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, axis]) | The interpolating polynomial for a set of points |
| KroghInterpolator(xi, yi[, axis]) | Interpolating polynomial for a set of points. |
| PchipInterpolator(x, y[, axis, extrapolate]) | PCHIP 1-d monotonic cubic interpolation. |
| barycentric_interpolate(xi, yi, x[, axis]) | 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. |
| Akima1DInterpolator(x, y[, axis]) | 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-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:
| interpn(points, values, xi[, method, ...]) | Multidimensional interpolation on regular grids. |
| RegularGridInterpolator(points, values[, ...]) | Interpolation on a regular grid in arbitrary dimensions |
| RectBivariateSpline(x, y, z[, bbox, kx, ky, s]) | Bivariate spline approximation over a rectangular mesh. |
See also
Tensor product polynomials:
| NdPPoly(c, x[, extrapolate]) | Piecewise tensor product polynomial |
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 B-spline. |
Functional interface to FITPACK routines:
| 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 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, ...]) | One-dimensional smoothing spline fit to a given set of data points. |
| InterpolatedUnivariateSpline(x, y[, w, ...]) | 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. |
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) | Return Pade approximation to a polynomial as the ratio of two polynomials. |
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.
Functions existing for backward compatibility (should not be used in new code):
| ppform(coeffs, breaks[, fill, sort]) | Deprecated piecewise polynomial class. |
| spleval(*args, **kwds) | spleval is deprecated! |
| spline(*args, **kwds) | spline is deprecated! |
| splmake(*args, **kwds) | splmake is deprecated! |
| spltopp(*args, **kwds) | spltopp is deprecated! |
| pchip | alias of PchipInterpolator |