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-neighbor interpolation are supported. After setting up the interpolator object, the interpolation method ( *linear* or *nearest* ) may be chosen at each evaluation.
Parameters ---------- points : tuple of ndarray of float, with shapes (m1, ), ..., (mn, ) The points defining the regular grid in n dimensions.
values : array_like, shape (m1, ..., mn, ...) The data on the regular grid in n dimensions.
method : str, 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_error : bool, 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_value : number, optional If provided, the value to use for points outside of the interpolation domain. If None, values outside the domain are extrapolated.
Methods ------- __call__
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.
.. versionadded:: 0.14
Examples -------- Evaluate a simple example function on the points of a 3-D 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 3-D array with ``datai,j,k = f(xi, yj, zk)``. 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)``.
See also -------- NearestNDInterpolator : Nearest neighbor interpolation on unstructured data in N dimensions
LinearNDInterpolator : Piecewise linear interpolant on unstructured data in N dimensions
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