Help with specific fplot

I have no problem using fplot with any other function I have created except for one. I am trying to graph f(x)=x^2-sin(x)+1/x over -pi<x<pi and cannot get the proper graph to save my life. Here is my code:

EDU>> f=@(x)x.^2-sin(x)+1./x;

EDU>> fplot(f,[-pi,pi]);

The resulting incorrect graph is a horizontal line y=0 with a spike towards y=inf as you approach x=0.

Any help would be appreciated, pulling my hair out over this one haha.

Answer 1

[Star Strider]

The plot is correct. You’re plotting it from [-pi,pi]. That includes zero, and the 1/x term approaches +Inf as x approaches zero.

[Andrew]

The plot is not correct though. When I plot using plot(x,y) it is the correct graph. If you look at the function, f(x) should be going to inf from the right of 0 and -inf from the left, which is not what I am getting with fplot, hence the hairpulling haha. How do you post graphs on this forum? I will post the correct and incorrect graph.

[Star Strider]

That is an artefact of the way fplot divides the interval. You can get the x-data from fplot:

xd = fplot(f, [-pi,pi]);

that shows (as part of an 89-element vector):

     -50.2655e-003
     -37.6991e-003
     -25.1327e-003
     -12.5664e-003
       2.1406e-015
      12.5664e-003
      25.1327e-003
      50.2655e-003

so it’s evaluating the 1/x term here at 2.1406e-015, producing only a positive deflection as the values approach zero. Using linspace to define x with the default 100 values, then using plot to plot it produces the expected result. So fplot is not actually wrong, but simply imprecise.

[Walter Roberson]

The plot is correct to the scaling. Look at

fplot(f,[-pi,-10/1000])

and you will see that the drop to -inf is quite narrow; as you try with -9/1000 and -8/1000 and so on you can see that with that small change in range the plot gets much sharper. If fplot does not happen to try a value in the range about between -1/100 and 0 then it is not going to have much of downstroke to counter the massive upstroke at exactly 0.

Compare:

fplot(f,[-pi-1/100,pi-1/100])

which slightly changes the sampling positions, reducing the huge spike.

[Andrew]

Awesome. Thanks guys.

[Star Strider]

Our pleasure!