4.7.11.1.1. statsmodels.tools.rootfinding.brentq_expanding

statsmodels.tools.rootfinding.brentq_expanding(func, low=None, upp=None, args=(), xtol=1e-05, start_low=None, start_upp=None, increasing=None, max_it=100, maxiter_bq=100, factor=10, full_output=False)[source]

find the root of a function in one variable by expanding and brentq

Assumes function func is monotonic.

Parameters:

func : callable

function for which we find the root x such that func(x) = 0

low : float or None

lower bound for brentq

upp : float or None

upper bound for brentq

args : tuple

optional additional arguments for func

xtol : float

parameter x tolerance given to brentq

start_low : float (positive) or None

starting bound for expansion with increasing x. It needs to be positive. If None, then it is set to 1.

start_upp : float (negative) or None

starting bound for expansion with decreasing x. It needs to be negative. If None, then it is set to -1.

increasing : bool or None

If None, then the function is evaluated at the initial bounds to determine wether the function is increasing or not. If increasing is True (False), then it is assumed that the function is monotonically increasing (decreasing).

max_it : int

maximum number of expansion steps.

maxiter_bq : int

maximum number of iterations of brentq.

factor : float

expansion factor for step of shifting the bounds interval, default is 10.

full_output : bool, optional

If full_output is False, the root is returned. If full_output is True, the return value is (x, r), where x is the root, and r is a RootResults object.
Returns:

x : float

root of the function, value at which func(x) = 0.

info : RootResult (optional)

returned if full_output is True. attributes:

  • start_bounds : starting bounds for expansion stage
  • brentq_bounds : bounds used with brentq
  • iterations_expand : number of iterations in expansion stage
  • converged : True if brentq converged.
  • flag : return status, ‘converged’ if brentq converged
  • function_calls : number of function calls by brentq
  • iterations : number of iterations in brentq

Notes

If increasing is None, then whether the function is monotonically increasing or decreasing is inferred from evaluating the function at the initial bounds. This can fail if there is numerically no variation in the data in this range. In this case, using different starting bounds or directly specifying increasing can make it possible to move the expansion in the right direction.

If