pchip — Shape-preserving piecewise cubic Hermite interpolation.

pchip(x, y) builds a shape-preserving cubic Hermite interpolant. pchip(x, y, xq) evaluates it at query points.

Syntax

pp = pchip(x, y)
yq = pchip(x, y, xq)

• x is a strictly increasing vector of sample locations.
• y contains the sampled values to interpolate.
• pchip(x, y) returns a piecewise-polynomial structure compatible with ppval.
• pchip(x, y, xq) evaluates the shape-preserving interpolant directly at query points.
• PCHIP is usually preferred over spline interpolation when monotonicity and avoiding overshoot matter.

How pchip works

• Returns the same pp-structure shape used by spline.
• Uses monotonicity-preserving slopes so monotone data does not overshoot between samples.
• Dense real numeric inputs are supported in the initial implementation.

Example

Shape-preserving interpolation

x = [1 2 3];
y = [1 4 9];
yq = pchip(x, y, [1.5 2.5])

Expected output:

yq = [2.21875 6.21875]

Related Math functions

Open-source implementation

Unlike proprietary runtimes, every RunMat function is open-source. Read exactly how pchip works, line by line, in Rust.

• View pchip.rs on GitHub
• Learn how the runtime works
• Found a bug? Open an issue with a minimal reproduction.

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