sjev / interp2d

Fast bilinear interpolation in python.

interp2d

Fast bilinear interpolation in Python. Only to be used on a regular 2D grid, where it is more efficient than scipy.interpolate.RectBivariateSpline in the case of a continually changing interpolation grid (see Comparison with scipy.interpolate below).

Usage

There is only one function (defined in __init__.py), interp2d. This works much like the interp function in numpy.

Given a regular coordinate grid and gridded data defined as follows:

import numpy as np
from interp2d import interp2d

# define coordinate grid, xp and yp both 1D arrays
xp = np.linspace(0, 1, 200)
yp = np.linspace(-6 * np.pi, 6 * np.pi, 200)

# gridded data, zp is 2D array
zp = xp[:, None]**2 * np.sin(yp[None])

Subsequently, one can then interpolate within this grid. The interpolation points can either be single scalars or arrays of points.

>>> interp2d(0.5, 0.78*np.pi, xp, yp, zp)
0.15866472278446267

>>> x = np.linspace(0.1, 0.2, 5)
>>> y = 0.5 * np.pi * np.ones_like(x)
>>> interp2d(x, y, xp, yp, zp)
array([0.00997272, 0.01558158, 0.02243672, 0.03053814, 0.03988582])

Interpolation points outside the given coordinate grid will be evaluated on the boundary.

Comparison with scipy.interpolate

The standard way to do two-dimensional interpolation in the Python scientific ecosystem is with the various interpolators defined in the scipy.interpolate sub-package. If one is interpolating on a regular grid, the fastest option there is the object RectBivariateSpline. To use this, you first construct an instance of RectBivariateSpline feeding in the coordinate grids and data. This then provides a function, which can be called to give interpolated values. While these function calls are cheap, setting up the grid is less so. So, if one is interpolating from a continually changing grid (e.g. interpolating density from a grid in a time-evolving simulation), the scipy options are not ideal. To see this consider the following example, where x, y, xp, yp, zp are defined as in the previous example (in Usage above).

>>> %timeit interp2d(x, y, xp, yp, zp)
31.2 µs ± 197 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)

>>> %timeit RectBivariateSpline(xp, yp, zp, kx=1, ky=1)(x, y, grid=False)
1.14 ms ± 5.1 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)

Thus, we have a 40x speedup.

Prerequisites

The only prerequisite is numpy. My code was developed and tested using version 1.20.3, but earlier/later versions likely to work also.