Tabulated derivatives#

This section shows how to compute derivatives using derivkit.derivative_kit.DerivativeKit.differentiate() when your model is available only as tabulated data on a one-dimensional grid, rather than as an explicit Python function.

In this case, DerivKit first constructs an interpolated representation of the tabulated values, and then applies the selected derivative backend to that interpolant.

This is useful when working with simulation outputs, precomputed theory tables, or externally generated data products where the underlying function cannot be evaluated analytically.

For more information on this and other implemented derivative methods, see DerivativeKit.

Basic usage#

>>> import numpy as np
>>> from derivkit.derivative_kit import DerivativeKit
>>> # Tabulate y = x^2 on a coarse grid
>>> x_tab = np.linspace(0.0, 3.0, 7)
>>> y_tab = x_tab**2
>>> x0 = 1.5  # point where to evaluate the derivative
>>> # Initialize DerivativeKit with tabulated data
>>> dk = DerivativeKit(x0=x0, tab_x=x_tab, tab_y=y_tab)
>>> # First derivative (default method is "adaptive")
>>> deriv = dk.differentiate(order=1)
>>> err = abs(deriv - 2.0 * x0)  # reference: d/dx x^2 = 2x
>>> bool(np.isfinite(deriv) and (err < 1e-5))
True

Finite differences on tabulated data#

>>> import numpy as np
>>> from derivkit.derivative_kit import DerivativeKit
>>> # Tabulate y = sin(x) on a coarse grid
>>> x_tab = np.linspace(0.0, 3.0, 21)
>>> y_tab = np.sin(x_tab)
>>> x0 = 0.7  # derivative evaluation point
>>> # Initialize DerivativeKit with tabulated data
>>> dk = DerivativeKit(x0=x0, tab_x=x_tab, tab_y=y_tab)
>>> # First derivative using finite differences
>>> deriv = dk.differentiate(
...     method="finite",
...     order=1,
...     stepsize=1e-2,
...     num_points=5,
...     extrapolation="ridders",
...     levels=4,
... )
>>> err = abs(deriv - np.cos(x0))  # reference
>>> bool(np.isfinite(deriv) and (err < 0.1))
True

Adaptive fit on tabulated data#

>>> import numpy as np
>>> from derivkit.derivative_kit import DerivativeKit
>>> # Tabulate y = sin(x) on a coarse grid
>>> x_tab = np.linspace(0.0, 3.0, 21)
>>> y_tab = np.sin(x_tab)
>>> x0 = 0.7  # point where to evaluate the derivative
>>> # Initialize DerivativeKit with tabulated data
>>> dk = DerivativeKit(x0=x0, tab_x=x_tab, tab_y=y_tab)
>>> # First derivative using adaptive polynomial fit
>>> deriv = dk.differentiate(
...     method="adaptive",
...     order=1,
...     n_points=12,
...     spacing="auto",
...     ridge=1e-10,
... )
>>> err = abs(deriv - np.cos(x0))  # reference
>>> bool(np.isfinite(deriv) and (err < 0.1))
True

Notes#

tab_x and tab_y must be provided together.
Derivative accuracy depends on the tabulation density and the interpolation behavior of the underlying tabulated model.
As with other backends, you can pass an array to x0 to evaluate derivatives at multiple points (stacked with leading shape x0.shape).