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# Interpolation (`scipy.interpolate`)

## Univariate interpolation

`interp1d`(x, y[, kind, axis, copy, ...]) | Interpolate a 1D 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.

Data given on a regular grid:

`interp2d`(x, y, z[, kind, copy, ...]) | Interpolate over a 2D grid.

## 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

See also

scipy.ndimage.map_coordinates

`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, None, None[, ...]) | Smooth bivariate spline approximation.
`LSQBivariateSpline`(x, y, z, tx, ty, None, None) | 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.

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