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scipy.optimize.

# bisect

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

  Find root of a function within an interval using bisection.

  Basic bisection routine to find a root of the function f between the arguments a and b. `f(a)` and `f(b)` cannot have the same signs. Slow but sure.

  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]`.

    args tuple, optional

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

    xtol number, optional

      The computed root `x0` will satisfy `np.isclose(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.isclose(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.

    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 a `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`
  `fixed_point`

    scalar fixed-point finder

  `fsolve`

    n-dimensional root-finding

  `elementwise.find_root`

    efficient elementwise 1-D root-finder

  Notes

  As mentioned in the parameter documentation, the computed root `x0` will satisfy `np.isclose(x, x0, atol=xtol, rtol=rtol)`, where `x` is the exact root. In equation form, this terminating condition is `abs(x - x0) <= xtol + rtol * abs(x0)`.

  The default value `xtol=2e-12` may lead to surprising behavior if one expects `bisect` to always compute roots with relative error near machine precision. Care should be taken to select xtol for the use case at hand. Setting `xtol=5e-324`, the smallest subnormal number, will ensure the highest level of accuracy. Larger values of xtol may be useful for saving function evaluations when a root is at or near zero in applications where the tiny absolute differences available between floating point numbers near zero are not meaningful.

  Examples

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

      >>> from scipy import optimize

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

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