scipy.optimize.ridder¶
- scipy.optimize.ridder(f, a, b, args=(), xtol=2e-12, rtol=8.8817841970012523e-16, maxiter=100, full_output=False, disp=True)[source]¶
Find a root of a function in an interval.
Parameters: f : function
Python function returning a number. f must be continuous, and f(a) and f(b) must have opposite signs.
a : number
One end of the bracketing interval [a,b].
b : number
The other end of the bracketing interval [a,b].
xtol : number, optional
The computed root x0 will satisfy np.allclose(x, x0, atol=xtol, rtol=rtol), where x is the exact root. The parameter must be nonnegative.
rtol : number, optional
The computed root x0 will satisfy np.allclose(x, x0, atol=xtol, rtol=rtol), where x is the exact root. The parameter cannot be smaller than its default value of 4*np.finfo(float).eps.
maxiter : number, optional
if convergence is not achieved in maxiter iterations, an error is raised. Must be >= 0.
args : tuple, optional
containing extra arguments for the function f. f is called by apply(f, (x)+args).
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.
disp : bool, optional
If True, raise RuntimeError if the algorithm didn’t converge.
Returns: x0 : float
Zero of f between a and b.
r : RootResults (present if full_output = True)
Object containing information about the convergence. In particular, r.converged is True if the routine converged.
Notes
Uses [Ridders1979] method to find a zero of the function f between the arguments a and b. Ridders’ method is faster than bisection, but not generally as fast as the Brent rountines. [Ridders1979] provides the classic description and source of the algorithm. A description can also be found in any recent edition of Numerical Recipes.
The routine used here diverges slightly from standard presentations in order to be a bit more careful of tolerance.
References
[Ridders1979] (1, 2, 3) Ridders, C. F. J. “A New Algorithm for Computing a Single Root of a Real Continuous Function.” IEEE Trans. Circuits Systems 26, 979-980, 1979.