SciPy

scipy.interpolate.PPoly

class scipy.interpolate.PPoly(c, x, extrapolate=None)[source]

Piecewise polynomial in terms of coefficients and breakpoints

The polynomial in the ith interval is x[i] <= xp < x[i+1]:

S = sum(c[m, i] * (xp - x[i])**(k-m) for m in range(k+1))

where k is the degree of the polynomial. This representation is the local power basis.

Parameters :

c : ndarray, shape (k, m, ...)

Polynomial coefficients, order k and m intervals

x : ndarray, shape (m+1,)

Polynomial breakpoints. These must be sorted in increasing order.

extrapolate : bool, optional

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

See also

BPoly
piecewise polynomials in the Bernstein basis

Notes

High-order polynomials in the power basis can be numerically unstable. Precision problems can start to appear for orders larger than 20-30.

Attributes

x (ndarray) Breakpoints.
c (ndarray) Coefficients of the polynomials. They are reshaped to a 3-dimensional array with the last dimension representing the trailing dimensions of the original coefficient array.

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(a, b[, extrapolate]) Compute a definite integral over a piecewise polynomial.
roots([discontinuity, extrapolate]) Find real roots of the piecewise polynomial.
extend(c, x[, right]) Add additional breakpoints and coefficients to the polynomial.
from_spline(tck[, extrapolate]) Construct a piecewise polynomial from a spline
from_bernstein_basis(bp[, extrapolate]) Construct a piecewise polynomial in the power basis
construct_fast(c, x[, extrapolate]) Construct the piecewise polynomial without making checks.