scipy.optimize._differentiable_functions:ScalarFunction

Parameters

fun : callable

evaluates the scalar function. Must be of the form fun(x, *args), where x is the argument in the form of a 1-D array and args is a tuple of any additional fixed parameters needed to completely specify the function. Should return a scalar.

x0 : array-like

Provides an initial set of variables for evaluating fun. Array of real elements of size (n,), where 'n' is the number of independent variables.

args : tuple, optional

Any additional fixed parameters needed to completely specify the scalar function.

grad : {callable, '2-point', '3-point', 'cs'}

Method for computing the gradient vector. If it is a callable, it should be a function that returns the gradient vector:

grad(x, *args) -> array_like, shape (n,)

where x is an array with shape (n,) and args is a tuple with the fixed parameters. Alternatively, the keywords {'2-point', '3-point', 'cs'} can be used to select a finite difference scheme for numerical estimation of the gradient with a relative step size. These finite difference schemes obey any specified bounds.

hess : {callable, '2-point', '3-point', 'cs', HessianUpdateStrategy}

Method for computing the Hessian matrix. If it is callable, it should return the Hessian matrix:

hess(x, *args) -> {LinearOperator, spmatrix, array}, (n, n)

where x is a (n,) ndarray and args is a tuple with the fixed parameters. Alternatively, the keywords {'2-point', '3-point', 'cs'} select a finite difference scheme for numerical estimation. Or, objects implementing HessianUpdateStrategy interface can be used to approximate the Hessian. Whenever the gradient is estimated via finite-differences, the Hessian cannot be estimated with options {'2-point', '3-point', 'cs'} and needs to be estimated using one of the quasi-Newton strategies.

finite_diff_rel_step : None or array_like

Relative step size to use. The absolute step size is computed as h = finite_diff_rel_step * sign(x0) * max(1, abs(x0)), possibly adjusted to fit into the bounds. For method='3-point' the sign of h is ignored. If None then finite_diff_rel_step is selected automatically,

finite_diff_bounds : tuple of array_like

Lower and upper bounds on independent variables. Defaults to no bounds, (-np.inf, np.inf). Each bound must match the size of x0 or be a scalar, in the latter case the bound will be the same for all variables. Use it to limit the range of function evaluation.

epsilon : None or array_like, optional

Absolute step size to use, possibly adjusted to fit into the bounds. For method='3-point' the sign of epsilon is ignored. By default relative steps are used, only if epsilon is not None are absolute steps used.

workers : map-like callable, optional

A map-like callable, such as multiprocessing.Pool.map for evaluating any numerical differentiation in parallel. This evaluation is carried out as workers(fun, iterable), or workers(grad, iterable), depending on what is being numerically differentiated. Alternatively, if workers is an int the task is subdivided into workers sections and the function evaluated in parallel (uses multiprocessing.Pool <multiprocessing>). Supply -1 to use all available CPU cores. It is recommended that a map-like be used instead of int, as repeated calls to approx_derivative will incur large overhead from setting up new processes.