This class defines a scalar function F: R^n->R and methods for computing or approximating its first and second derivatives.

Notes

This class implements a memoization logic. There are methods :None:None:`fun`, grad , hess` and corresponding attributes f, g and :None:None:`H`. The following things should be considered:

1. Use only public methods :None:None:`fun`, grad and :None:None:`hess`.

2. After one of the methods is called, the corresponding attribute will be set. However, a subsequent call with a different argument of any of the methods may overwrite the attribute.

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 :None:None:`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 :None:None:`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 :None:None:`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 :None:None:`epsilon` is ignored. By default relative steps are used, only if epsilon is not None are absolute steps used.

Scalar function and its derivatives.

Examples

See :

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GitHub : /scipy/optimize/_differentiable_functions.py#11
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