''' 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) < 0.0: dx = -dx
x = c + dx; fx = f(x)
# Test for convergence
if i > 0:
if abs(x - xOld) < tol*max(abs(x),1.0): return x
xOld = x
# Re-bracket the root as tightly as possible
if fc*fx > 0.0:
if fa*fx < 0.0: b = x; fb = fx
else: a = x; fa = fx
else:
a = c; b = x; fa = fc; fb = fx
return None
print 'Too many iterations'
#//python/7401