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Talk:Numerical integration: Difference between revisions
→Copying Bad Code: more explanation of rectangles and trapezoids
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--[[User:TimToady|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. --[[User:Mwn3d|Mwn3d]] 16:19, 11 September 2010 (UTC)
::A correct implementation in C of the mid rect can be seen at [[http://en.wikipedia.org/wiki/Rectangle_method]]. 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.)
--[[User:TimToady|TimToady]] 03:18, 12 September 2010 (UTC)
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