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[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
__call__
(x[, nu, extrapolate])Evaluate the piecewise polynomial or its derivative
derivative
(nu)Construct a new piecewise polynomial representing the derivative.
antiderivative
(nu)Construct a new piecewise polynomial representing the antiderivative.
integrate
(ranges[, extrapolate])Compute a definite integral over a piecewise polynomial.
integrate_1d
(a, b, axis[, extrapolate])Compute NdPPoly representation for one dimensional definite integral
construct_fast
(c, x[, extrapolate])Construct the piecewise polynomial without making checks.