`scipy.interpolate._cubic:PchipInterpolator`

source: /scipy/interpolate/_cubic.py :172

Signature

class PchipInterpolator ( x , y , axis = 0 , extrapolate = None )

Members

Summary

PCHIP shape-preserving interpolator (C1 smooth).

Extended Summary

x and y are arrays of values used to approximate some function f, with y = f(x). The interpolant uses monotonic cubic splines to find the value of new points. (PCHIP stands for Piecewise Cubic Hermite Interpolating Polynomial).

Parameters

x : ndarray, shape (npoints, ): A 1-D array of monotonically increasing real values. x cannot include duplicate values (otherwise f is overspecified)
y : ndarray, shape (..., npoints, ...): An N-D array of real values. y's length along the interpolation axis must be equal to the length of x. Use the axis parameter to select the interpolation axis.
axis : int, optional: Axis in the y array corresponding to the x-coordinate values. Defaults to axis=0.
extrapolate : bool, optional: Whether to extrapolate to out-of-bounds points based on first and last intervals, or to return NaNs.

Methods

__call__
derivative
antiderivative
integrate
solve
roots

Notes

The interpolator preserves monotonicity in the interpolation data and does not overshoot if the data is not smooth.

The first derivatives are guaranteed to be continuous, but the second derivatives may jump at $x_{k}$ .

Determines the derivatives at the points $x_{k}$ , $f_{k}^{'}$ , by using PCHIP algorithm ^[1].

Let $h_{k} = x_{k + 1} - x_{k}$ , and $d_{k} = (y_{k + 1} - y_{k}) / h_{k}$ are the slopes at internal points $x_{k}$ . If the signs of $d_{k}$ and $d_{k - 1}$ are different or either of them equals zero, then $f_{k}^{'} = 0$ . Otherwise, it is given by the weighted harmonic mean

\frac{w _{1} + w _{2}}{f _{k}^{'}} = \frac{w _{1}}{d _{k - 1}} + \frac{w _{2}}{d _{k}}

where $w_{1} = 2 h_{k} + h_{k - 1}$ and $w_{2} = h_{k} + 2 h_{k - 1}$ .

The end slopes are set using a one-sided scheme ^[2].

Array API Standard Support

PchipInterpolator has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

====================  ====================  ====================
Library               CPU                   GPU
====================  ====================  ====================
NumPy                 ✅                     n/a                 
CuPy                  n/a                   ⛔                   
PyTorch               ✅                     ⛔                   
JAX                   ⚠️ no JIT             ⛔                   
Dask                  ⛔                     n/a                 
====================  ====================  ====================

See dev-arrayapi for more information.

Aliases

scipy.interpolate.PchipInterpolator