scipy.optimize.ridder(f, a, b, args=(), xtol=1e-12, rtol=4.4408920985006262e-16, maxiter=100, full_output=False, disp=True)[source]

Find a root of a function in an interval.


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 routine converges when a root is known to lie within xtol of the value return. Should be >= 0. The routine modifies this to take into account the relative precision of doubles.

rtol : number, optional

The routine converges when a root is known to lie within rtol times the value returned of the value returned. Should be >= 0. Defaults to np.finfo(float).eps * 2.

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.


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.

See also

brentq, brenth, bisect, newton

scalar fixed-point finder


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.


[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.

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