Kirby Urner wrote:
[snip]
def derivative(f):
"""
Factory function: accepts a function, returns a closure
"""
def df(x, h=1e-8):
return (f(x + h) - f(x))/h
return df
Sorry for being picky, but while your derivative factory
function follows the mathematical definiti
> Sorry for being picky, but while your derivative factory
> function follows the mathematical definition, it is not the
> "best" way to do it numerically. The preferred way is:
>
> def derivative(f):
> """
> Factory function: accepts a function, returns a closure
> """
>
Kirby got the trapezoidal integration rule wrong.
This is the corrected version.
def integrate(f,a,b,n=1000):
sum = 0
h = (b-a)/float(n)
for i in range(1,n):
sum += f(a+i*h)
return h*(0.5*f(a)+sum+0.5*f(b))
The interval must be divided into n equal parts, so
an arbitrar
>From Charles O. Hartman, Professor of English and Poet in Residence at
Conneticut College:
http://cherry.conncoll.edu/cohar/COH%20programs%20page.htm
"""
The Scandroid is a program that scans iambic pentameters. You can load
the text file of a poem, or type lines in by hand. As you "Step" thro
> Kirby got the trapezoidal integration rule wrong.
Right, I was just doing a simple average, not any trapezoid. My rectangles
took the mean between f(x-h) and f(x+h), nothing more. Not the best
approximation, I agree, but simple to think about, and some text books show
it.
> This is the correc
> So, the "smart" algorithm should be (untested here left as an
> exercise :-)
>
> sum = ( f(a) + f(b) ) / 2.
> x = a + h
> B = b-h/2 # takes care of round-off error at end point.
>
> .while x <= B:
> .sum += f(x)
> .x += h
> .
> . sum *= h
> . return sum
>
>
> André
Your
> Kirby got the trapezoidal integration rule wrong.
> This is the corrected version.
>
> def integrate(f,a,b,n=1000):
> sum = 0
> h = (b-a)/float(n)
> for i in range(1,n):
>sum += f(a+i*h)
> return h*(0.5*f(a)+sum+0.5*f(b))
>
Here's the same thing using a generator e
> But you never use the trapezoidal rule in real life!
> Simpson gives much smaller error for the same amount
> of computation. In fact, it is exact for Kirby's example!
>
> Henrik
Here's my implementation of Simpson's, except it divides the interval into
2n segments.
>>> def simpson(f,a,b,n):
> Here's my implementation of Simpson's, except it divides the interval into
> 2n segments.
>
> >>> def simpson(f,a,b,n):
>h = float(b-a)/(2*n)
>sum1 = sum(f(a + 2*k *h) for k in range(1,n))
>sum2 = sum(f(a + (2*k-1)*h) for k in range(1,n+1))
>return (h/3)*(f(a)
From: Kirby Urner <[EMAIL PROTECTED]>
> @simpson
> def g(x): return x*x
>
> >>> g(0, 3)
> 9.0036
My resistance to decorators is not unrelated to the fact that I don't seem
capable of getting my mind around them.
I do find it quite disconcerting that the arguments "g" is expecti
> From: Kirby Urner <[EMAIL PROTECTED]>
> > @simpson
> > def g(x): return x*x
> >
> > >>> g(0, 3)
> > 9.0036
>
> My resistance to decorators is not unrelated to the fact that I don't seem
> capable of getting my mind around them.
>
Hi Art --
Actually, I'm with you. The above use i
[EMAIL PROTECTED] wrote:
From: Kirby Urner <[EMAIL PROTECTED]>
@simpson
def g(x): return x*x
g(0, 3)
9.0036
My resistance to decorators is not unrelated to the fact that I don't
> seem capable of getting my mind around them.
>
> I do find it quite disconcerting that the arguments "g"
> And with a decorator:
>
> def simpson(f):
>def defint(a,b,n=1000):
> [...]
>return defint
>
> @simpson
> def g(x): return x*x
>
> >>> g(0, 3)
> 9.0036
No matter how cool decorators are, I don't think this is a good
example of how to use them. The function g(x) is a
Kirby Urner wrote:
From: Kirby Urner <[EMAIL PROTECTED]>
[snip ... Kirby, Art and many others including myself discuss
the possible misuse of decorators in the context of calculating
> derivatives and integrals numerically end snip]
Now, if g(x) really *did* go on for 30-40 lines, OK, then
Kirby Urner wrote:
[snip - deleted stuff about numerical integration]
So my general question is, as usual: wouldn't this be an interesting and
intelligent way to teach math? You get concepts, and you get programming
skills, and you start to think about analyzing and fine tuning algorithms.
Plus y
Kirby Urner wrote:
Again, I think you're probably right, that this particular example is
perverse. Edu-sig is a scratch pad for bad ideas too. :-D
Sorry, Kirby, I see we all seemed to jump on top of you here.
--Scott David Daniels
[EMAIL PROTECTED]
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