57 lines
1.6 KiB
Matlab
57 lines
1.6 KiB
Matlab
function [N_b, N_s] = block_phase_transition(N, M)
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tau_min = 0;
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tau_max = 10;
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tau_interval = 0.05;
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tau_range = tau_min:tau_interval:tau_max;
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K_min = 1;
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K_max = 15;
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K_range = K_min:K_max;
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N_b = zeros(length(K_range), 1);
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N_s = zeros(length(K_range), 1);
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cache_filename_1 = "I_2.mat";
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cache_filename_2 = "I_" + string(2 * M) + ".mat";
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if exist(cache_filename_1, "file")
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load(cache_filename_1, "I_2");
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else
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I_2 = zeros(length(tau_range), 0);
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for tau_idx = 1:length(tau_range)
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tau = tau_range(tau_idx);
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I_2(tau_idx) = calc_block_integral(tau, 2);
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end
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save(cache_filename_1, "I_2");
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end
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if exist(cache_filename_2, "file")
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load(cache_filename_2, "I_2M");
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else
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I_2M = zeros(length(tau_range), 0);
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parfor tau_idx = 1:length(tau_range)
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tau = tau_range(tau_idx);
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I_2M(tau_idx) = calc_block_integral(tau, 2 * M);
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end
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save(cache_filename_2, "I_2M");
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end
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for K_idx = 1:length(K_range)
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K = K_range(K_idx);
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f_set_1 = zeros(length(tau_range), 1);
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f_set_2 = zeros(length(tau_range), 1);
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for tau_idx = 1:length(tau_range)
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tau = tau_range(tau_idx);
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f_set_1(tau_idx) = 1/2 * (K * (2 * M + tau ^ 2) + (N - K) * I_2M(tau_idx));
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f_set_2(tau_idx) = M/2 * (K * (2 + tau ^ 2) + (N - K) * I_2(tau_idx));
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end
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N_b(K_idx) = min(f_set_1);
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N_s(K_idx) = min(f_set_2);
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end
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end
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