steps = [ min_x + i*delta_x for i in range(steps) ] totalarea = sum([ eval(func_x)*delta_x for x in steps ])
Since list comprehensions are significantly faster than while loops, this could be a big speed boost.
There may be a mistake or two in the above code, but hopefully the idea will be helpful.
Bill
TJ wrote:
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
Jacob,
You can get better accuracy with orders of magnitude fewer steps by evaluating the function at the midpoint of each step rather than the low value. This has the added benefit of yielding the same result when stepping x up (2 to 5) or down (5 to 2).
Here's some modified code (I don't have psyco):
######################## from __future__ import division import time def reimannSum(func_x, min_x, max_x, steps): start = time.time() totalArea = 0 #precalculate step size delta_x = 1 / steps #set x to midpoint of first step x = min_x + delta_x / 2 while min_x <= x <= max_x: totalArea += eval(func_x) * delta_x x += delta_x return totalArea, steps, time.time() - start
stepsList = [100000, 10000, 1000, 500, 200, 100] fmt = 'Area: %f Steps: %d Time: %f'
for steps in stepsList: print fmt % reimannSum('3 * x * x', 2, 5, steps) ########################
The results on my machine are:
Area: 117.000000 Steps: 100000 Time: 44.727405 Area: 117.000000 Steps: 10000 Time: 4.472391 Area: 116.999999 Steps: 1000 Time: 0.454841 Area: 116.999997 Steps: 500 Time: 0.223208 Area: 116.999981 Steps: 200 Time: 0.089651 Area: 116.999925 Steps: 100 Time: 0.044431
TJ
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