Differentiation consistency in matlab

Question

I'm trying to write a program in matlab that checks how consistent the definition of the derivative becomes:

(f(x+h)-f(x))/h ~= f'(x)

when h is small enough. Thus far i have this:

function [errList] = diffConsistency(f,df,x,iMax,h0)
h=h0;
for i=1:iMax
    leftSide = (f(x+h) - f(x)) / h;
    rightSide = df(x);
    errList = abs(leftSide - rightSide);
    h = h*10^(-1);
end

I then use f=@(x)sin(x) and df=@(x)cosx, I'm new to using function handles so this might be wrong completely. iMax is set to 10 and h0 = 1, x=rand(10)

Could anyone check if this is even remotely correct. Especially the use of the function handles inside the diffConsistency function and use of the rand.

Should i define x differently, leftside rightside are correct? etc

Any feedback would help. Thanks in advance

Answer 1

You use some specific data that obscures the result. You input 10x10 random numbers, and output a 10x10 matrix of errors, but this is only for the last i, as you overwrite errList every iteration!

change the function to:

function [errList] = diffConsistency(f,df,x,iMax,h0)
h=h0;
for i=1:iMax
    leftSide = (f(x+h) - f(x)) / h;
    rightSide = df(x);
    errList(i) = abs(leftSide - rightSide);
    h = h*10^(-1);
end

and if you call it as :

err=diffConsistency(@sin,@cos,rand,10,1)

and plot(err), you can clearly see how the error gets reduced each smaller h.