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 ofx
. 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 ofx
. Values must be finite.- axisint, optional
Axis along which y is assumed to be varying. Meaning that for
x[i]
the corresponding values arenp.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, thenc[k, i]
is a coefficient for(x-x[i])**(3-k)
on the segment betweenx[i]
andx[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 piecewise polynomial.
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.