# finite_difference.py¶

Finite difference derivative approximations.

class openmdao.approximation_schemes.finite_difference.FiniteDifference[source]

Bases: openmdao.approximation_schemes.approximation_scheme.ApproximationScheme

Approximation scheme using finite differences to estimate derivatives.

For example, using the ‘forward’ form with a step size of ‘h’ will approximate the derivative in the following way:

$f'(x) = \frac{f(x+h) - f(x)}{h} + O(h).$
Attributes
_starting_outsndarray

A copy of the starting outputs array used to restore the outputs to original values.

_starting_insndarray

A copy of the starting inputs array used to restore the inputs to original values.

_results_tmpndarray

An array the same size as the system outputs. Used to store the results temporarily.

DEFAULT_OPTIONS = {'directional': False, 'form': 'forward', 'minimum_step': 1e-12, 'order': None, 'step': 1e-06, 'step_calc': 'abs'}
__init__()[source]

Initialize the ApproximationScheme.

Use this approximation scheme to approximate the derivative d(of)/d(wrt).

Parameters
abs_keytuple(str,str)

Absolute name pairing of (of, wrt) for the derivative.

systemSystem

Containing System.

kwargsdict

Additional keyword arguments, to be interpreted by sub-classes.

vectorndarray or None

Direction for difference when using directional derivatives.

apply_directional(data, direction)[source]

Apply stepsize to direction and embed into approximation data.

Parameters
datatuple

Tuple contains step size, and other info.

directionndarray

Vector containing derivative direction.

Returns
ndarray

New tuple with new step direction.

compute_approx_col_iter(system, under_cs=False)[source]

Execute the system to compute the approximate sub-Jacobians.

Parameters
systemSystem

System on which the execution is run.

under_csbool

True if we’re currently under complex step at a higher level.

Yields
int

column index

ndarray

solution array corresponding to the jacobian column at the given column index

compute_approximations(system, jac=None)

Execute the system to compute the approximate sub-Jacobians.

Parameters
systemSystem

System on which the execution is run.

jacNone or dict-like

If None, update system with the approximated sub-Jacobians. Otherwise, store the approximations in the given dict-like object.