scipy.optimize.brenth¶
- scipy.optimize.brenth(f, a, b, args=(), xtol=2e-12, rtol=8.8817841970012523e-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: 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. As with brentq, for nice functions the method will often satisfy the above condition will xtol/2 and rtol/2.
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. As with brentq, for nice functions the method will often satisfy the above condition will xtol/2 and rtol/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.
See also
- leastsq
- nonlinear least squares minimizer
fmin_l_bfgs_b, fmin_tnc, fmin_cobyla, basinhopping, differential_evolution, brute, fminbound, brent, golden, bracket
- fsolve
- n-dimensional root-finding
brentq, brenth, ridder, bisect, newton
- fixed_point
- scalar fixed-point finder