Interpolation (scipy.interpolate)

There are several general facilities available in SciPy for interpolation and smoothing for data in 1, 2, and higher dimensions. The choice of a specific interpolation routine depends on the data: whether it is one-dimensional, is given on a structured grid, or is unstructured. One other factor is the desired smoothness of the interpolator. In short, routines recommended for interpolation can be summarized as follows:

	kind	routine	continuity	comment
1D	linear	numpy.interp	piecewise continuous	comes from numpy
	cubic spline	CubicSpline	2nd derivative
	monotone cubic spline	PchipInterpolator	1st derivative	non-overshooting
	non-cubic spline	make_interp_spline	(k-1)th derivative	k=3 is equivalent to CubicSpline
	nearest	interp1d		kind=’nearest’, ‘previous’, ‘next’
N-D curve	nearest, linear, spline	make_interp_spline	(k-1)th derivative	use N-dim y array
N-D regular (rectilinear) grid	nearest	RegularGridInterpolator		method=’nearest’
	linear			method=’linear’
	splines		2nd derivatives	method=’cubic’, ‘quintic’
	monotone splines		1st derivatives	method=’pchip’
N-D scattered	nearest	NearestNDInterpolator		alias: griddata
	linear	LinearNDInterpolator
	cubic (2D only)	CloughTocher2DInterpolator	1st derivatives
	radial basis function	RBFInterpolator

For data smoothing, functions are provided for 1- and 2-D data using cubic splines, based on the FORTRAN library FITPACK.

Additionally, routines are provided for interpolation / smoothing using radial basis functions with several kernels.

Futher details are given in the links below.

• 1-D interpolation
  • Piecewise linear interpolation
  • Cubic splines
  • Monotone interpolants
  • Interpolation with B-splines
  • Parametric spline curves
  • Legacy interface for 1-D interpolation (interp1d)
  • Missing data
• Piecewise polynomials and splines
  • Manipulating PPoly objects
  • B-splines: knots and coefficients
    • B-spline basis elements
    • Design matrices in the B-spline basis
• Smoothing splines
  • Spline smoothing in 1-D
    • Procedural (splrep)
    • Object-oriented (UnivariateSpline)
  • 2-D smoothing splines
    • Bivariate spline fitting of scattered data
    • Bivariate spline fitting of data on a grid
    • Bivariate spline fitting of data in spherical coordinates
• Multivariate data interpolation on a regular grid (RegularGridInterpolator)
  • Uniformly spaced data
• Scattered data interpolation (griddata)
• Using radial basis functions for smoothing/interpolation
  • 1-D Example
  • 2-D Example
• Extrapolation tips and tricks
  • interp1d : replicate numpy.interp left and right fill values
  • CubicSpline extend the boundary conditions
  • Manually implement the asymptotics
    • The setup
    • Use the known asymptotics
  • Exrapolation in D > 1