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# Interpolation (`scipy.interpolate`)

## Univariate interpolation

`interp1d` | Interpolate a 1D function.
`BarycentricInterpolator` | The interpolating polynomial for a set of points
`KroghInterpolator` | The interpolating polynomial for a set of points
`PiecewisePolynomial` | 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[, orders, der]) | Convenience function for piecewise polynomial interpolation

## Multivariate interpolation

`interp2d` (x, y, z[, kind, copy, bounds_error, ...]) | Interpolate over a 2D grid.
`Rbf` (*args) | A class for radial basis function approximation/interpolation of n-dimensional scattered data.

## 1-D Splines

`UnivariateSpline` | Univariate spline s(x) of degree k on the interval [xb,xe] calculated from a given set of data points (x,y).
`InterpolatedUnivariateSpline` | Interpolated univariate spline approximation. Identical to UnivariateSpline with less error checking.
`LSQUnivariateSpline` | Weighted least-squares univariate spline approximation. Appears to be identical to UnivariateSpline with more error checking.

The above univariate spline classes have the following methods:

`UnivariateSpline.__call__` (self, x[, nu]) | Evaluate spline (or its nu-th derivative) at positions x. Note: x can be unordered but the evaluation is more efficient if x is (partially) ordered.
`UnivariateSpline.derivatives` (self, x) | Return all derivatives of the spline at the point x.
`UnivariateSpline.integral` (self, a, b) | Return definite integral of the spline between two given points.
`UnivariateSpline.roots` (self) | Return the zeros of the spline.
`UnivariateSpline.get_coeffs` (self) | Return spline coefficients.
`UnivariateSpline.get_knots` (self) | Return the positions of (boundary and interior) knots of the spline.
`UnivariateSpline.get_residual` (self) | Return weighted sum of squared residuals of the spline approximation: sum ((w[i]*(y[i]-s(x[i])))**2,axis=0)
`UnivariateSpline.set_smoothing_factor` (self, s) | Continue spline computation with the given smoothing factor s and with the knots found at the last call.

Low-level interface to FITPACK functions:

`splrep` (x, y[, w, xb, xe, k, task, ...]) | Find the B-spline representation of 1-D curve.
`splprep` (x[, w, u, ub, ue, k, ...]) | Find the B-spline representation of an N-dimensional curve.
`splev` (x, tck[, der]) | Evaulate a B-spline and 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, ...]) | 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` | Smooth bivariate spline approximation.
`LSQBivariateSpline` | Weighted least-squares spline approximation. See also:

Low-level interface to FITPACK functions:

`bisplrep` (x, y, z[, w, xb, xe, yb, ye, ...]) | 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 the Lagrange interpolating polynomial of the data-points (x,w)
`approximate_taylor_polynomial` (f, x, degree, scale[, order]) | Estimate the Taylor polynomial of f at x by polynomial fitting

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