root_scalar(f, args=(), method=None, bracket=None, fprime=None, fprime2=None, x0=None, x1=None, xtol=None, rtol=None, maxiter=None, options=None)¶
Find a root of a scalar function.
A function to find a root of.
- argstuple, optional
Extra arguments passed to the objective function and its derivative(s).
- methodstr, optional
Type of solver. Should be one of
- bracket: A sequence of 2 floats, optional
An interval bracketing a root. f(x, *args) must have different signs at the two endpoints.
- x0float, optional
- x1float, optional
A second guess.
- fprimebool or callable, optional
If fprime is a boolean and is True, f is assumed to return the value of derivative along with the objective function. fprime can also be a callable returning the derivative of f. In this case, it must accept the same arguments as f.
- fprime2bool or callable, optional
If fprime2 is a boolean and is True, f is assumed to return the value of 1st and 2nd derivatives along with the objective function. fprime2 can also be a callable returning the 2nd derivative of f. In this case, it must accept the same arguments as f.
- xtolfloat, optional
Tolerance (absolute) for termination.
- rtolfloat, optional
Tolerance (relative) for termination.
- maxiterint, optional
Maximum number of iterations.
- optionsdict, optional
A dictionary of solver options. E.g.
The solution represented as a
RootResultsobject. Important attributes are:
rootthe solution ,
convergeda boolean flag indicating if the algorithm exited successfully and
flagwhich describes the cause of the termination. See
RootResultsfor a description of other attributes.
This section describes the available solvers that can be selected by the ‘method’ parameter.
The default is to use the best method available for the situation presented. If a bracket is provided, it may use one of the bracketing methods. If a derivative and an initial value are specified, it may select one of the derivative-based methods. If no method is judged applicable, it will raise an Exception.
Find the root of a simple cubic
>>> from scipy import optimize >>> def f(x): ... return (x**3 - 1) # only one real root at x = 1
>>> def fprime(x): ... return 3*x**2
brentqmethod takes as input a bracket
>>> sol = optimize.root_scalar(f, bracket=[0, 3], method='brentq') >>> sol.root, sol.iterations, sol.function_calls (1.0, 10, 11)
newtonmethod takes as input a single point and uses the derivative(s)
>>> sol = optimize.root_scalar(f, x0=0.2, fprime=fprime, method='newton') >>> sol.root, sol.iterations, sol.function_calls (1.0, 11, 22)
The function can provide the value and derivative(s) in a single call.
>>> def f_p_pp(x): ... return (x**3 - 1), 3*x**2, 6*x
>>> sol = optimize.root_scalar(f_p_pp, x0=0.2, fprime=True, method='newton') >>> sol.root, sol.iterations, sol.function_calls (1.0, 11, 11)
>>> sol = optimize.root_scalar(f_p_pp, x0=0.2, fprime=True, fprime2=True, method='halley') >>> sol.root, sol.iterations, sol.function_calls (1.0, 7, 8)