bisection
- sherpa.utils.bisection(fcn, xa, xb, fa=None, fb=None, args=(), maxfev=48, tol=1e-06)[source] [edit on github]
A basic root finding algorithm that uses standard bisection
Bisection is a relatively slow method for root finding, but it guaranteed to work for a continuous function with a root in a bracketed interval; in other words the function must undergo a sign change between the bracketing values.
See https://en.wikipedia.org/wiki/Bisection_method for a description of the bisection method.
- Parameters:
fcn (callable) – The function with a root. The function signature is
fcn(x, *args)
.xa (float) – Lower limit of the bracketing interval
xb (float) – Upper limit of the bracketing interval
fa (float or None) – Function value at
xa
. This parameter is optional and can be passed to save time in cases wherefcn(xa, *args)
is already known and function evaluation takes a long time. IfNone
, it will be calculated.fb (float or None) – Function value at
xb
. This parameter is optional and can be passed to save time in cases wherefcn(xb, *args)
is already known and function evaluation takes a long time. IfNone
, it will be calculated.args (tuple) – Additional parameters that will be passed through to
fcn
.maxfev (int) – Maximal number of function evaluations
tol (float) – The root finding algorithm stops if a value x with
abs(fcn(x)) < tol
is found.
- Returns:
out – The output has the form of a list:
[[x, fcn(x)], [x1, fcn(x1)], [x2, fcn(x2)], nfev]
wherex
is the location of the root, andx1
andx2
are the previous steps. The function value for those steps is returned as well.nfev
is the total number of function evaluations. If any of those values is not available,None
will be returned instead.- Return type: