3dMATLABwolfram alpha
I'm trying to plot the function $z = 6x^2 – 4x^2y^2$ in Matlab. The code I'm using for this in matlab is the one below, also the plot is shown:
v = [-2:0.1:2];
w = [-2:0.1:2];
[X,Y] = meshgrid(v,w);
Z = 6*X.^2-4*X.^2*Y.^2;
figure(3);
surf(X,Y,Z)
Now I when I plot this same function in Wolram Alpha I'm getting something different and I can't figure it out why. Here is the plot on Wolfram: Wolfram
Thanks!
You have truncated the series at $n=20$. The error term, for either function, is roughly $\dfrac{|x|^{21}}{ 21!}$. This error is very small when $x$ is small, and is of moderate size when $|x|\approx n/e$, but grows rapidly beyond that. When $x=20$, the size of the error is measured in millions.
So: either narrow down the range of $x$, or use more terms: for $|x|\le 100$, try $100e$ terms.
First of all, you need to define x0 before you use it. Then you are just plotting a single point each time which is visible but only one pixel. I recommend using
plot(h,err,'o-');
loglog(h,err,'o-');
This shows you where the points are. As @mathreadler pointed out, if you want to see all points of each iteration, you have to plug the plot commands into the loop and use hold, or you save the results for each $i$ in a vector:
f=@(x)cos(x)
x0=pi/4;
f_exact=-sin(x0)
for i=1:21;
h(i)=10^(1-i);
f_approx=(f(x0+h(i))-f(x0-h(i)))./(2*h(i));
err(i)=abs(f_approx-f_exact);
d_error(i)=abs(((h(i)^2)*sin(x0))./6);
end
plot(h,err,'o-');
figure; %opens a new plot window
loglog(h,err,'o-');
The loglog plot loooks decent enough, The problem you are running into (I think) is a loss of accuracy due to cancellation (i.e. when you substract two numbers that are very close).
Best Answer
When you have some problems with 3D plots in Matlab, it is often helpful to use different grids for $x$ and $y$. For example, if you change your code as
v = [-2:0.1:3];, you will have a helpful error message:Error using *. Incorrect dimensions for matrix multiplication.It means that you have matrix multiplication in your equation and not the element-wise. TryZ = 6*X.^2-4*X.^2.*Y.^2.