scipy.optimize.brenth¶

scipy.optimize.brenth(f, a, b, args=(), xtol=1e-12, rtol=4.4408920985006262e-16, maxiter=100, full_output=False, disp=True)[source]¶

Find root of f in [a,b].

A variation on the classic Brent routine to find a zero of the function f between the arguments a and b that uses hyperbolic extrapolation instead of inverse quadratic extrapolation. There was a paper back in the 1980’s ... f(a) and f(b) cannot have the same signs. Generally on a par with the brent routine, but not as heavily tested. It is a safe version of the secant method that uses hyperbolic extrapolation. The version here is by Chuck Harris.

Parameters:

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 routine converges when a root is known to lie within xtol of the value return. Should be >= 0. The routine modifies this to take into account the relative precision of doubles. rtol : number, optional The routine converges when a root is known to lie within rtol times the value returned of the value returned. Should be >= 0. Defaults to `np.finfo(float).eps * 2`. 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.

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 routine converges when a root is known to lie within xtol of the value return. Should be >= 0. The routine modifies this to take into account the relative precision of doubles.

rtol : number, optional

The routine converges when a root is known to lie within rtol times the value returned of the value returned. Should be >= 0. Defaults to np.finfo(float).eps * 2.

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.