I'm am having trouble writing a derivative function.

I have to assume that a vector vect contains nsamp samples of a function taken at a spacing of dx per sample. Write a function that will calculate the derivative of this vector from the equation f'(x_i)= (f(x_i+1) - f(x_i)) / (x_i+1 - x_i). Also the function should check to make sure that dx is greater than zero to prevent divide-by-zero errors in the function. The function must also be able to have a starting at x = 0.

Here is what I have so far:

function [ der ] = derivative( f, nsamp,x, dx )

%derivative This function solves problem 5.19 in Chapman (2008).
%   x - starting value
%   dx - step size
%   nsamp - number of samples of the function
%   f - function

n = nsamp*dx;
vect = x:dx:n-dx;
L = length(vect);

while dx > 0
   for i = 0:L
       der(i) = (f(i+dx)-f(i))/((i+dx)-(i));
   end
end

end

And when I go to the command window I get:

>> f=@(x)sin(x);

>> derivative(f,100,0,0.05)

Attempted to access der(0); index must be a positive integer or logical.

Error in derivative (line 21)

    der(i) = (f(i+dx)-f(i))/((i+dx)-(i));

I'm having trouble fixing the errors and getting the program to run. Any help will be appreciated.

[Jan]

I've formatted your code as explained here. Please use meaningful tags, because they are used to classify the questions. Then "error" is not useful. Thanks.

Answer 1

[Jan]

At first you have to consider that Matlab's indices are 1-based. So 1 is the minimal index and you'd need: for i = 0:L.

But your function contains much more problems:

• while dx > 0 will produce an infinite loop, because dx does not change its value inside the loop.
• ((i+dx)-(i) is exactly dx.
• vect is not used for the calculations.

I'd restart from scratch:

1. Redefine vect: It should start at x, have nsamp elements, and stop at x + nsamp * dx, correct?
2. Evaluate the function in one step: y = f(vect);
3. Use diff to calculate the difference between the elements of y with a loop. Dividing the result by dx produces the derivative already.
4. The replied NaNs for dx==0 are ok, because this is mathematically consistent. And negative dx are ok also.

So you actually need 2 to 3 lines of code.

[abdur-Rahmaan]

thanks so much , I got it :)

Answer 2

[Youssef Khmou]

Hi, try this :

 function [ der ] = derivative(f,nsamp,dx)

 %derivative This function solves problem 5.19 in Chapman (2008).
 %   x - starting value
 %   dx - step size
 %   nsamp - number of samples of the function
 %   f - function

 n = nsamp*dx;
 vect = 0:dx:n-dx;
 L = length(vect);
 der=zeros(1,L);

    for i = 1:L-1
       der(i) = (f(i+dx)-f(i))/dx;
       %OR : der(i) = (f(i+dx)-f(i))/(vect(i+1)-vect(i));
   end
 der(end)=der(end-1);

[Youssef Khmou]

Compare it with "diff" function , i think this function needs more resolution,

[Jan]

No, this does not work also: You do not want "f(i+dx)", where "i" is the run index of the FOR loop. The derivative should be evaluated at the points x:dx:(x+nsamp*dx).

[Youssef Khmou]

yes, right, i post new answ.

Answer 3

[Youssef Khmou]

Hi, Becca

The first answer has prob, here is a fast way :

 function [ der ] = derivative(f,x,dx)

 %derivative This function solves problem 5.19 in Chapman (2008).
 %   x - starting value, or vector
 %   dx - step size
 %   nsamp - number of samples of the function
 %   f - function

 % Original function
 Y=feval(f,x);
 xp=x+dx;
 YP=feval(f,xp);
 der=(YP-Y)/dx;
 if length(x)>2    
 figure, plot(x,Y,x,der,'r')
 end