scipy.optimize.bisect¶

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

Find root of a function within an interval using bisection.

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

Parameters:

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 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 `4np.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 a `RootResults` return object.
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.

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 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 : 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 a RootResults return object.

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.