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# scipy.optimize.ridder

`scipy.optimize.``ridder`(f, a, b, args=(), xtol=2e-12, rtol=8.8817841970012523e-16, maxiter=100, full_output=False, disp=True)

  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.

  See also

  `brentq`, `brenth`, `bisect`, `newton`

  `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 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.