% 调用示例1
N = 1e6;
seed = 12345;
u_lc = linear_congruential(N, seed);
fprintf('线性同余法：均值=%.4f，方差=%.4f\n', mean(u_lc), var(u_lc));
histogram(u_lc, 20, 'Normalization', 'pdf');
% 调用示例2
seed1 = [123, 456, 789];
seed2 = [321, 654, 987];
u_mrg = mrg32k3a(N, seed1, seed2);
fprintf('MRG32k3a：均值=%.4f，方差=%.4f\n', mean(u_mrg), var(u_mrg));
histogram(u_mrg, 20, 'Normalization', 'pdf');
% 调用示例3
u_mt = rand(1, N);
fprintf('Mersenne Twister：均值=%.4f，方差=%.4f\n', mean(u_mt), var(u_mt));
histogram(u_mt, 20, 'Normalization', 'pdf');
% 调用示例4
seed_fsr = [1, zeros(1,15)]; % 初始种子不可全0
u_fsr = lfsr_fsr(N, seed_fsr);
fprintf('FSR：均值=%.4f，方差=%.4f\n', mean(u_fsr), var(u_fsr));
histogram(u_fsr, 20, 'Normalization', 'pdf');
function u = linear_congruential(n, seed)
m = 2147483647;
a = 16807;
x = seed;
u = zeros(1, n);
for i = 1:n
x = schrage(x, a, m); % 使用Schrage方法避免溢出
u(i) = x / m;
end
end
function x_next = schrage(x, a, m)
q = floor(m / a);
r = mod(m, a);
k = floor(x / q);
x_next = a * (x - k * q) - k * r;
if x_next < 0
x_next = x_next + m;
end
end
function u = mrg32k3a(n, seed1, seed2)
m1 = 4294967087; m2 = 4294944443;
a12 = 1403580; a13 = -810728;
a21 = 527612; a23 = -1370589;
x1 = seed1; x2 = seed2;
u = zeros(1, n);
for i = 1:n
new_x1 = mod(a12 * x1(2) + a13 * x1(1), m1);
x1 = [x1(2), x1(3), new_x1];
new_x2 = mod(a21 * x2(1) + a23 * x2(3), m2);
x2 = [x2(2), x2(3), new_x2];
u(i) = mod(new_x1/m1 - new_x2/m2, 1);
end
end
function u = lfsr_fsr(n, seed)
register = seed(:)';
bits = zeros(1, n*16);
for i = 1:n*16
feedback = xor(xor(xor(register(16), register(12)), register(3)), register(1));
bits(i) = register(16);
register = [feedback, register(1:15)];
end
u = sum(reshape(bits, 16, n)' .* 2.^(15:-1:0), 2) / 65536;
end
请解释以上代码的作用并对输出的结果进行分析
这段代码实现了一个卢卡斯-莱默检验法的MATLAB程序，用于检查2的n次方减1是否为素数。通过迭代计算模运算，当s等于0时输出n值。
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