Matlab Trapezoid Rule Code

Question

Okay so I'm doing numerical integration using the trapezoid rule. I wrote the m file as such:

function y = trap(f,a,b,N)  
h= (b-a)/N; y=0;  
for i=1: N-1  
    x=(a+i*h);y=y+eval(f);  
end  
y=2*y; x=a; y=y+eval(f); x=b; y=y+eval(f);  
y= (h/2)*y;  

It says that the value assigned to x might be unused and I don't know why. If someone could tell me what I am doing wrong that would be awesome.

Answer 1

You need to pass $x$ into the function $f$ for evaluation; MATLAB is giving you the "X may not be used" warning because $x$ is changing in every loop without ever being passed into $f$

I have made a couple changes to the code (for readability, changing eval to feval...)

function y = trap(f,a,b,N)  
h = (b-a)/(N);
y=0;
for i=1:N-1
    x=(a+i*h);
    y=y+feval(f,x);
end
y = y+feval(f,a)+feval(f,b)
y = h*y;

Answer 2

I'm assuming everything else is OK, just considering performance in Matlab. If (1:N-1) is many values you will be much better off storing the vector than using a for loop.

function y = trap(f,a,b,N)  
h = (b-a)/(N);
y=0;
% Instead of a for loop we make a vector v storing the values (1,2,...N-1):
v = 1:N-1;
x = (a+v*h);
y = sum(feval(f,x));

y = y+feval(f,a)+feval(f,b); 
y = h*y;

Avoiding for-loops can easily give a speed up of 100-1000 times or more. Maybe it doesn't matter right now, but it will start mattering once you build more advanced and useful stuff.

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Edit As mentioned by costrom in the comments : The above assumes that function f can take an array of inputs. If it can not do so, we can still replace the line

y = sum(feval(f,x));

with

y = sum(arrayfun(f,x));

for example the function

f = @(x) x^2;

feval(f,x);

will give error if x is a vector , but the following will work:

arrayfun(f,x);