# scipy.interpolate.CubicHermiteSpline¶

class scipy.interpolate.CubicHermiteSpline(x, y, dydx, axis=0, extrapolate=None)[source]

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.

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.

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__(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 the piecewise polynomial.

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