Check whether interpolation creates unsupported reversals

Define the task

An interpolated line can pass through all recorded points while introducing a peak or dip between them. If the measurements should be monotone, first distinguish that scientific assumption from a chance monotone sample. Review the original values and their uncertainty before constraining the interpolated shape.

Carry out the check

PCHIP is a piecewise cubic method that preserves monotonicity in monotone data and limits overshoot. It is continuously differentiable, while second derivatives can jump at knots. Evaluate a dense grid within each observed interval and compare its range with the two endpoint values. Keep extrapolation separate because preservation inside the sampled domain does not justify predictions beyond it.

Worked hypothetical example

For hypothetical increasing points (0,0), (1,1) and (2,1.1), an interpolation that exceeds 1.1 between x=1 and x=2 introduces an unsupported overshoot. Within that interval a monotone interpolator should stay between 1 and 1.1. This range check tests a property rather than prescribing an exact intermediate value. Record the method and domain whenever a curve supports a threshold or area calculation.

Method checked 14 November 2026 against SciPy documentation: PchipInterpolator.