3.5.1.11. scipy.interpolate.PPoly¶

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

axis : int, optional

Interpolation axis. Default is zero.

See also

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.
axis	(int) 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.
`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 from a polynomial in Bernstein basis.
`construct_fast`(c, x[, extrapolate, axis])	Construct the piecewise polynomial without making checks.

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[, right])	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.

Attributes