InterpDerivativeEstimator

class InterpDerivativeEstimator(time_domain: ndarray, InterpolatorClass='cubic', new_time_domain: ndarray = None, **options)

Time derivative estimator based on interpolation.

For a set of (compressed) snapshots \(\Qhat = [~\qhat_0~~\cdots~~\qhat_{k-1}~] \in \RR^{r \times k}\), this class forms one-dimensional differentiable interpolants for each of the \(r\) rows of \(\Qhat\).

Parameters:

time_domain(k,) ndarray

Time domain of the snapshot data.

InterpolatorClassstr or scipy.interpolate class

Class for performing the interpolation. Must obey the following syntax:

>>> intrp = InterpolatorClass(time_domain, states, **options)
>>> new_states = intrp(new_time_domain, 0)
>>> state_ddts = intrp(new_time_domain, 1)

The following strings are also accepted.

• "cubic" (default): use scipy.interpolate.CubicSpline.

• "akima": use scipy.interpolate.Akima1DInterpolator. This is a local interpolation method and is more resitant to outliers than scipy.interpolate.CubicSpline. However, it is not recommended if the time points are not uniformly spaced.

• "pchip": use scipy.interpolate.PchipInterpolator. The interpolator preserves monotonicity in the interpolation data and does not overshoot if the data is not smooth.

new_time_domain(k’,) ndarray or None

If given, evaluate the interpolator at these points to generate new state snapshots and corresponding time derivatives. If input snapshots are also given, interpolate them as well and evaluate the interpolant at these new points. The new_time_domain should lie within the range of the original time_domain; a warning is raised if extrapolation is requested.

optionsdict

Keyword arguments for the constructor of the InterpolatorClass.

Properties:

InterpolatorClass

One-dimensional differentiable interpolator class.

new_time_domain

Time domain at which to evaluate the interpolator and its first derivative.

options

Keyword arguments for the constructor of the InterpolatorClass.

time_domain

Time domain of the snapshot data, a (k,) ndarray.

Methods:

estimate	Estimate the first time derivatives of the states.
verify	Verify that estimate() is consistent in the sense that the all outputs have the same number of columns and test the accuracy of the results on a few test problems.
verify_shapes	Verify that estimate() is consistent in the sense that the all outputs have the same number of columns.