Talk:Numerical integration

The Trap function in the Java example does not call F(X). Is this an error? --Waldorf 14:21, 21 December 2007 (MST)

Good catch. I'm working on it now. --Mwn3d 14:29, 21 December 2007 (MST)

Parser note (C)

Writing the C code, I've used the var name If (Integrated function, in my mind), and noticed the syntax highlighter highlights If as if! It should be case sensitive! --ShinTakezou 23:38, 16 December 2008 (UTC)

Copying Bad Code

It seems a lot of people copied the Java and Ada entries without actually thinking about the code or testing it. The right rectangle examples were leaving out the final rectangle; this was originally probably a copy/paste error from the left-rectangle, which does want to stop 1 h early. The mid rectangle routines were all just averaging the beginning and endpoint of each rectangle rather than sampling the middle. This is essentially recreating trapezium. In some cases, trapezium is also wrong, because while you count the endpoints only once, each interior function is used twice, and should be multiplied by 2. These particular entries were not doing that. Testing would have found most of these problems. --TimToady 07:51, 11 September 2010 (UTC)

IIRC I copied the C example to make the Java example. I had used the C example for a homework assignment in college on these algorithms. I'd like a little more explanation on these problems. Maybe some pseudocode? You understand my resistance since I probably spent a week or two talking about these integration rules in a class with a reputable professor at my college. It is highly possible that I still didn't code them right, though. --Mwn3d 16:19, 11 September 2010 (UTC)

A correct implementation in C of the mid rect can be seen at [[1]]. The important thing to notice is that the interval (h in most of the rosettacode examples) is divided in half to find the middle point at which to evaluate the function (the i * 0.5 in the middle). If you're not dividing the interval in half, you cannot determine the value of the function at that point. Averaging the beginning and ending function values of the rectangle is the same number only if the function is linear, because doing that (and multiplying by the width) is simply another way of calculating the area of a right trapezoid. For good "pseudo code" that isn't so pseudo, I suggest the Algol 68 example. Notice how it has h/2 in the mid rect to get to the middle of the rectangle. The trapezium is careful to weight the inner points twice as much as the endpoints. (But don't copy the right rect, I think it's wrong to subtract h from the end position, because we already added h to the start position, and that leaves out one of the rectangles.)

--TimToady 03:18, 12 September 2010 (UTC)