Interpolation (`scipy.interpolate`)#

Sub-package for objects used in interpolation.

As listed below, this sub-package contains spline functions and classes, 1-D and multidimensional (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, wi, ...])	Interpolating polynomial for a set of points.
`KroghInterpolator`(xi, yi[, axis])	Interpolating polynomial for a set of points.
`barycentric_interpolate`(xi, yi, x[, axis, der])	Convenience function for polynomial interpolation.
`krogh_interpolate`(xi, yi, x[, der, axis])	Convenience function for polynomial interpolation.
`pchip_interpolate`(xi, yi, x[, der, axis])	Convenience function for pchip interpolation.
`CubicHermiteSpline`(x, y, dydx[, axis, ...])	Piecewise-cubic interpolator matching values and first derivatives.
`PchipInterpolator`(x, y[, axis, extrapolate])	PCHIP 1-D monotonic cubic interpolation.
`Akima1DInterpolator`(x, y[, axis, method])	Akima interpolator
`CubicSpline`(x, y[, axis, bc_type, extrapolate])	Cubic spline data 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-D data.
`LinearNDInterpolator`(points, values[, ...])	Piecewise linear interpolator in N > 1 dimensions.
`NearestNDInterpolator`(x, y[, rescale, ...])	NearestNDInterpolator(x, y).
`CloughTocher2DInterpolator`(points, values[, ...])	CloughTocher2DInterpolator(points, values, tol=1e-6).
`RBFInterpolator`(y, d[, neighbors, ...])	Radial basis function (RBF) interpolation in N dimensions.
`Rbf`(args, *kwargs)	A class for radial basis function interpolation of functions from N-D scattered data to an M-D domain.
`interp2d`(x, y, z[, kind, copy, ...])	Deprecated since version 1.10.0.

For data on a grid:

`interpn`(points, values, xi[, method, ...])	Multidimensional interpolation on regular or rectilinear grids.
`RegularGridInterpolator`(points, values[, ...])	Interpolator on a regular or rectilinear grid in arbitrary dimensions.
`RectBivariateSpline`(x, y, z[, bbox, kx, ky, s])	Bivariate spline approximation over a rectangular mesh.

1-D Splines#

`BSpline`(t, c, k[, extrapolate, axis])	Univariate spline in the B-spline basis.
`make_interp_spline`(x, y[, k, t, bc_type, ...])	Compute the (coefficients of) interpolating B-spline.
`make_lsq_spline`(x, y, t[, k, w, axis, ...])	Compute the (coefficients of) an LSQ (Least SQuared) based fitting B-spline.
`make_smoothing_spline`(x, y[, w, lam])	Compute the (coefficients of) smoothing cubic spline function using `lam` to control the tradeoff between the amount of smoothness of the curve and its proximity to the data.

Functional interface to FITPACK routines:

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

Object-oriented FITPACK interface:

`UnivariateSpline`(x, y[, w, bbox, k, s, ext, ...])	1-D smoothing spline fit to a given set of data points.
`InterpolatedUnivariateSpline`(x, y[, w, ...])	1-D interpolating spline for a given set of data points.
`LSQUnivariateSpline`(x, y, t[, w, bbox, k, ...])	1-D spline with explicit internal knots.

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.

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.
`pade`(an, m[, n])	Return Pade approximation to a polynomial as the ratio of two polynomials.

`NdPPoly`(c, x[, extrapolate])	Piecewise tensor product polynomial
`NdBSpline`(t, c, k, *[, extrapolate])	Tensor product spline object.

Interpolation (scipy.interpolate)#