scipy.interpolate.PPoly

class PPoly(c, x, extrapolate=None, axis=0)

Piecewise polynomial in terms of coefficients and breakpoints

The polynomial between x[i] and x[i + 1] is written in the local power basis:

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

where k is the degree of the polynomial.

Parameters

cndarray, shape (k, m, …)

Polynomial coefficients, order k and m intervals.

xndarray, shape (m+1,)

Polynomial breakpoints. Must be sorted in either increasing or decreasing order.

extrapolatebool or ‘periodic’, optional

If bool, determines whether to extrapolate to out-of-bounds points based on first and last intervals, or to return NaNs. If ‘periodic’, periodic extrapolation is used. Default is True.

axisint, optional

Interpolation axis. Default is zero.

Attributes

xndarray

Breakpoints.

cndarray

Coefficients of the polynomials. They are reshaped to a 3-D array with the last dimension representing the trailing dimensions of the original coefficient array.

axisint

Interpolation axis.

Methods

__call__ derivative antiderivative integrate solve roots extend from_spline from_bernstein_basis construct_fast

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.

__init__(c, x, extrapolate=None, axis=0)

Methods

__init__(c, x[, extrapolate, axis])
antiderivative([nu])	Construct a new piecewise polynomial representing the antiderivative.
construct_fast(c, x[, extrapolate, axis])	Construct the piecewise polynomial without making checks.
derivative([nu])	Construct a new piecewise polynomial representing the derivative.
extend(c, x)	Add additional breakpoints and coefficients to the polynomial.
from_bernstein_basis(bp[, extrapolate])	Construct a piecewise polynomial in the power basis from a polynomial in Bernstein basis.
from_spline(tck[, extrapolate])	Construct a piecewise polynomial from a spline
integrate(a, b[, extrapolate])	Compute a definite integral over a piecewise polynomial.
roots([discontinuity, extrapolate])	Find real roots of the piecewise polynomial.
solve([y, discontinuity, extrapolate])	Find real solutions of the equation pp(x) == y.

Attributes

c
x
extrapolate
axis