Interpolation (scipy.interpolate)

Sub-package for objects used in interpolation.

As listed below, this sub-package contains spline functions and classes, 1-D and multidimensional (univariate and multivariate) interpolation classes, Lagrange and Taylor polynomial interpolators, and wrappers for FITPACK and DFITPACK functions.

Univariate interpolation

interp1d(x, y[, kind, axis, copy, …])	Interpolate a 1-D function.
BarycentricInterpolator(xi[, yi, axis])	The interpolating polynomial for a set of points
KroghInterpolator(xi, yi[, axis])	Interpolating polynomial for a set of points.
barycentric_interpolate(xi, yi, x[, axis])	Convenience function for polynomial interpolation.
krogh_interpolate(xi, yi, x[, der, axis])	Convenience function for polynomial interpolation.
pchip_interpolate(xi, yi, x[, der, axis])	Convenience function for pchip interpolation.
CubicHermiteSpline(x, y, dydx[, axis, …])	Piecewise-cubic interpolator matching values and first derivatives.
PchipInterpolator(x, y[, axis, extrapolate])	PCHIP 1-D monotonic cubic interpolation.
Akima1DInterpolator(x, y[, axis])	Akima interpolator
CubicSpline(x, y[, axis, bc_type, extrapolate])	Cubic spline data interpolator.
PPoly(c, x[, extrapolate, axis])	Piecewise polynomial in terms of coefficients and breakpoints
BPoly(c, x[, extrapolate, axis])	Piecewise polynomial in terms of coefficients and breakpoints.

Multivariate interpolation

Unstructured data:

griddata(points, values, xi[, method, …])	Interpolate unstructured D-D data.
LinearNDInterpolator(points, values[, …])	Piecewise linear interpolant in N dimensions.
NearestNDInterpolator(x, y)	Nearest-neighbor interpolation in N dimensions.
CloughTocher2DInterpolator(points, values[, tol])	Piecewise cubic, C1 smooth, curvature-minimizing interpolant in 2D.
Rbf(*args)	A class for radial basis function interpolation of functions from N-D scattered data to an M-D domain.
interp2d(x, y, z[, kind, copy, …])	Interpolate over a 2-D grid.

For data on a grid:

interpn(points, values, xi[, method, …])	Multidimensional interpolation on regular grids.
RegularGridInterpolator(points, values[, …])	Interpolation on a regular grid in arbitrary dimensions
RectBivariateSpline(x, y, z[, bbox, kx, ky, s])	Bivariate spline approximation over a rectangular mesh.

See also

scipy.ndimage.map_coordinates

Tensor product polynomials:

NdPPoly(c, x[, extrapolate])

Piecewise tensor product polynomial

1-D Splines

BSpline(t, c, k[, extrapolate, axis])	Univariate spline in the B-spline basis.
make_interp_spline(x, y[, k, t, bc_type, …])	Compute the (coefficients of) interpolating B-spline.
make_lsq_spline(x, y, t[, k, w, axis, …])	Compute the (coefficients of) an LSQ B-spline.

Functional interface to FITPACK routines:

splrep(x, y[, w, xb, xe, k, task, s, t, …])	Find the B-spline representation of a 1-D curve.
splprep(x[, w, u, ub, ue, k, task, s, t, …])	Find the B-spline representation of an N-D curve.
splev(x, tck[, der, ext])	Evaluate a B-spline or its derivatives.
splint(a, b, tck[, full_output])	Evaluate the definite integral of a B-spline between two given points.
sproot(tck[, mest])	Find the roots of a cubic B-spline.
spalde(x, tck)	Evaluate all derivatives of a B-spline.
splder(tck[, n])	Compute the spline representation of the derivative of a given spline
splantider(tck[, n])	Compute the spline for the antiderivative (integral) of a given spline.
insert(x, tck[, m, per])	Insert knots into a B-spline.

Object-oriented FITPACK interface:

UnivariateSpline(x, y[, w, bbox, k, s, ext, …])	1-D smoothing spline fit to a given set of data points.
InterpolatedUnivariateSpline(x, y[, w, …])	1-D interpolating spline for a given set of data points.
LSQUnivariateSpline(x, y, t[, w, bbox, k, …])	1-D spline with explicit internal knots.

2-D Splines

For data on a grid:

RectBivariateSpline(x, y, z[, bbox, kx, ky, s])	Bivariate spline approximation over a rectangular mesh.
RectSphereBivariateSpline(u, v, r[, s, …])	Bivariate spline approximation over a rectangular mesh on a sphere.

For unstructured data:

BivariateSpline	Base class for bivariate splines.
SmoothBivariateSpline(x, y, z[, w, bbox, …])	Smooth bivariate spline approximation.
SmoothSphereBivariateSpline(theta, phi, r[, …])	Smooth bivariate spline approximation in spherical coordinates.
LSQBivariateSpline(x, y, z, tx, ty[, w, …])	Weighted least-squares bivariate spline approximation.
LSQSphereBivariateSpline(theta, phi, r, tt, tp)	Weighted least-squares bivariate spline approximation in spherical coordinates.

Low-level interface to FITPACK functions:

bisplrep(x, y, z[, w, xb, xe, yb, ye, kx, …])	Find a bivariate B-spline representation of a surface.
bisplev(x, y, tck[, dx, dy])	Evaluate a bivariate B-spline and its derivatives.

Additional tools

lagrange(x, w)	Return a Lagrange interpolating polynomial.
approximate_taylor_polynomial(f, x, degree, …)	Estimate the Taylor polynomial of f at x by polynomial fitting.
pade(an, m[, n])	Return Pade approximation to a polynomial as the ratio of two polynomials.

See also

scipy.ndimage.map_coordinates, scipy.ndimage.spline_filter, scipy.signal.resample, scipy.signal.bspline, scipy.signal.gauss_spline, scipy.signal.qspline1d, scipy.signal.cspline1d, scipy.signal.qspline1d_eval, scipy.signal.cspline1d_eval, scipy.signal.qspline2d, scipy.signal.cspline2d.

pchip is an alias of PchipInterpolator for backward compatibility (should not be used in new code).