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[0][i[0]] <= x' < x[0][i[0]+1]
x[1][i[1]] <= y' < x[1][i[1]+1]

and then computing:

S = sum(c[k0-m0-1,...,kn-mn-1,i[0],...,i[n]]
        * (xp[0] - x[0][i[0]])**m0
        * ...
        * (xp[n] - x[n][i[n]])**mn
        for m0 in range(k[0]+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.


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.

See also

piecewise polynomials in 1D


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


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


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