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# scipy.interpolate.NdPPoly

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

  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
  `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.