4 0; 1/2 0 0 1/4 1/2; 1/2 1/2 1/3 1/4 0; 0 0 0 0 1/2; 0 0 1/3 1/4 0];
+B = 0.8;
+N = 5;
+%M(1:N,1:N) = 1/N;
+%A = B*H + (1-B)*M
+A = B*H + (1-B)*ones(N)/N
+
+% b)
+fprintf("2.b)\n")
+x0 = ones(N,1)/N;
+x10 = H^10*x0
+prC = x10(1)
+prD = x10(2)
+prE = x10(3)
+prF = x10(4)
+prG = x10(5)
+
+%% Ex3
+% a)
+fprintf("3.a)\n")
+T = [0.7 0.2 0 0 0 0; 0.2 0 0.3 0 0 0; 0 0.6 0.3 0 0 0; 0.1 0.2 0.3 0.1 0 0; 0 0 0.1 0.5 1 0; 0 0 0 0.4 0 1]
+
+%b)
+fprintf("3.b)\n")
+x0 = [1 0 0 0 0 0]';
+x9 = T^9*x0;
+prob_10serc = x9(3)
+x14 = T^14*x0;
+prob_15serd = x14(4)
+
+% c)
+fprintf("3.c)\n")
+Q = T(1:4,1:4);
+I = eye(size(Q));
+F = inv(I-Q);
+S = sum(F);
+media = S(3)
+
+%% Exemplo
+N = 20;
+[U,L] = surfer('http://www.ua.pt',N);
+
+imagesc(L);
+colormap(gray);
+
+H=full(L);
+c=sum(full(L)); % número de ligações(d)
+H=H./repmat(c,N,1)
+p=0.85
+A=p*H+(1-p)* ones(N)/N % matriz da Google
+A(isnan(A))=1/N % resolver dead ends
+
+x0=ones(N,1)/N;
+iter=1;
+x=x0;
+epsilon=1e-3;
+while 1
+    fprintf(1,'iteração %d\n',iter);
+    xold=x
+    x=A*x;
+    if max(abs(x-xold))<epsilon break ; end
+    iter=iter+1;
+end
+x
+
+[xs idx]=sort(x,'descend');
+for p=1:N
+    fprintf(1,'PageRank=%.3f: %s\n',x(idx(p)), U{idx(p)});
+end
+