''' root = ridder(f,a,b,tol=1.0e-9).
Finds a root of f(x) = 0 with Ridder's method.
The root must be bracketed in (a,b).
'''
import error
from math import sqrt
def ridder(f,a,b,tol=1.0e-9):
fa = f(a)
if fa == 0.0: return a
fb = f(b)
if fb == 0.0: return b
if fa*fb > 0.0: error.err('Root is not bracketed')
for i in range(30):
# Compute the improved root x from Ridder's formula
c = 0.5*(a + b); fc = f(c)
s = sqrt(fc**2 - fa*fb)
if s == 0.0: return None
dx = (c - a)*fc/s
if (fa - fb) 0:
if abs(x - xOld) 0.0:
if fa*fx
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