% Scripts for MAT 331, Nov 16, 2017
% Random Walks

% plot a n-step random walk on the integers as a 
% function of time

function rw(n)
    x=2*randi(2,n,1)-3
    y=cumsum(x)
    figure;
    grid on;
    hold on;
    title(['Simple random walk, steps = ',num2str(n)]);
    plot(y)
return 

%--------------------------------------------

% plot multiple  n-step random walk on the integers as a
% function of time

function rw_mult(n,N)
    clear endpt;
    figure;
    grid on;
    hold on;
    title(['Simple random walk, steps = ',num2str(n)]);
    for k=1:N
       clear y;
       x=2*randi(2,n,1)-3;
       y=cumsum(x);
       endpt(k)=y(end);
       %plot(y)
    end
    figure;
    hold on;
    grid on;
    title('Histogram of final point');
    a=min(endpt);
    b=max(endpt);
    delta=2*ceil((b-a)/100);
    edges=[a-.5:delta:b+.5]
    histogram(endpt,edges);
return

%----------------------------------------------

% plot a n-step random walk  in the plane as a
% function of time

function rw_2d(n)
    flag=3;
    % there are  many ways to make a random walk 
    % in the plane; here are three possibilities
    switch flag
    case 1
       % choose each coordinate to be a random walk
       x1=2*randi(2,n,1)-3;
       y1=cumsum(x1);
       x2=2*randi(2,n,1)-3;
       y2=cumsum(x2);
    % choose one of four dirctions to move 
    case 2
       x=randi(4,n,1);
       y=cumsum(1i.^x);
       y1=real(y);
       y2=imag(y);
    case 3
       %  choose a random direction to move in
       x=exp(2*pi*1i*rand(n,1));
       y=cumsum(x);
       y1=real(y);
       y2=imag(y);
    end % switch flag

    figure;
    grid on;
    hold on;
    title(['Simple random walk, steps = ',num2str(n)]);
    plot(y1,y2)

    return
    % compute distance from origin
    clear d;
    for k=1:n
       d(k)=sqrt(y1(k)^2+y2(k)^2);
    end % for
    figure;
    grid on;
    hold on;
    title(['Distance from origin in 2D, steps = ',num2str(n)]);
    plot(d)

return

%---------------------------------------------
% plot a n-step random walk  in the plane as a
% function of time

function rw_3d(n)
    flag=2;
    % there are  many ways to make a random walk 
    % in the plane; here are three possibilities
    switch flag
    case 1
       % choose each coordinate to be a random walk
       x1=2*randi(2,n,1)-3;
       y1=cumsum(x1);
       x2=2*randi(2,n,1)-3;
       y2=cumsum(x2);
       x3=2*randi(2,n,1)-3;
       y3=cumsum(x3);
    % choose one of four dirctions to move 
    case 2
       y1=cumsum(2*rand(n,1)-1);
       y2=cumsum(2*rand(n,1)-1);
       y3=cumsum(2*rand(n,1)-1);
    end % switch flag

    figure;
    grid on;
    hold on;
    title(['Random walk in 3D, steps = ',num2str(n)]);
    plot3(y1,y2,y3)


    return
    % compute distance from origin
    for k=1:n
       d(k)=sqrt(y1(k)^2+y2(k)^2+y3(k)^2);
    end % for
    figure;
    grid on;
    hold on;
    title(['Distance from origin in 3D, steps = ',num2str(n)]);
    plot(d)
return

% ------------------------------------------

% plot a n-step random walk  in the plane as a
% function of time

function rw_3d(n)
    flag=2;
    % there are  many ways to make a random walk 
    % in the plane; here are three possibilities
    switch flag
    case 1
       % choose each coordinate to be a random walk
       x1=2*randi(2,n,1)-3;
       y1=cumsum(x1);
       x2=2*randi(2,n,1)-3;
       y2=cumsum(x2);
       x3=2*randi(2,n,1)-3;
       y3=cumsum(x3);
    % choose one of four dirctions to move 
    case 2
       y1=cumsum(2*rand(n,1)-1);
       y2=cumsum(2*rand(n,1)-1);
       y3=cumsum(2*rand(n,1)-1);
    end % switch flag

    figure;
    grid on;
    hold on;
    title(['Random walk in 3D, steps = ',num2str(n)]);
    plot3(y1,y2,y3)


    return
    % compute distance from origin
    for k=1:n
       d(k)=sqrt(y1(k)^2+y2(k)^2+y3(k)^2);
    end % for
    figure;
    grid on;
    hold on;
    title(['Distance from origin in 3D, steps = ',num2str(n)]);
    plot(d)
return