NdPPoly — SciPy v1.15.3 Manual (original) (raw)

scipy.interpolate.

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.

Parameters:

cndarray, shape (k0, …, kn, m0, …, mn, …)

Polynomial coefficients, with polynomial order kj and_mj+1_ intervals for each dimension j.

xndim-tuple of ndarrays, shapes (mj+1,)

Polynomial breakpoints for each dimension. These must be sorted in increasing order.

extrapolatebool, optional

Whether to extrapolate to out-of-bounds points based on first and last intervals, or to return NaNs. Default: True.

See also

PPoly

piecewise polynomials in 1D

Notes

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

Attributes:

xtuple of ndarrays

Breakpoints.

cndarray

Coefficients of the polynomials.

Methods