How to make a graph of a three-branches function in matlab

Question

How can I make this function\'s graph in Matlab, so that its body is depicted in the same graph (plot or subplot)?

    t0=0.15 
    x(t)= 1, if 0<=t<(         


        

Answer 1

The real question you should be asking is "How to define a function that has branches?", since plotting is easy once the function is defined.

1. Here's a way using anonymous functions:

   x_t = @(t,t0)1*(0<=t & t<t0/2)-2*(t0/2<=t & t<=(3/2)*t0); %// the 1* is redundant, I only
                                                             %// left it there for clarity
   

   Note that the & operator expects arrays and not scalars.

2. Here's a way using heaviside (aka step) functions (not exactly what you wanted, due to its behavior on the transition point, but worth mentioning):

   x_t = @(t,t0)1*heaviside(t)+(-1-2)*heaviside(t-t0/2)+2*heaviside(t-t0*3/2);
   

   Note that in this case, you need to "negate" the previous heaviside once you leave its area of validity.

After defining this function, simply evaluate and plot.

t0 = 0.15;
tt = -0.1:0.01:0.5;
xx = x_t(tt,t0);
plot(tt,xx); %// Or scatter(), or any other plotting function

BTW, t0 does not have to be an input to x_t - if it is defined before x_t, the value of t0 that exists in the workspace at that time will be captured and used, but this also means that if t0 changes later, this will not affect x_t.

Answer 2

I'm not sure of what you want, but would it be it?

clc
close all
clear

t0 = 0.15;

t = 0:0.01:0.15;

x = zeros(size(t));

x(0 <= t & t < (t0/2)) = 1;
x((t0/2) <= t & t <= (3/2)*t0) = -2;

figure, plot(t, x, 'rd')

which gives,

Everything depends on the final t, for example if the end t is 0.3, then you'll get,