# 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, wi, ...]) Interpolating polynomial for a set of points. KroghInterpolator(xi, yi[, axis]) Interpolating polynomial for a set of points. barycentric_interpolate(xi, yi, x[, axis, der]) 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, method, ...]) 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 interpolator in N > 1 dimensions. NearestNDInterpolator(x, y[, rescale, ...]) NearestNDInterpolator(x, y). CloughTocher2DInterpolator(points, values[, ...]) CloughTocher2DInterpolator(points, values, tol=1e-6). RBFInterpolator(y, d[, neighbors, ...]) Radial basis function (RBF) interpolation in N dimensions. Rbf(*args, **kwargs) 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, ...]) Removed in version 1.14.0.

For data on a grid:

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

Tensor product polynomials:

 NdPPoly(c, x[, extrapolate]) Piecewise tensor product polynomial NdBSpline(t, c, k, *[, extrapolate]) Tensor product spline object.

## 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 (Least SQuared) based fitting B-spline. make_smoothing_spline(x, y[, w, lam]) Compute the (coefficients of) smoothing cubic spline function using lam to control the tradeoff between the amount of smoothness of the curve and its proximity to the data.

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 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.

## 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:

 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.

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