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Module « scipy.optimize »

Fonction ridder - module scipy.optimize

Signature de la fonction ridder

def ridder(f, a, b, args=(), xtol=2e-12, rtol=np.float64(8.881784197001252e-16), maxiter=100, full_output=False, disp=True) 

Description

help(scipy.optimize.ridder)

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

Parameters
----------
f : function
    Python function returning a number. f must be continuous, and f(a) and
    f(b) must have opposite signs.
a : scalar
    One end of the bracketing interval [a,b].
b : scalar
    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 positive.
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 : int, 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.
    Otherwise, the convergence status is recorded in any `RootResults`
    return object.

Returns
-------
root : float
    Root 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 : 1-D root-finding
fixed_point : scalar fixed-point finder

Notes
-----
Uses [Ridders1979]_ method to find a root 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]
   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


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