scipy.interpolate.

PPoly

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

Piecewise polynomial in the power basis.

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+1, m, …)

Polynomial coefficients, degree k and m intervals.

xndarray, shape (m+1,)

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

extrapolate{bool, ‘periodic’, None}, 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. If None (default), it is set to True. See Out-of-bounds behavior.

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__(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.
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.

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.

Array API Standard Support

PPoly has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

Library	CPU	GPU
NumPy	✅	n/a
CuPy	n/a	✅
PyTorch	✅	⛔
JAX	⚠️ no JIT	⛔
Dask	⛔	n/a

The methods solve and roots are currently not supported with CuPy. solve and roots with c.ndim > 2 are currently only supported with NumPy.

If a ppoly object is called on an input array x with namespace different from the namespace xp of the breakpoints and coefficients with which the ppoly object was instantiated, an attempt will be made to coerce x to the xp namespace. If the conversion succeeds, the output will be an array from the xp namespace. Mixing namespaces in this way is not recommended.

See Support for the array API standard for more information.