class scipy.interpolate.PPoly(c, x, extrapolate=None, axis=0)[source]#

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.

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.

See also


piecewise polynomials in the Bernstein basis


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




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.


Interpolation axis.


__call__(x[, nu, extrapolate])

Evaluate the piecewise polynomial or its derivative.


Construct a new piecewise polynomial representing the derivative.


Construct a new piecewise polynomial representing the antiderivative.

integrate(a, b[, extrapolate])

Compute a definite integral over a piecewise polynomial.

solve([y, discontinuity, extrapolate])

Find real solutions of the equation pp(x) == y.

roots([discontinuity, extrapolate])

Find real roots of the piecewise polynomial.

extend(c, x)

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 from a polynomial in Bernstein basis.

construct_fast(c, x[, extrapolate, axis])

Construct the piecewise polynomial without making checks.