scipy.optimize.ridder#
- scipy.optimize.ridder(f, a, b, args=(), xtol=2e-12, rtol=8.881784197001252e-16, maxiter=100, full_output=False, disp=True)[source]#
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 satisfynp.allclose(x, x0, atol=xtol, rtol=rtol)
, wherex
is the exact root. The parameter must be positive.- rtolnumber, optional
The computed root
x0
will satisfynp.allclose(x, x0, atol=xtol, rtol=rtol)
, wherex
is the exact root. The parameter cannot be smaller than its default value of4*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 aRootResults
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:
- rootfloat
Root of f between a and b.
- r
RootResults
(present iffull_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
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