scipy.interpolate.PchipInterpolator

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

PCHIP 1-d monotonic cubic interpolation

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

A 1-D array of monotonically increasing real values. x cannot include duplicate values (otherwise f is overspecified)

y : ndarray

A 1-D array of real values. y‘s length along the interpolation axis must be equal to the length of x. If N-D array, use axis parameter to select correct axis.

axis : int, optional

Axis in the y array corresponding to the x-coordinate values.

extrapolate : bool, optional

Whether to extrapolate to ouf-of-bounds points based on first and last intervals, or to return NaNs.

See also

Akima1DInterpolator

Notes

The first derivatives are guaranteed to be continuous, but the second derivatives may jump at x_k.

Preserves monotonicity in the interpolation data and does not overshoot if the data is not smooth.

Determines the derivatives at the points x_k, d_k, by using PCHIP algorithm:

Let m_k be the slope of the kth segment (between k and k+1) If m_k=0 or m_{k-1}=0 or sgn(m_k) != sgn(m_{k-1}) then d_k == 0 else use weighted harmonic mean:

w_1 = 2h_k + h_{k-1}, w_2 = h_k + 2h_{k-1} 1/d_k = 1/(w_1 + w_2)*(w_1 / m_k + w_2 / m_{k-1})

where h_k is the spacing between x_k and x_{k+1}.

Methods

__call__(x[, der, extrapolate])	Evaluate the PCHIP interpolant or its derivative.
derivative([der])	Construct a piecewise polynomial representing the derivative.