# 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]) The interpolating polynomial for a set of points KroghInterpolator(xi, yi) The interpolating polynomial for a set of points PiecewisePolynomial(xi, yi[, orders, direction]) Piecewise polynomial curve specified by points and derivatives barycentric_interpolate(xi, yi, x) Convenience function for polynomial interpolation krogh_interpolate(xi, yi, x[, der]) Convenience function for polynomial interpolation. piecewise_polynomial_interpolate(xi, yi, x) Convenience function for piecewise polynomial interpolation

## Multivariate interpolation¶

Unstructured data:

 griddata(points, values, xi[, method, ...]) Interpolate unstructured N-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:

 RectBivariateSpline(x, y, z[, bbox, kx, ky, s]) Bivariate spline approximation over a rectangular mesh.

scipy.ndimage.map_coordinates

## 1-D Splines¶

 UnivariateSpline(x, y[, w, bbox, k, s]) One-dimensional smoothing spline fit to a given set of data points. InterpolatedUnivariateSpline(x, y[, w, bbox, k]) 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.

The above univariate spline classes have the following methods:

 UnivariateSpline.__call__(x[, nu]) Evaluate spline (or its nu-th derivative) at positions x. UnivariateSpline.derivatives(x) Return all derivatives of the spline at the point x. UnivariateSpline.integral(a, b) Return definite integral of the spline between two UnivariateSpline.roots() Return the zeros of the spline. UnivariateSpline.get_coeffs() Return spline coefficients. UnivariateSpline.get_knots() Return the positions of (boundary and interior) UnivariateSpline.get_residual() Return weighted sum of squared residuals of the spline UnivariateSpline.set_smoothing_factor(s) Continue spline computation with the given smoothing

Low-level 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. 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.

## 2-D Splines¶

For data on a grid:

 RectBivariateSpline(x, y, z[, bbox, kx, ky, s]) Bivariate spline approximation over a rectangular mesh.

For unstructured data:

 BivariateSpline Bivariate spline s(x,y) of degrees kx and ky on the rectangle [xb,xe] x [yb, ye] calculated from a given set of data points (x,y,z). SmoothBivariateSpline(x, y, z[, w, bbox, ...]) Smooth bivariate spline approximation. LSQBivariateSpline(x, y, z, tx, ty[, w, ...]) Weighted least-squares bivariate spline approximation.

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.

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.