Problem graphing the % error between a real function and its linearization using contourf in MATLAB

I am trying to visualize the percentage error between a real function and its linearized version in a contour map (contourf). I have defined my reference variables and calculated the relative error as:

Where:

• g = X./Y is the real function.
• z is the linearized function
• Xref = 5, Yref = 4 are the references.

The code I am using is the following:

Xref = 5;
Yref = 4;
[X,Y] = meshgrid(linspace(0,10,50),linspace(3,5,50));
g = X./Y;
z = Xref/Yref+1/Yref*(X-Xref)-Xref/Yref.^2*(Y-Yref);
surf(X,Y,g,"FaceColor","#EDB120","LineStyle","none")
hold on
surf(X,Y,z,"FaceColor","#0072BD","LineStyle","none")
xlim([0 10])
ylim([3 5])
zlim([-0.5 3.5])
box on
legend("g=X/Y","Linearized")
xlabel("X(t)")
ylabel("Y(t)")
zlabel("g=X/Y")
hold off

% Error Graph (%)
Error3 = abs(z-g)./g*100;
contourf(X, Y, Error3)
xlabel("X(t)")
ylabel("Y(t)")

The result I should get would look like this:

I think the problem is the way I'm calculating the %Error between those two functions rather than how I'm using the contourf function, but i don't know.

Answer 1

[Stephen23]

"I think the problem is the way I'm calculating the %Error between those two functions..."

That is the problem, because you are dividing by very small values in g, so of course the relative error ends up being quite large. In fact the smallest absolute value in g is zero: how many percent of zero is any finite value of z? (hint: infinite). So in the worst case, those "relative error" values blow up to infinity:

Xref = 5;
Yref = 4;
[X,Y] = meshgrid(linspace(0,10,50),linspace(3,5,50));
g = X./Y;
z = Xref/Yref+1/Yref*(X-Xref)-Xref/Yref.^2*(Y-Yref);

mnz = min(abs(z(:)))

mnz = 0.0064

mng = min(abs(g(:)))

mng = 0

mnz./mng

ans = Inf

This is not a MATLAB problem, this is a conceptual problem: first answer the question "how many times greater than zero is zero point zero zero six four?" then you can plot your "relative error" calculation.

Plotting the absolute error is much simpler:

E = abs(z-g);
contourf(X,Y,E)

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