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
pchip(x, y) PCHIP 1-d monotonic cubic interpolation
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.

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 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.

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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