root(method=’broyden1’)

scipy.optimize.root(fun, x0, args=(), method='hybr', jac=None, tol=None, callback=None, options=None)

See also

For documentation for the rest of the parameters, see scipy.optimize.root

Options:

——-

nitint, optional

Number of iterations to make. If omitted (default), make as many as required to meet tolerances.

dispbool, optional

Print status to stdout on every iteration.

maxiterint, optional

Maximum number of iterations to make. If more are needed to meet convergence, NoConvergence is raised.

ftolfloat, optional

Relative tolerance for the residual. If omitted, not used.

fatolfloat, optional

Absolute tolerance (in max-norm) for the residual. If omitted, default is 6e-6.

xtolfloat, optional

Relative minimum step size. If omitted, not used.

xatolfloat, optional

Absolute minimum step size, as determined from the Jacobian approximation. If the step size is smaller than this, optimization is terminated as successful. If omitted, not used.

tol_normfunction(vector) -> scalar, optional

Norm to use in convergence check. Default is the maximum norm.

line_search{None, ‘armijo’ (default), ‘wolfe’}, optional

Which type of a line search to use to determine the step size in the direction given by the Jacobian approximation. Defaults to ‘armijo’.

jac_optionsdict, optional

Options for the respective Jacobian approximation.

alphafloat, optional

Initial guess for the Jacobian is (-1/alpha).

reduction_methodstr or tuple, optional

Method used in ensuring that the rank of the Broyden matrix stays low. Can either be a string giving the name of the method, or a tuple of the form (method, param1, param2, ...) that gives the name of the method and values for additional parameters.

Methods available:

• restart

  Drop all matrix columns. Has no extra parameters.

• simple

  Drop oldest matrix column. Has no extra parameters.

• svd

  Keep only the most significant SVD components.

  Extra parameters:

  • to_retain

    Number of SVD components to retain when rank reduction is done. Default is max_rank - 2.

max_rankint, optional

Maximum rank for the Broyden matrix. Default is infinity (i.e., no rank reduction).

Examples

>>> def func(x):
...     return np.cos(x) + x[::-1] - [1, 2, 3, 4]
...
>>> from scipy import optimize
>>> res = optimize.root(func, [1, 1, 1, 1], method='broyden1', tol=1e-14)
>>> x = res.x
>>> x
array([4.04674914, 3.91158389, 2.71791677, 1.61756251])
>>> np.cos(x) + x[::-1]
array([1., 2., 3., 4.])