Five commonly used random number generators-MATLAB implementation

Five commonly used random number generators include the square median generator, the product median generator, the linear congruential generator, the constant multiplier generator, and the Fibonacci generator. You can ask Baidu for the principle, so I won't introduce it here, but only summarize the code implementation.

Square median generator

clc

clear all

close all

% Call function---parameters can be modified

[x0,u0] = Square_mid_rand(156, 2, 20);

% define function

function [xu] = Square_mid_rand(x0, k, maxIter)  

    x = []; % Initialize an empty matrix

    u = [];

    x(1) = x0; % Assignment operation, that is, x0 is placed in the first component of vector x

    u(1) = x(1) / 10^(2*k);

    for i = 2 : maxIter % loop

        x(i) = rem(floor(x(i-1)^2 / 10^k), 10^(2*k)); % Random number iteration generator

        u(i) = x(i) / 10^(2*k);

    end

    % Draw the image

    subplot(1,2,1);  

    hold on; % Maintain the current state.

    plot(u(3:end), '*-'); % The data is from the third component of u to the last component, * marks the key point

    sTitle = sprintf('Square middle random number generator (x0=%d, k=%d)', x0, k); % format the output string

    title(sTitle); 

    hold off;

    subplot(1,2,2); 

    hold on;

    hist(u(3:end));

    title('Random number histogram distribution');

    hold off;

end

Product Center Generator

clc

clear all

close all

% Call function---parameters can be modified

[x0, u0] = multiply_mid_rand(5167, 3729, 2, 20)

% define function       

function [xu] = multiply_mid_rand(x0, x1, k, maxIter)

    x = [];

    u = [];

    x(1) = x0; x(2) = x1;

    u(1) = x(1) / 10^(2*k);

    for i = 3 : maxIter

        x(i) = rem(floor(x(i-1) * x(i-2) / 10^k), 10^(2*k));

        u(i) = x(i) / 10^(2*k);

    end

    hold on;

    subplot(1,2,1);

    plot(u(3:end), '*-');

    sTitle = sprintf('Random number generator for product (x0=%d, x1=%d, k=%d)', x0, x1, k);

    title(sTitle);

    subplot(1,2,2);

    hist(u(3:end));

    title('Random number histogram distribution');

    hold off;

end

3. Linear congruential generator

clc

clear all

close all

% Call function---parameters can be modified

[x0,u0] = linear_mod_random(5, 5, 9, 5, 20)

% define function      

function [x,u] = linear_mod_random(a, c, m, x0, iterMax)

    x = [];

    u = [];

    x(1) = x0;

    u(1) = x(1) / m;

    for i = 2 : iterMax

        x(i) = a * x(i-1) + c;

        x(i) = mod(x(i), m);

        u(i) = x(i) / m;

    end

    hold on;

    subplot(1,2,1);

    plot(x(2:end), '*-');

    sTitle = sprintf('Linear congruential random number generator (a=%d, c=%d, m=%d, x0=%d)', a, c, m, x0);

    title(sTitle);    

    subplot(1,2,2);

    hist(u(2:end));

    title('Random number histogram distribution');

    hold off;

end

4. Constant multiplier generator

clc

clear all

close all

% Call function---parameters can be modified

[x0,u0] = con_mid_rand(6983, 2687, 2, 20);

% define function

function [xu] = con_mid_rand(x0, M, k, maxIter)

    x = [];

    u = [];

    x(1) = x0; 

    u(1) = x(1) / 10^(2*k);

    for i = 2 : maxIter

        x(i) = rem(floor(x(i-1) * M / 10^k), 10^(2*k));

        u(i) = x(i) / 10^(2*k);

    end

    hold on;

    subplot(1,2,1);

    plot(u(2:end), 'r*-');

    Title = sprintf('Constant multiplier random number generator (x0=%d, M=%d, k=%d)', x0, M, k);

    title(Title);

    subplot(1,2,2);

    hist(u(2:end));

    title('Random number histogram distribution');

    hold off;

end

5. Fibonacci Generator

clc

clear all

close all

% Call function---parameters can be modified

[x0,u0] = fib_rand(9, 20);

% define function

function [xu] = fib_rand(m, MaxIter)

    x = []; modX = [];

    u = [];

    x(1) = 1; x(2) = 1; 

    for i = 3 : MaxIter

        x(i) = x(i-1) + x(i-2);

        modX(i) = rem(x(i), m);

        u(i) = modX(i) / m;

    end

    hold on;

    subplot(1,2,1);

    plot(modX(3:end), 'r*-');

    sTitle = sprintf('Fibonacci random number generator (m=%d)',m);

    title(sTitle);

    subplot(1,2,2);

    hist(u(3:end));

    title('Random number histogram distribution');

    hold off;

end

The above are five random number generators simply implemented using MATLAB. In the future, we will add the performance test of the combination generator and the generated random number sequence.