Jacob,
Apart from all the other comments you received, here are my thoughts.
I think you could do one more thing to speed up your calculations and
that is to use a more efficient method. The Reimann sum is not a very
efficient.
One simple method that is rahter popular is Simpson's rule.
The calculations are not much more complicated than what you already
have
![equation347]()
You then you just need to make sure that the number of intervals are
even.
Johan
Jacob S. wrote:
Hi all.
Long time no see. (About five days, right?)
Anyway, I know the first thing that some of you are going to say is
using eval(). I don't want a whole
guilt trip on security risks and all that. I do not want to share the
code with anyone else while it's on my
computer, and I sure don't have anyone near me that knows python. I
would be surprised if more than 50
people in Portland, IN knew anything about python. So security is not a
problem. I guess what I'm
looking for is someone who knows the Reimann Sum better than I do and
can tell me whether I can do
something to make it more efficient. It's horribly slow with ten
thousand steps-- I don't know the notation
very well, but it loops the loop O(step*(maximum-minimum)) times, which
is horribly sucky.
In case anyone doesn't know, Reimann's sum is the computer's version
of the definite integral, the area
under a curve in a particular domain.
Basic input and output.
If a curve is a straight line, say y = x, the area under the line on an
interval can be found by geometric means.
However, if you use a parabola, or any other function, say y = 3*x**2,
What is the function? 3*x*x
What is the minimum? 2
What is the maximum? 5
117.000435
Which, considering that it is supposed to be exactly 117, It's darn
good. Unfortunately, it also takes about
10 seconds to do all that.
Any suggestions? Any advice? TIA
Jacob Schmidt
############################
from __future__ import division
import psyco
psyco.full()
fofx = raw_input("What is the function? ")
minimum = raw_input("What is the minimum? ")
maximum = raw_input("What is the maximum? ")
minimum = float(minimum)
maximum = float(maximum)
total = 0
step = 100000
x = minimum
while minimum <= x <= maximum:
area = eval(fofx)*1/step
total = total+area
x = x+1/step
print total
#############################
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