root_scalar(f, args=(), method=None, bracket=None, fprime=None, fprime2=None, x0=None, x1=None, xtol=None, rtol=None, maxiter=None, options=None)

Notes

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.

Parameters

f : callable

A function to find a root of.

args : tuple, optional

Extra arguments passed to the objective function and its derivative(s).

method : str, optional

Type of solver. Should be one of

• 'bisect' (see here) <optimize.root_scalar-bisect>

• 'brentq' (see here) <optimize.root_scalar-brentq>

• 'brenth' (see here) <optimize.root_scalar-brenth>

• 'ridder' (see here) <optimize.root_scalar-ridder>

• 'toms748' (see here) <optimize.root_scalar-toms748>

• 'newton' (see here) <optimize.root_scalar-newton>

• 'secant' (see here) <optimize.root_scalar-secant>

• 'halley' (see here) <optimize.root_scalar-halley>

bracket: A sequence of 2 floats, optional :

An interval bracketing a root. :None:None:`f(x, *args)` must have different signs at the two endpoints.

x0 : float, optional

Initial guess.

x1 : float, optional

A second guess.

fprime : bool or callable, optional

If fprime is a boolean and is True, f is assumed to return the value of the objective function and of the derivative. fprime can also be a callable returning the derivative of f. In this case, it must accept the same arguments as f.

fprime2 : bool or callable, optional

If fprime2 is a boolean and is True, f is assumed to return the value of the objective function and of the first and second derivatives. fprime2 can also be a callable returning the second derivative of f. In this case, it must accept the same arguments as f.

xtol : float, optional

Tolerance (absolute) for termination.

rtol : float, optional

Tolerance (relative) for termination.

maxiter : int, optional

Maximum number of iterations.

options : dict, optional

A dictionary of solver options. E.g., k , see show_options() for details.

Returns

sol : RootResults

The solution represented as a RootResults object. Important attributes are: root the solution , converged a boolean flag indicating if the algorithm exited successfully and flag which describes the cause of the termination. See RootResults for a description of other attributes.

Find a root of a scalar function.

See Also

root

Find a root of a vector function.

show_options

Additional options accepted by the solvers

Examples

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

The brentq method 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)

The newton method 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)

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

scipy.optimize scipy.optimize._optimize.show_options scipy.optimize._root_scalar.root_scalar scipy.optimize._zeros_py.newton

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