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animation to show generation of certain random line segments

I am trying to understand these by myself

C,

I want to simulate some straight lines, in Matlab, as follows:

f(t,z)=a(z)t+b(z) where a(z) and b(z) are uniformly distributed random variable in the interval [-1,1] and t is time between [-2,2]. More simply: f(t)= at+b, and z is the random index of the constant (a,b) and let say [-1,+1] is the sample space for z and z is uniformly distributed.

Could anyone help me with the code? Is there any way to show the random generation of the straight line as an animation? Thank you very much for any help.

I am trying like this:

a= rand(-1,1);
b=rand(-1,1);
-2<t<2;
f=a*t+b;
plot(t, f);
But I am getting error Unrecognized function or variable 't'.
Solution

  • Your attempt is not valid MATLAB syntax,

    • -2<t<2 does not do anything, other than produce the error you're seeing because t does not exist

    • f = a*t+b you can't define functions like this, you probably want to use an anonymous function.

    • You can't plot t because you haven't defined it, and you can't plot f because you haven't properly defined that either in terms of a valid t.

    You need to define some discrete values for t. In this case two values is enough, because you're only plotting straight lines anyway. You could use linspace or the colon operator to create a finer spaced array for whatever reason.

    N = 10; % Number of lines to plot
t = [-2,2]; % We want lines between -2 and 2

a = rand(N,1)*2-1; % N random values between -1 and +1
b = rand(N,1)*2-1; % N random values between -1 and +1

f = @(t,z) a(z)*t + b(z); % Define f in terms of axis t and index z

% Plotting
figure; hold on;
for iz = 1:N
    plot( t, f(t,iz) );
end

    This gives an image something like this:

    plot

    If you need an "animation", you could add a pause, e.g. pause(1) inside the loop