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# 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]) | 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.

## 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.

See also

`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 given points.
`UnivariateSpline.roots`() | Return the zeros of the spline.
`UnivariateSpline.get_coeffs`() | Return spline coefficients.
`UnivariateSpline.get_knots`() | Return positions of (boundary and interior) knots of the spline.
`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.
`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.
`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.

## 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.

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`.

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