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

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

1-D Splines

UnivariateSpline(x, y[, w, bbox, k, s]) Univariate spline s(x) of degree k on the interval [xb,xe] calculated from a given set of data points (x,y).
InterpolatedUnivariateSpline(x, y[, w, bbox, k]) Interpolated univariate spline approximation.
LSQUnivariateSpline(x, y, t[, w, bbox, k]) Weighted least-squares univariate spline approximation.

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]) 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, 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 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 the Lagrange interpolating polynomial of the data-points (x,w)
approximate_taylor_polynomial(f, x, degree, ...) Estimate the Taylor polynomial of f at x by polynomial fitting

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