伪随机数的随机性基本检测方法的matlab程序

以下是常用的伪随机数的随机性基本检测方法的 Matlab 程序：

1. 频数检测

function [p_value] = frequency_test(numbers)
    n = length(numbers);
    count = sum(numbers);
    p_value = 2*min(count, n-count)/n;
end

2. 块频数检测

function [p_value] = block_frequency_test(numbers, block_size)
    n = length(numbers);
    num_blocks = floor(n/block_size);
    counts = zeros(num_blocks, 1);
    for i = 1:num_blocks
        block = numbers((i-1)*block_size+1:i*block_size);
        counts(i) = sum(block);
    end
    chi2 = ((counts - block_size/2).^2) / (block_size/2);
    p_value = 1 - gammainc(num_blocks/2, chi2/2);
end

3. 游程总数检测

function [p_value] = runs_test(numbers)
    n = length(numbers);
    runs = 1;
    for i = 2:n
        if numbers(i) ~= numbers(i-1)
            runs = runs + 1;
        end
    end
    pi = runs / n;
    tau = 2 / sqrt(n);
    if abs(pi - 0.5) >= tau
        p_value = 0;
    else
        vobs = 1;
        for i = 2:n
            if numbers(i) ~= numbers(i-1)
                vobs = vobs + 1;
            else
                break;
            end
        end
        for i = n:-1:2
            if numbers(i) ~= numbers(i-1)
                vobs = vobs + 1;
            else
                break;
            end
        end
        mu = (2*n - 1) / 3;
        sigma2 = (16*n - 29) / 90;
        sigma = sqrt(sigma2);
        z = (vobs - mu) / sigma;
        p_value = erfc(abs(z) / sqrt(2));
    end
end

4. 累加和检测

function [p_value] = cumulative_sums_test(numbers)
    n = length(numbers);
    s = cumsum(2*numbers-1);
    a = max(abs(s));
    p_value = erfc(a/sqrt(n)/sqrt(2));
end

5. 近似熵检测

function [p_value] = approximate_entropy_test(numbers, m)
    n = length(numbers);
    c = zeros(n-m+1, 1);
    for i = 1:n-m+1
        block = numbers(i:i+m-1);
        count = 0;
        for j = 1:n-m+1
            if i ~= j
                if isequal(numbers(j:j+m-1), block)
                    count = count + 1;
                end
            end
        end
        c(i) = count / (n-m);
    end
    phi_m = mean(log(c));
    c = zeros(n-m-1, 1);
    for i = 1:n-m-1
        block = numbers(i:i+m);
        count = 0;
        for j = 1:n-m-1
            if i ~= j
                if isequal(numbers(j:j+m), block)
                    count = count + 1;
                end
            end
        end
        c(i) = count / (n-m-1);
    end
    phi_m_plus_1 = mean(log(c));
    p_value = gammainc((n-m)*phi_m - (n-m-1)*phi_m_plus_1, m/2);
end

这些程序可以用于对伪随机数序列进行基本的随机性检测，以评估伪随机数生成器的随机性。请注意，不同的检测方法适用于不同的随机性问题，因此需要根据具体情况选择适当的检测方法。