scipy.interpolate.RegularGridInterpolator

class scipy.interpolate.RegularGridInterpolator(points, values, method='linear', bounds_error=True, fill_value=nan)

Interpolation on a regular grid in arbitrary dimensions

The data must be defined on a regular grid; the grid spacing however may be uneven. Linear and nearest-neighbour interpolation are supported. After setting up the interpolator object, the interpolation method (linear or nearest) may be chosen at each evaluation.

Parameters

pointstuple of ndarray of float, with shapes (m1, ), …, (mn, )

The points defining the regular grid in n dimensions.

valuesarray_like, shape (m1, …, mn, …)

The data on the regular grid in n dimensions.

methodstr, optional

The method of interpolation to perform. Supported are “linear” and “nearest”. This parameter will become the default for the object’s __call__ method. Default is “linear”.

bounds_errorbool, optional

If True, when interpolated values are requested outside of the domain of the input data, a ValueError is raised. If False, then fill_value is used.

fill_valuenumber, optional

If provided, the value to use for points outside of the interpolation domain. If None, values outside the domain are extrapolated.

See also

NearestNDInterpolator

Nearest neighbour interpolation on unstructured data in N dimensions

LinearNDInterpolator

Piecewise linear interpolant on unstructured data in N dimensions

Notes

Contrary to LinearNDInterpolator and NearestNDInterpolator, this class avoids expensive triangulation of the input data by taking advantage of the regular grid structure.

If any of points have a dimension of size 1, linear interpolation will return an array of nan values. Nearest-neighbor interpolation will work as usual in this case.

New in version 0.14.

References

1

Python package regulargrid by Johannes Buchner, see https://pypi.python.org/pypi/regulargrid/

2

Wikipedia, “Trilinear interpolation”, https://en.wikipedia.org/wiki/Trilinear_interpolation

3

Weiser, Alan, and Sergio E. Zarantonello. “A note on piecewise linear and multilinear table interpolation in many dimensions.” MATH. COMPUT. 50.181 (1988): 189-196. https://www.ams.org/journals/mcom/1988-50-181/S0025-5718-1988-0917826-0/S0025-5718-1988-0917826-0.pdf

Examples

Evaluate a simple example function on the points of a 3D grid:

>>> from scipy.interpolate import RegularGridInterpolator
>>> def f(x, y, z):
...     return 2 * x**3 + 3 * y**2 - z
>>> x = np.linspace(1, 4, 11)
>>> y = np.linspace(4, 7, 22)
>>> z = np.linspace(7, 9, 33)
>>> data = f(*np.meshgrid(x, y, z, indexing='ij', sparse=True))

data is now a 3D array with data[i,j,k] = f(x[i], y[j], z[k]). Next, define an interpolating function from this data:

>>> my_interpolating_function = RegularGridInterpolator((x, y, z), data)

Evaluate the interpolating function at the two points (x,y,z) = (2.1, 6.2, 8.3) and (3.3, 5.2, 7.1):

>>> pts = np.array([[2.1, 6.2, 8.3], [3.3, 5.2, 7.1]])
>>> my_interpolating_function(pts)
array([ 125.80469388,  146.30069388])

which is indeed a close approximation to [f(2.1, 6.2, 8.3), f(3.3, 5.2, 7.1)].

Methods

__call__(xi[, method])

Interpolation at coordinates