How do I plot this piecewise function?

I am trying to plot a piecewsie function. I followed the instructions on the following page:

https://www.mathworks.com/help/symbolic/piecewise.html#bu_sl0c-5

However, I keep getting this error message:

Error using fplot

Input must be a function handle or symbolic function.

Error in piecwise (line 9)

fplot(x)

This is my code:

clear all;

clc;

grid on;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

syms t

x = piecwise(t <= -2, 0, -2 <= t <= 0, ((2 + t) / 2)^2, 0 <= t <= 2, 1, 2 <= t <= 4, ((4 - t) / 2)^2, t >= 4);

fplot(x)

This is the piecewise function I am trying to plot:

Any help is greatly appreciate!

Answer 1

[Sam Chak]

Hi @Zac

Because you mispelled 'piecwise'?

Anyhow, you can try using one of these methods:

t = -3:1e-3:5;

%% Method 1
x = @(t) 0*(t<-2) + (((2 + t)/2).^2).*((-2 <= t) & (t < 0)) + 1*((0 <= t) & (t < 2)) + (((4 - t)/2).^2).*((2 <= t) & (t < 4)) + 0*(4 <= t);
subplot(3,1,1)
plot(t, x(t), 'linewidth', 1.5, 'Color', [0.8500, 0.3250, 0.0980])
ylim([-0.5 1.5]), grid on, xlabel('t'), ylabel('x(t)'), title('Method 1')

%% Method 2
x1 = 0*(t<-2);                                  % segment 1
x2 = (((2 + t)/2).^2).*((-2 <= t) & (t < 0));   % segment 2
x3 = 1*((0 <= t) & (t < 2));                    % segment 3
x4 = (((4 - t)/2).^2).*((2 <= t) & (t < 4));    % segment 4
x5 = 0*(4 <= t);                                % segment 5
x  = x1 + x2 + x3 + x4 + x5;                    % combine all segments
subplot(3,1,2)
plot(t, x, 'linewidth', 1.5, 'Color', [0.9290, 0.6940, 0.1250])
ylim([-0.5 1.5]), grid on, xlabel('t'), ylabel('x(t)'), title('Method 2')

%% Method 3
syms t
x = piecewise(t<-2,0, -2<t<0,((2 + t)/2)^2, 0<t<2,1, 2<t<4,((4 - t) / 2)^2, 4<t,0);
subplot(3,1,3)
fplot(x, [-3 5], 'linewidth', 1.5, 'Color', [0.4660, 0.6740, 0.1880])
ylim([-0.5 1.5]), grid on, xlabel('t'), ylabel('x(t)'), title('Method 3')

[Zac]

Thank you so much for taking the time to put together such a thorough answer!

Method 3 did exactly what I needed it to.

I appreciate you.

[dongshan xie]

The second method is pretty cool!

[Sam Chak]

You're welcome, @Zac. Hope others like @dongshan xie would benefit from the methods shared here.

Answer 2

[dongshan xie]

First, I think it's "piecewise" instead of "piecwise"

Second, you should write "fplot(t,x)".

So, the code should be

syms t
x = piecewise(t <= -2, 0, -2 <= t <= 0, ((2 + t) / 2)^2, 0 <= t <= 2, 1, 2 <= t <= 4, ((4 - t) / 2)^2, t >= 4);
fplot(t,x)

[Carter Sorensen]

Good catch with the fplot(). I completely missed that...

[dongshan xie]

Thank you!

Answer 3

[Carter Sorensen]

Hello,

Couldn't quite get fplot() to work with the piecewise() function. One workaround I found is to store the values you want to test in a matrix. Afterwards, pass each value in the matrix to the piecewise() function. From here, plot the outputs against the inputs using the plot() command. The described process may not be the most efficient, but it should work.

Sample code (inputs and outputs) has been included. Are you required to use fplot()?

Let me know if anything is unclear. Thanks!

clear all;
clc;
grid on;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
num = [-10:1:10]; % Sample numbers in matrix
syms x(t)
x(t) = piecewise(t <= -2, 0, -2 <= t <= 0, ((2 + t) / 2)^2, 0 <= t <= 2, 1, 2 <= t <= 4, ((4 - t) / 2)^2, t >= 4); % Your piecewise functions
results = x(num); % Plug numbers in matrix 'num' into x(t)

grid on
plot(num, results, 'linewidth', 3) % Plot all num values against corresponding x(t) values
xlabel('num')
ylabel('x(t)')