apache_muller

sherpa.utils.apache_muller(fcn, xa, xb, fa=None, fb=None, args=(), maxfev=32, tol=1e-06)[source] [edit on github]

An alternative implementation of Muller’s method for root finding.

Unlike the rest of Sherpa, this method is available the Apache Software Foundation (ASF) licence - see code for this method for details.

Parameters:

  • fcn (callable) – The function with a root. The function signature is fcn(x, *args).

  • xa (float) – Muller’s method requires three initial values.

  • xb (float) – Muller’s method requires three initial values.

  • fa (float or None) – Function values at xa and xb. These parameters are optional and can be passed to save time in cases where fcn(xa, *args) is already known and function evaluation takes a long time. If None, they will be calculated.

  • fb (float or None) – Function values at xa and xb. These parameters are optional and can be passed to save time in cases where fcn(xa, *args) is already known and function evaluation takes a long time. If None, they 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 the function value 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] where x is the location of the root, and x1 and x2 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:

list