gemseo.utils.derivatives.finite_differences module#
Gradient approximation by finite differences.
- class FirstOrderFD(f_pointer, step=None, design_space=None, normalize=True, parallel=False, **parallel_args)[source]#
Bases:
BaseGradientApproximator
First-order finite differences approximator.
\[\begin{split}\frac{df(x)}{dx}\approx\frac{f(x+\\delta x)-f(x)}{\\delta x}\end{split}\]- Parameters:
f_pointer (Callable[[ndarray, Any, ...], ndarray]) -- The pointer to the function to derive.
step (complex | ndarray | None) -- The default differentiation step.
design_space (DesignSpace | None) -- The design space containing the upper bounds of the input variables. If
None
, consider that the input variables are unbounded.normalize (bool) --
Whether to normalize the function.
By default it is set to True.
parallel (bool) --
Whether to differentiate the function in parallel.
By default it is set to False.
**parallel_args (Any) -- The parallel execution options, see
gemseo.core.parallel_execution
.
- compute_optimal_step(x_vect, numerical_error=2.220446049250313e-16, **kwargs)[source]#
Compute the gradient by real step.
- Parameters:
x_vect (ndarray) -- The input vector.
numerical_error (float) --
The numerical error associated to the calculation of \(f\). By default, machine epsilon (appx 1e-16), but can be higher. when the calculation of \(f\) requires a numerical resolution.
By default it is set to 2.220446049250313e-16.
**kwargs -- The additional arguments passed to the function.
- Returns:
The optimal steps. The errors.
- Return type: