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: 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
- 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.