def bisect(f, min, max, tol, max_its):
"""Bisection method
The quadratic y(x) = x^2 + 2x -1 has roots
-1 - sqrt(2) = -2.4142135623730950488016887242097
and -1 + sqrt(2) = 0.4142135623730950488016887242097.
>>> bisect(lambda x: x*x + 2*x - 1, -3, -2, lambda x, y: math.fabs(x-y) < 0.000001, 10)
(-2.4142141342163086, -2.4142131805419922, 3)
>>> bisect(lambda x: x*x + 2*x - 1, 0, 1, lambda x, y: math.fabs(x-y) < 0.000001, 10)
(0.41421318054199219, 0.41421413421630859, 3)
"""
fmin, fmax = f(min), f(max)
if fmin == 0: return (min, min, 0)
if fmax == 0: return (max, max, 0)
if min >= max: raise RuntimeError, "Arguments in wrong order"
if fmin * fmax >= 0: raise RuntimeError, "Root not bracketed"
count = max_its
if count < 3:
count = 0
else:
count -= 3
while count and tol(min, max) == 0:
mid = (min + max) / 2.
fmid = f(mid)
if mid == max or mid == min:
break
if fmid == 0:
min = max = mid
break
elif sign(fmid) * sign(fmin) < 0:
max, fmax = mid, fmid
else:
min, fmin = mid, fmid
--count
max_its -= count
return (min, max, max_its)
def bisect(f, min, max, tol, max_its):
"""Bisection method
The quadratic y(x) = x^2 + 2x -1 has roots
-1 - sqrt(2) = -2.4142135623730950488016887242097
and -1 + sqrt(2) = 0.4142135623730950488016887242097.
>>> bisect(lambda x: x*x + 2*x - 1, -3, -2, lambda x, y: math.fabs(x-y) < 0.000001, 10)
(-2.4142141342163086, -2.4142131805419922, 3)
>>> bisect(lambda x: x*x + 2*x - 1, 0, 1, lambda x, y: math.fabs(x-y) < 0.000001, 10)
(0.41421318054199219, 0.41421413421630859, 3)
"""
fmin, fmax = f(min), f(max)
if fmin == 0: return (min, min, 0)
if fmax == 0: return (max, max, 0)
if min >= max: raise RuntimeError, "Arguments in wrong order"
if fmin*fmax >= 0: raise RuntimeError, "Root not bracketed"
count = max_its
if count < 3:
count = 0
else: count -= 3
while count and tol(min, max) == 0:
mid = (min + max)/2.
fmid = f(mid)
if mid == max or mid ==min:
break
if fmid == 0:
min = max = mid
break
elif sign(fmid)*sign(fmin) < 0:
max, fmax = mid, fmid
else:
min, fmin = mid, fmid
--count
max_its -= count
return (min, max, max_its)
def _handle_zero_derivative(f, last_f0, f0, delta, result, guess, min, max):
if last_f0 == 0:
# must be first iteration
if result == min: guess = max
else: guess = min
last_f0, _ = f(guess)
delta = guess - result
if sign(last_f0)*sign(f0) < 0:
# we've crossed over so move in opposite
# direction to last step
if delta < 0:
delta = (result - min)/2.0
else:
delta = (result - max)/2.0
else:
# move in same direction of last step
if delta < 0:
delta = (result - max)/2.0
else:
delta = (result - min)/2.0
return (last_f0, delta, result, guess)
def _handle_zero_derivative(f, last_f0, f0, delta, result, guess, min,
max):
if last_f0 == 0:
# must be first iteration
if result == min: guess = max
else: guess = min
last_f0, _ = f(guess)
delta = guess - result
if sign(last_f0) * sign(f0) < 0:
# we've crossed over so move in opposite
# direction to last step
if delta < 0:
delta = (result - min) / 2.0
else:
delta = (result - max) / 2.0
else:
# move in same direction of last step
if delta < 0:
delta = (result - max) / 2.0
else:
delta = (result - min) / 2.0
return (last_f0, delta, result, guess)
