# scipy.interpolate.NdPPoly¶

class scipy.interpolate.NdPPoly(c, x, extrapolate=None)[source]

Piecewise tensor product polynomial

The value at point xp = (x’, y’, z’, ...) is evaluated by first computing the interval indices i such that:

x[i] <= x' < x[i+1]
x[i] <= y' < x[i+1]
...


and then computing:

S = sum(c[k0-m0-1,...,kn-mn-1,i,...,i[n]]
* (xp - x[i])**m0
* ...
* (xp[n] - x[n][i[n]])**mn
for m0 in range(k+1)
...
for mn in range(k[n]+1))


where k[j] is the degree of the polynomial in dimension j. This representation is the piecewise multivariate power basis.

Parameters: c : ndarray, shape (k0, ..., kn, m0, ..., mn, ...) Polynomial coefficients, with polynomial order kj and mj+1 intervals for each dimension j. x : ndim-tuple of ndarrays, shapes (mj+1,) Polynomial breakpoints for each dimension. These must be sorted in increasing order. extrapolate : bool, optional Whether to extrapolate to out-of-bounds points based on first and last intervals, or to return NaNs. Default: True.

PPoly
piecewise polynomials in 1D

Notes

High-order polynomials in the power basis can be numerically unstable.

Attributes

 x (tuple of ndarrays) Breakpoints. c (ndarray) Coefficients of the polynomials.

Methods

 __call__(x[, nu, extrapolate]) Evaluate the piecewise polynomial or its derivative construct_fast(c, x[, extrapolate]) Construct the piecewise polynomial without making checks.

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scipy.interpolate.NdPPoly.__call__