Derivatives

Finite-difference utilities for first and second derivatives on uniformly spaced one-dimensional grids.

Finite-difference derivative helpers on uniformly spaced 1D grids.

This module provides simple central-difference routines for first and second derivatives. Both functions return the derivative evaluated on the interior points only (the first and last grid points are dropped).

edlgt.tools.derivatives.first_derivative(grid_values, function_values, dx)[source]

Compute the first derivative using a central-difference stencil.

Parameters:

grid_values (numpy.ndarray) – One-dimensional grid values. Only interior points are returned.
function_values (numpy.ndarray) – Function values sampled on grid_values.
dx (float) – Uniform grid spacing.

Returns:

(x_interior, df_dx) as two NumPy arrays, both of length len(grid_values) - 2.

Return type:

tuple

Notes

This routine assumes a uniformly spaced grid and uses the standard second-order central-difference approximation on interior points.

edlgt.tools.derivatives.second_derivative(grid_values, function_values, dx)[source]

Compute the second derivative using a central-difference stencil.