> derivatives and integrals numerically .... end snip]From: Kirby Urner <[EMAIL PROTECTED]>[snip ... Kirby, Art and many others including myself discuss the possible misuse of decorators in the context of calculating
Now, if g(x) really *did* go on for 30-40 lines, OK, then maybe a decorator adds to readability.
Something to think about.
Kirby
Well, I don't think that decorators would add to readability once you've defined your functions. I've played around with using decorators (and not) for a while, and here's what I would like to submit to this list
as a possible "summary". This non-decorator approach is very clean imho.
def derivative(f): """ Computes the numerical derivative of a function. Intended to be used as a decorator. """ def df(x, h=0.1e-5): return ( f(x+h/2) - f(x-h/2) )/h return df
def simpson_integral(f, a, b, n=1000):
"""
Computes the numerical integral of a function
using the extended Simpson's rule. This gives exact results
for polynomials of O(3).
"""
h = float(b-a)/n
sum1 = sum(f(a+k*h) for k in range(1, n, 2))
sum2 = sum(f(a+k*h) for k in range(2, n, 2))
return (h/3)*( f(a)+f(b) + 4*sum1 + 2*sum2 )# test functions def g2(x): return x*x def g3(x): return x*x*x
# first derivatives dg2 = derivative(g2) dg3 = derivative(g3) # second derivatives d2g2 = derivative(derivative(g2)) d2g3 = derivative(derivative(g3)) # integrals intg2 = simpson_integral(g2, 0, 1) intg3 = simpson_integral(g3, 0, 1)
print ' functions: ', g2(2.), g3(2.) print ' first derivatives: ', dg2(2.), dg3(2.) print 'second derivatives: ', d2g2(2.), d2g3(2.) print 'numerical integral: ', intg2, intg3
# functions: 4.0 8.0 # first derivatives: 4.00000000012 12.0000000008 #second derivatives: 2.00017780116 12.001066807 #numerical integral: 0.333333333333 0.25
#== WARNING == #-- derivatives computed numerically do not #-- necessarily converge for small h --
h = .1
for i in range(1, 7):
h /= 100
print h, 'first = ', dg2(2, h), 'second =', dg3(2, h)#0.001 first = 4.0 second = 12.00000025 #1e-005 first = 3.99999999989 second = 11.9999999997 #1e-007 first = 4.00000000234 second = 12.0000000159 #1e-009 first = 4.00000033096 second = 12.0000009929 #1e-011 first = 4.00000033096 second = 12.0000009929 #1e-013 first = 4.00568467285 second = 12.0170540185
#####################
André
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