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.. _tutorial-interpolate:
========================================
Interpolation (:mod:`scipy.interpolate`)
========================================
.. sectionauthor:: Travis E. Oliphant
.. sectionauthor:: Pauli Virtanen
.. sectionauthor:: Evgeni Burovski
.. currentmodule:: scipy.interpolate
There are several general facilities available in SciPy for interpolation and
smoothing for data in 1, 2, and higher dimensions. The choice of a specific
interpolation routine depends on the data: whether it is one-dimensional,
is given on a structured grid, or is unstructured. One other factor is the
desired smoothness of the interpolator. In short, routines recommended *for
interpolation* can be summarized as follows:
+------------------+-------------------------+------------------------------+------------------------+---------------------------------------+
| | **kind** | **routine** | **continuity** | **comment** |
+==================+=========================+==============================+========================+=======================================+
| | linear | `numpy.interp` | piecewise continuous | Alternatively, |
| | | | | ``make_interp_spline(..., k=1)`` |
+ +-------------------------+------------------------------+------------------------+---------------------------------------+
| | cubic spline | `CubicSpline` | 2nd derivative | |
+ +-------------------------+------------------------------+------------------------+---------------------------------------+
| 1D | monotone cubic spline | `PchipInterpolator` | 1st derivative | non-overshooting |
+ +-------------------------+------------------------------+------------------------+---------------------------------------+
| | non-cubic spline | `make_interp_spline` | (k-1)th derivative | ``k=3`` is equivalent to `CubicSpline`|
+ +-------------------------+------------------------------+------------------------+---------------------------------------+
| | nearest | `interp1d` | | kind='nearest', 'previous', 'next' |
+------------------+-------------------------+------------------------------+------------------------+---------------------------------------+
| N-D curve | nearest, linear, spline | `make_interp_spline` | (k-1)th derivative | use N-dim `y` array |
+------------------+-------------------------+------------------------------+------------------------+---------------------------------------+
| | nearest | | | method='nearest' |
+ +-------------------------+ + +---------------------------------------+
| N-D regular | linear | `RegularGridInterpolator` | | method='linear' |
+ (*rectilinear*) +-------------------------+ +------------------------+---------------------------------------+
| grid | splines | | 2nd derivatives | method='cubic', 'quintic' |
+ +-------------------------+ +------------------------+---------------------------------------+
| | monotone splines | | 1st derivatives | method='pchip' |
+------------------+-------------------------+------------------------------+------------------------+---------------------------------------+
| | nearest | `NearestNDInterpolator` | | |
+ +-------------------------+------------------------------+ + +
| N-D scattered | linear | `LinearNDInterpolator` | | alias: `griddata` |
+ +-------------------------+------------------------------+------------------------+ +
| | cubic (2D only) | `CloughTocher2DInterpolator` | 1st derivatives | |
+ +-------------------------+------------------------------+------------------------+---------------------------------------+
| | radial basis function | `RBFInterpolator` | | |
+------------------+-------------------------+------------------------------+------------------------+---------------------------------------+
Smoothing and approximation of data
===================================
+-------------------------------+-------------------------+-------------------------------+
| | `make_smoothing_spline` | classic smoothing splines, |
| | | GCV penalty |
| 1D spline functions +-------------------------+-------------------------------+
| | `make_splrep` | automated/semi-automated knot |
| | | selection |
+-------------------------------+-------------------------+-------------------------------+
| spine curves in N-D | `make_splprep` | |
+-------------------------------+-------------------------+-------------------------------+
| unconstrained least squares | `make_lsq_spline` | |
| spline fit | | |
+-------------------------------+-------------------------+-------------------------------+
| 2D smoothing surfaces | `bisplrep` | scattered data |
+-------------------------------+-------------------------+-------------------------------+
| | `RectBivariateSpline` | gridded data |
+-------------------------------+-------------------------+-------------------------------+
| Radial basis functions in N-D | `RBFInterpolator` | |
+-------------------------------+-------------------------+-------------------------------+
**Further details are given in the links below**
.. toctree::
:maxdepth: 3
interpolate/1D
interpolate/splines_and_polynomials
interpolate/smoothing_splines
interpolate/ND_regular_grid
interpolate/ND_unstructured
interpolate/extrapolation_examples
interpolate/interp_transition_guide.md
|
