scipy.interpolate.CubicHermiteSpline

class CubicHermiteSpline(x, y, dydx, axis=0, extrapolate=None)

Piecewise-cubic interpolator matching values and first derivatives.

The result is represented as a PPoly instance.

Parameters

xarray_like, shape (n,)

1-D array containing values of the independent variable. Values must be real, finite and in strictly increasing order.

yarray_like

Array containing values of the dependent variable. It can have arbitrary number of dimensions, but the length along axis (see below) must match the length of x. Values must be finite.

dydxarray_like

Array containing derivatives of the dependent variable. It can have arbitrary number of dimensions, but the length along axis (see below) must match the length of x. Values must be finite.

axisint, optional

Axis along which y is assumed to be varying. Meaning that for x[i] the corresponding values are np.take(y, i, axis=axis). Default is 0.

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.

Attributes

xndarray, shape (n,)

Breakpoints. The same x which was passed to the constructor.

cndarray, shape (4, n-1, …)

Coefficients of the polynomials on each segment. The trailing dimensions match the dimensions of y, excluding axis. For example, if y is 1-D, then c[k, i] is a coefficient for (x-x[i])**(3-k) on the segment between x[i] and x[i+1].

axisint

Interpolation axis. The same axis which was passed to the constructor.

Methods

__call__ derivative antiderivative integrate roots

See Also

Akima1DInterpolator : Akima 1D interpolator. PchipInterpolator : PCHIP 1-D monotonic cubic interpolator. CubicSpline : Cubic spline data interpolator. PPoly : Piecewise polynomial in terms of coefficients and breakpoints

Notes

If you want to create a higher-order spline matching higher-order derivatives, use BPoly.from_derivatives.

References

[1]

Cubic Hermite spline on Wikipedia.

__init__(x, y, dydx, axis=0, extrapolate=None)

Methods

__init__(x, y, dydx[, axis, extrapolate])
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)	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.
solve([y, discontinuity, extrapolate])	Find real solutions of the equation pp(x) == y.

Attributes

c
x
extrapolate
axis