# Interpolation (scipy.interpolate)¶

Sub-package for objects used in interpolation.

As listed below, this sub-package contains spline functions and classes, one-dimensional and multi-dimensional (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. PiecewisePolynomial(xi, yi[, orders, ...]) Piecewise polynomial curve specified by points and derivatives PchipInterpolator(x, y[, axis, extrapolate]) PCHIP 1-d monotonic cubic interpolation. barycentric_interpolate(xi, yi, x[, axis]) Convenience function for polynomial interpolation. krogh_interpolate(xi, yi, x[, der, axis]) Convenience function for polynomial interpolation. piecewise_polynomial_interpolate(xi, yi, x) Convenience function for piecewise polynomial interpolation. pchip_interpolate(xi, yi, x[, der, axis]) Convenience function for pchip interpolation. Akima1DInterpolator(x, y[, axis]) Akima 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-dimensional data. LinearNDInterpolator(points, values[, ...]) Piecewise linear interpolant in N dimensions. NearestNDInterpolator(points, values) Nearest-neighbour 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 approximation/interpolation of n-dimensional scattered data. 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.

scipy.ndimage.interpolation.map_coordinates

## 1-D Splines¶

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

Functional interface to FITPACK functions:

 splrep(x, y[, w, xb, xe, k, task, s, t, ...]) Find the B-spline representation of 1-D curve. splprep(x[, w, u, ub, ue, k, task, s, t, ...]) Find the B-spline representation of an N-dimensional 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. 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.

## 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.

 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.

Functions existing for backward compatibility (should not be used in new code):

 ppform(coeffs, breaks[, fill, sort]) Deprecated piecewise polynomial class. spleval(xck, xnew[, deriv]) Evaluate a fixed spline represented by the given tuple at the new x-values spline(xk, yk, xnew[, order, kind, conds]) Interpolate a curve at new points using a spline fit splmake(xk, yk[, order, kind, conds]) Return a representation of a spline given data-points at internal knots spltopp(xk, cvals, k) Return a piece-wise polynomial object from a fixed-spline tuple. pchip alias of PchipInterpolator

#### Previous topic

scipy.integrate.complex_ode.successful

#### Next topic

scipy.interpolate.interp1d