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, ...)
x : ndarray, shape (m+1,)
extrapolate : bool, optional
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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. |
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]) | Construct the piecewise polynomial without making checks. |