Trapezoid Rule discrete data input

function[I]=trap(f,a,b)

if numel(f)>1
    n=numel(f);
    h=(b-a)/(n-1);
    I=(h/2)*(f(1)+2*sum(f(2:end-1))+f(end));
elseif numel(f)==1
    n=100;
    h=(b-a)/(n-1);
    x=a:h:b;
    I=(h/2)*(f(x(1))+2*sum(f(x(2:end-1)))+f(x(end)));
end

This is the code I have so far. I am trying to create a function to approximate an integral based on the trapezoid rule that can take in either an array or an anonymous function. F is the anonymous function or array, and a and b are the bounds of the integral. I am not sure how to index the trapezoid equation (line 6) when the input is an array and I am given values for x and f(x).

[Jan]

You did not clarify what the inputs of the function are. So suggestion a solution for indexing requires to guess your intention.

If you provide f as a vector, what is the meaning of a and b? Are they the x values of the first and last element? What's the problem with the posted code?

Distinguishing vectors and function handles by numel is not stable. Better use isnumeric or isa(f, 'function_handle').

[student]

I fixed my code to be this:

function[I]=trap(f,a,b)

if isnumeric(f)==1
    n=numel(f)-1;
    h=(b-a)/(n-1);
    I=(h/2)*(f(1)+2*sum(f(2:end-1))+f(end));
elseif isnumeric(f)==0
    n=100;
    h=(b-a)/(n-1);
    x=a:h:b;
    I=(h/2)*(f(x(1))+2*sum(f(x(2:end-1)))+f(x(end)));
end

For the arrays I will be integrating, a and b are the x values of the first and last element. I am still confused about how to index. How do I get the x values to correspond with their f(x) values?

[Jan]

@student: I do not understand, what you are confused about. The show code is working already, isn't it? The values of a and b matter only for the determination of h. You do not need to do anything to let "x values correspond to their f(x) values". f(1) is the fist element of the vector and the value of a has no effect for the calculations.

Hint:

if isnumeric(f)
    ...
else
    ...
end

is enough. Alternatively:

if isnumeric(f)
    ...
elseif isa(f, 'function_handle')
    ...
else
    error('1st input must be a vector or function handle.')
end

[Kaashyap Pappu]

The values of ‘a’ and ‘b’ are useful if the intervals are unevenly spaced. Otherwise as mentioned, this should run correctly.