I am trying to plot a simple equation in MATLAB.
The equation is
z = x^2 - y^2, for -3 <= x <= 3, -3 <= y <= 3.
The current code that I have is
x = -3:3;
y = -3:3;
z = (x.^2) - (y.^2);
plot(z)
The result is
Please help me in this case because I am not sure if the code and graph is correct. Thank you very much.
CodePudding user response:
There is a lot going wrong here: Let's start at the beginning:
x = -3:3;
y = -3:3;
If we evaluate these they both will return an vector of integers:
x =
-3 -2 -1 0 1 2 3
This means that the grid on which the function is evaluated is going to be very coarse. To alleviate this you can define a step size, e.g. x = 3:0.1:3
or use linspace
, in which case you set the number of samples, so e.g. x = linspace(-3, 3, 500)
. Now consider the next line:
z = (x.^2) - (y.^2);
If we evaluate this we get
z =
0 0 0 0 0 0 0
and you plot this vector with the 2d-plotting function
plot(z)
which perfectly explains why you get a straight line. This is because the automatic broadcasting of the arithmetic operators like minuse (-
) just subtracts values entry-wise. You however want to evaluate z
for each possible pair of values of x
and y
. To do this and to get a nice plot later you should use meshgrid
, and use a plotting function like mesh
to plot it. So I'd recommend using
[X,Y] = meshgrid(x,y);
to create the grid and then evaluate the function on the grid as follows
Z = X.^2 - Y.^2;
and finally plot your function with
mesh(X,Y,Z);
CodePudding user response:
This is not a piecewise function. A Piecewise Function is a function defined by multiple sub-functions, where each sub-function applies to a different interval in the domain. There is only one function here that takes two arrays of the same length. The calculations yield a vector of zeros, due to the input arrays. If you change either one of the vectors, that is "x" or "y", you will see a nonzero plot. Your code works as expected.