def ridder(f, a, b, args=(), xtol=_xtol, rtol=_rtol, maxiter=_iter, full_output=False, disp=True): """ Find a root of a function in an interval. 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. maxiter : number, optional if convergence is not achieved in maxiter iterations, and 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 -------- brentq, brenth, bisect, newton : one-dimensional root-finding fixed_point : scalar fixed-point finder Notes ----- Uses [Ridders1979]_ method to find a zero of the function `f` between the arguments `a` and `b`. Ridders' method is faster than bisection, but not generally as fast as the Brent rountines. [Ridders1979]_ provides the classic description and source of the algorithm. A description can also be found in any recent edition of Numerical Recipes. The routine used here diverges slightly from standard presentations in order to be a bit more careful of tolerance. References ---------- .. [Ridders1979] Ridders, C. F. J. "A New Algorithm for Computing a Single Root of a Real Continuous Function." IEEE Trans. Circuits Systems 26, 979-980, 1979. """ if type(args) != type(()): args = (args, ) r = _zeros._ridder(f, a, b, xtol, maxiter, args, full_output, disp) return results_c(full_output, r)
def ridder(f, a, b, args=(), xtol=_xtol, rtol=_rtol, maxiter=_iter, full_output=False, disp=True): """ Find a root of a function in an interval. 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. maxiter : number, optional if convergence is not achieved in maxiter iterations, and 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 -------- brentq, brenth, bisect, newton : one-dimensional root-finding fixed_point : scalar fixed-point finder Notes ----- Uses [Ridders1979]_ method to find a zero of the function `f` between the arguments `a` and `b`. Ridders' method is faster than bisection, but not generally as fast as the Brent rountines. [Ridders1979]_ provides the classic description and source of the algorithm. A description can also be found in any recent edition of Numerical Recipes. The routine used here diverges slightly from standard presentations in order to be a bit more careful of tolerance. References ---------- .. [Ridders1979] Ridders, C. F. J. "A New Algorithm for Computing a Single Root of a Real Continuous Function." IEEE Trans. Circuits Systems 26, 979-980, 1979. """ if type(args) != type(()) : args = (args,) r = _zeros._ridder(f,a,b,xtol,maxiter,args,full_output,disp) return results_c(full_output, r)
def ridder(f, a, b, args=(), xtol=_xtol, rtol=_rtol, maxiter=_iter, full_output=False, disp=False): """Find root of f in [a,b] Ridder routine to find a zero of the function f between the arguments a and b. f(a) and f(b) can not have the same signs. Faster than bisection, but not generaly as fast as the brent rountines. A description may be found in a recent edition of Numerical Recipes. The routine here is modified a bit to be more careful of tolerance. f : Python function returning a number. a : Number, one end of the bracketing interval. b : Number, the other end of the bracketing interval. xtol : Number, 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. maxiter : Number, if convergence is not achieved in maxiter iterations, and error is raised. Must be >= 0. args : tuple containing extra arguments for the function f. f is called by apply(f,(x)+args). 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 containing information about the convergence. In particular, r.converged is True if the the routine converged. See also: fmin, fmin_powell, fmin_cg, fmin_bfgs, fmin_ncg -- multivariate local optimizers leastsq -- nonlinear least squares minimizer fmin_l_bfgs_b, fmin_tnc, fmin_cobyla -- constrained multivariate optimizers anneal, brute -- global optimizers fminbound, brent, golden, bracket -- local scalar minimizers fsolve -- n-dimenstional root-finding brentq, brenth, ridder, bisect, newton -- one-dimensional root-finding fixed_point -- scalar fixed-point finder """ if type(args) != type(()) : args = (args,) r = _zeros._ridder(f,a,b,xtol,maxiter,args,full_output,disp) return results_c(full_output, r)