scipy.optimize.ridder

scipy.optimize.ridder(f, a, b, args=(), xtol=2e-12, rtol=8.881784197001252e-16, maxiter=100, full_output=False, disp=True)

Find a root of a function in an interval using Ridder’s method.

Parameters

ffunction

Python function returning a number. f must be continuous, and f(a) and f(b) must have opposite signs.

ascalar

One end of the bracketing interval [a,b].

bscalar

The other end of the bracketing interval [a,b].

xtolnumber, 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.

rtolnumber, 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.

maxiterint, optional

if convergence is not achieved in maxiter iterations, an error is raised. Must be >= 0.

argstuple, optional

containing extra arguments for the function f. f is called by apply(f, (x)+args).

full_outputbool, 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.

dispbool, optional

If True, raise RuntimeError if the algorithm didn’t converge. Otherwise the convergence status is recorded in any RootResults return object.

Returns

x0float

Zero of f between a and b.

rRootResults (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

one-dimensional root-finding

fixed_point

scalar fixed-point finder

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 routines. [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)

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.

Examples

>>> def f(x):
...     return (x**2 - 1)

>>> from scipy import optimize

>>> root = optimize.ridder(f, 0, 2)
>>> root
1.0

>>> root = optimize.ridder(f, -2, 0)
>>> root
-1.0