51 lines
1.8 KiB
Python
51 lines
1.8 KiB
Python
|
# method to find a bracket that encloses a root of f
|
||
|
|
from math import *
|
||
|
|
|
||
|
|
def findEnclosingBracket(f, x, factor):
|
||
|
|
""" Finds a bracket [a b] that encloses a root of f : f(a)*f(b) < 0.
|
||
|
|
A typical value for the factor is 2.
|
||
|
|
The initial guess must be on the correct side of the real line : the algorithm will never cross the zero during the search.
|
||
|
|
The factor is increased every 10 iterations in order to speed up convergence for when the root is orders of magnitude away from the initial guess.
|
||
|
|
If the bracket returned by the function is too wide, try reducing the factor (while always keeping it > 1).
|
||
|
|
"""
|
||
|
|
a = x
|
||
|
|
b = x*factor # try higher
|
||
|
|
fa = f(a)
|
||
|
|
fb = f(b)
|
||
|
|
|
||
|
|
i = 0
|
||
|
|
while i in range(100) and fa*fb > 0:
|
||
|
|
if fabs(fa) < fabs(fb): # fa is closer to 0 than fb, extend the interval in the a direction (reducing it)
|
||
|
|
a = a / factor
|
||
|
|
fa = f(a)
|
||
|
|
else: # fb is closer to 0 than fa, extend the interval in the b direction (augmenting it)
|
||
|
|
b = b * factor
|
||
|
|
fb = f(b)
|
||
|
|
i = i+1
|
||
|
|
|
||
|
|
if i % 10 == 0: # every 10 iterations, bump up the factor to speed up convergence
|
||
|
|
factor = factor * 5
|
||
|
|
|
||
|
|
return (a, b, fa, fb)
|
||
|
|
|
||
|
|
f = lambda x : exp(sin(x))-2
|
||
|
|
a, b, fa, fb = findEnclosingBracket(f, 0.005, 2)
|
||
|
|
print((a,b)); print((fa, fb))
|
||
|
|
|
||
|
|
f = lambda x : exp(-x)-1e-200
|
||
|
|
a, b, fa, fb = findEnclosingBracket(f, 0.001, 2)
|
||
|
|
print((a,b)); print((fa, fb))
|
||
|
|
|
||
|
|
a, b, fa, fb = findEnclosingBracket(f, 0.001, 5)
|
||
|
|
print((a,b)); print((fa, fb))
|
||
|
|
|
||
|
|
f = lambda x : x**(1/3)-1000
|
||
|
|
a, b, fa, fb = findEnclosingBracket(f, 1e-10, 2)
|
||
|
|
print((a,b)); print((fa, fb))
|
||
|
|
|
||
|
|
# from toms748 import TOMS748_solve1
|
||
|
|
# def f(x):
|
||
|
|
# print(x)
|
||
|
|
# return x**(1/3)-1000
|
||
|
|
# TOMS748_solve1(f,a,b)
|