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	Alternatively, make_interp_spline(..., k=1)
	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

Smoothing and approximation of data

1D spline functions	make_smoothing_spline	classic smoothing splines, GVC penalty
	make_splrep	automated/semi-automated knot selection
spine curves in N-D	make_splprep
unconstrained least squares spline fit	make_lsq_spline
2D smoothing surfaces	bisplrep	scattered data
	RectBivariateSpline	gridded data
Radial basis functions in N-D	RBFInterpolator

Further details are given in the links below

• 1-D interpolation
  • Piecewise linear interpolation
  • Cubic splines
  • Monotone interpolants
  • Interpolation with B-splines
    • Non-cubic splines
  • Parametric spline curves
  • Legacy interface for 1-D interpolation (interp1d)
    • Recommended replacements for interp1d modes
  • 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 1D
    • “Classic” smoothing splines and generalized cross-validation (GCV) criterion
    • Smoothing splines with automatic knot selection
    • Smoothing spline curves in \(d>1\)
    • Legacy routines for spline smoothing in 1-D
  • 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
  • Extrapolation in D > 1
• Interpolate transition guide
  • 1. How to transition away from using interp2d
    • 1.1 interp2d on a regular grid
    • 1.2. interp2d with full coordinates of points (scattered interpolation)
  • 2. Alternative to interp2d: regular grid
  • 3. Scattered 2D linear interpolation: prefer LinearNDInterpolator to SmoothBivariateSpline or bisplrep