# scipy.interpolate.PPoly#

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.

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.

`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:
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.