complex_step.py#
Complex Step derivative approximations.
- class openmdao.approximation_schemes.complex_step.ComplexStep[source]
Bases:
ApproximationSchemeApproximation scheme using complex step to calculate derivatives.
For example, using a step size of ‘h’ will approximate the derivative in the following way:
\[f'(x) = \Im{\frac{f(x+ih)}{h}}.\]
- Attributes:
- _fd<FiniteDifference>
When nested complex step is detected, we switch to Finite Difference.
- DEFAULT_OPTIONS = {'directional': False, 'step': 1e-40}
- __init__()[source]
Initialize the ApproximationScheme.
- add_approximation(abs_key, system, kwargs, vector=None)[source]
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:
- datafloat
Step size for complex step.
- directionndarray
Vector containing derivative direction.
- Returns:
- ndarray
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.