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 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.
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.
- 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.