scipy.optimize.cython_optimize.brentq的mitr参数用途及使用方式问询

Great question — it’s totally reasonable to scratch your head when official docs skip explaining a parameter! Let’s unpack what mitr does here:

• First, mitr is shorthand for maximum iterations. It’s a parameter specific to this Cython-optimized implementation of the Brentq root-finding algorithm, designed to cap the number of iterations the algorithm can run through while searching for a root.
• The default value of 10 acts as a safety guard: if the algorithm hasn’t converged to a root after 10 iterations, it will terminate early and raise a convergence error (typically a RuntimeError indicating failure to find a root within the iteration limit).
• This is similar in purpose to the maxiter parameter in the more commonly used scipy.optimize.brentq, but with a much smaller default value. The Cython version is optimized for speed in cases where roots converge quickly, hence the tighter default limit.
• If you’re working with a function that takes more iterations to converge (e.g., a highly oscillatory or slowly changing function), you can increase mitr to give the algorithm more room to find the root. For example:

  from scipy.optimize.cython_optimize import brentq
  
  def hard_to_converge_func(x):
      return (x**3 - 2*x + 2) * (x - 1)
  
  # Allow more iterations for convergence
  root = brentq(hard_to_converge_func, -2, 0, mitr=50)
  

This detail is missing from the official docs, but it’s clear from examining the underlying Cython source code that mitr exists to prevent infinite loops and control the algorithm’s runtime for different convergence scenarios.

内容的提问来源于stack exchange，提问作者Ricardo Gonçalves Molinari