Interpolation (scipy.interpolate)#

Sub-package for functions and objects used in interpolation.

See the user guide for recommendations on choosing a routine, and other usage details.

Univariate interpolation#

make_interp_spline(x, y[, k, t, bc_type, ...])

Create an interpolating B-spline with specified degree and boundary conditions.

CubicSpline(x, y[, axis, bc_type, extrapolate])

Piecewise cubic interpolator to fit values (C2 smooth).

PchipInterpolator(x, y[, axis, extrapolate])

PCHIP shape-preserving interpolator (C1 smooth).

Akima1DInterpolator(x, y[, axis, method, ...])

Akima "visually pleasing" interpolator (C1 smooth).

FloaterHormannInterpolator(points, values, *)

Floater-Hormann barycentric rational interpolator (C∞ smooth on real axis).

BarycentricInterpolator(xi[, yi, axis, wi, rng])

Barycentric (Lagrange with improved stability) interpolator (C∞ smooth).

KroghInterpolator(xi, yi[, axis])

Krogh interpolator (C∞ smooth).

CubicHermiteSpline(x, y, dydx[, axis, ...])

Piecewise cubic interpolator to fit values and first derivatives (C1 smooth).

Low-level data structures for univariate interpolation:

PPoly(c, x[, extrapolate, axis])

Piecewise polynomial in the power basis.

BPoly(c, x[, extrapolate, axis])

Piecewise polynomial in the Bernstein basis.

BSpline(t, c, k[, extrapolate, axis])

Univariate spline in the B-spline basis.

Multivariate interpolation#

Unstructured data

LinearNDInterpolator(points, values[, ...])

Piecewise linear interpolator in N > 1 dimensions.

NearestNDInterpolator(x, y[, rescale, ...])

Nearest-neighbor interpolator in N > 1 dimensions.

CloughTocher2DInterpolator(points, values[, ...])

Piecewise cubic, C1 smooth, curvature-minimizing interpolator in N=2 dimensions.

RBFInterpolator(y, d[, neighbors, ...])

Radial basis function interpolator in N ≥ 1 dimensions.

For data on a grid:

RegularGridInterpolator(points, values[, ...])

Interpolator of specified order on a rectilinear grid in N ≥ 1 dimensions.

See also

scipy.ndimage.map_coordinates, An example wrapper for map_coordinates

Low-level data structures for tensor product polynomials and splines:

NdPPoly(c, x[, extrapolate])

Piecewise tensor product polynomial

NdBSpline(t, c, k, *[, extrapolate])

Tensor product spline object.

1-D spline smoothing and approximation#

make_lsq_spline(x, y, t[, k, w, axis, ...])

Create a smoothing B-spline satisfying the Least SQuares (LSQ) criterion.

make_smoothing_spline(x, y[, w, lam, axis])

Create a smoothing B-spline satisfying the Generalized Cross Validation (GCV) criterion.

make_splrep(x, y, *[, w, xb, xe, k, s, t, nest])

Create a smoothing B-spline function with bounded error, minimizing derivative jumps.

make_splprep(x, *[, w, u, ub, ue, k, s, t, nest])

Create a smoothing parametric B-spline curve with bounded error, minimizing derivative jumps.

generate_knots(x, y, *[, w, xb, xe, k, s, nest])

Generate knot vectors until the Least SQuares (LSQ) criterion is satified.

Rational Approximation#

AAA(x, y, *[, rtol, max_terms, clean_up, ...])

AAA real or complex rational approximation.

Interfaces to FITPACK routines for 1D and 2D spline fitting#

This section lists wrappers for FITPACK functionality for 1D and 2D smoothing splines. In most cases, users are better off using higher-level routines listed in previous sections.

1D FITPACK splines#

This package provides two sets of functionally equivalent wrappers: object-oriented and functional.

Functional FITPACK interface:

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 a B-spline and all its derivatives at one point (or set of points) up to order k (the degree of the spline), being 0 the spline itself.

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.

2D FITPACK splines#

For data on a grid:

RectBivariateSpline(x, y, z[, bbox, kx, ky, ...])

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 (OOP interface):

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.

For unstructured data (functional interface):

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.

interpn(points, values, xi[, method, ...])

Multidimensional interpolation on regular or rectilinear grids.

griddata(points, values, xi[, method, ...])

Convenience function for interpolating unstructured data in multiple dimensions.

barycentric_interpolate(xi, yi, x[, axis, ...])

Convenience function for barycentric interpolation.

krogh_interpolate(xi, yi, x[, der, axis])

Convenience function for Krogh interpolation.

pchip_interpolate(xi, yi, x[, der, axis])

Convenience function for pchip interpolation.

Rbf(*args, **kwargs)

Class for radial basis function interpolation of functions from N-D scattered data to an M-D domain (legacy).

interp1d(x, y[, kind, axis, copy, ...])

Interpolate a 1-D function (legacy).

interp2d(x, y, z[, kind, copy, ...])

Class for 2D interpolation (deprecated and removed)

See also

scipy.ndimage.map_coordinates, scipy.ndimage.spline_filter,