His problem was composing four functions, each with a small error. The first
two applications work well enough, but there is a about a percent error in
the third composition. The big source of error is f(x+h)-f(x). Subtracting
two floating point numbers that are nearly equal is a known source of
innaccuracy. Scaling all the terms by a very large number reduced the error,
but not as well as fewer compositions.
Cheers
BIGNUM = 1
def D5(func, h=1e-5):
""' Return derivative of function func'''
def df(x):
return (BIGNUM*func(x+h)-BIGNUM*func(x))/(BIGNUM*h)
return df
import math
print D5(math.sin)(0.3)
print math.cos(0.3)
print D5(D5(math.sin))(0.3)
print -math.sin(0.3)
print
print D5(D5(D5(math.sin)))(0.3)
print -math.cos(0.3)
# actually, other powers, higher or lower, work less well..
BIGNUM = 1e10
print D5(D5(D5(math.sin)))(0.3)
print -math.cos(0.3)
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