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# scipy.optimize.brenth

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

  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

  `fmin`, `fmin_powell`, `fmin_cg`

  `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