`spline`

Cubic spline interpolation.

Syntax

yi = spline(x, y, xi)

Evaluates the not-a-knot cubic spline through (x, y) at xi.

pp = spline(x, y)

Returns the piecewise polynomial structure.

Description

A cubic spline is made of cubic pieces that join with continuous value, slope and curvature. With the default not-a-knot condition, the first two pieces share one cubic, and so do the last two. For this reason data that come from a cubic polynomial are reproduced exactly.

Giving two extra values in y selects the clamped condition instead, with the given slopes at the ends. Splines can oscillate between points when the data change abruptly; pchip and makima are alternatives for that case.

Input arguments

x: Vector of distinct sample points.
y: Sample values. If y has two more entries than x, the first and last are the end slopes of a clamped spline.
xi: Points at which to evaluate.

Output arguments

yi: Interpolated values.
pp: Piecewise polynomial structure, usable with ppval.

Example

Reproducing a cubic and inspecting the pieces

x = 0:4;
y = x.^3;
spline(x, y, 2.5)
pp = spline(x, y);
pp.pieces

Output

ans = 15.6250
ans = 4

spline