[Tutor] Advise...

[Bill Kranec]

There has been alot of talk on this list about using list comprehensions 
lately, and this could be one of those useful places.  While I don't 
have time to experiment with real code, I would suggest changing your 
function to look like:

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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