Introductoin

This python code will take x/y data and generate a spline using Antimony's piecewise function. This is useful when you need to provide an input based on some data. Below is an example of the output it generates. Once generated insert it into your antimony model.

Input := piecewise (((-0.031143*(time-0.000000)-0.000000)*(time-0.000000)+0.531143)*(time-0.000000)+0.000000, (time >=0.000000) && (time <= 1.000000),\ 
((0.155717*(time-1.000000)-0.093430)*(time-1.000000)+0.437713)*(time-1.000000)+0.500000, (time >=1.000000) && (time <= 2.000000),\ 
((-0.591724*(time-2.000000)+0.373720)*(time-2.000000)+0.718003)*(time-2.000000)+1.000000, (time >=2.000000) && (time <= 3.000000),\ 
((0.711177*(time-3.000000)-1.401451)*(time-3.000000)-0.309727)*(time-3.000000)+1.500000, (time >=3.000000) && (time <= 4.000000),\ 
((-0.121267*(time-4.000000)+0.732082)*(time-4.000000)-0.979096)*(time-4.000000)+0.500000, (time >=4.000000) && (time <= 6.000000),\ 
((-0.000747*(time-6.000000)+0.004480)*(time-6.000000)+0.494027)*(time-6.000000)+0.500000, (time >=6.000000) && (time <= 8.000000))

A few design notes worth knowing:

Spline boundary condition — bc_type="natural" sets the second derivative to zero at both endpoints, which is the standard "free" (not-a-knot) natural spline and matches the Delphi cubicSplineFree. If you ever need clamped endpoints (specifying derivatives), just swap in bc_type=("clamped", (dy0, dyn)).

Coefficient layout — scipy's cs.c[row, segment] has row 0 as the cubic term and row 3 as the constant, so the mapping to Horner form is direct with no reordering needed.

Non-uniform spacing — CubicSpline handles variable knot spacing natively, exactly as the Delphi routine's comment advertises.

Precision — The format string %.6f matches your Delphi Format('%8.6f', [...]). You can pass a different format string as a parameter if you need more or fewer decimal places.

The monotone flag won't help with the original test data because PCHIP still faithfully follows whatever shape the data describes — and y = [0, 1, 1.5, 0.5, 0.5, 0.5, 0.5] genuinely has a hump in it. PCHIP just prevents additional overshoot that isn't in the data; it can't smooth away a peak that is.

The data fix from my previous message is the primary fix. To see the difference between the two interpolators you need data that actually has a plateau:

# Hump data — BOTH interpolators will produce a hump (correct behaviour)
x = [0, 1,   2,   3,   6,   7,   8  ]
y = [0, 1,   1.5, 0.5, 0.5, 0.5, 0.5]   # ← peak at x=2, not a plateau

# Rise-then-plateau data — now the flag matters
x = [0, 1,   2,   3,   4,   6,   8  ]
y = [0, 0.5, 1.0, 1.5, 1.5, 1.5, 1.5]   # ← genuine flat region
#                            ^^^^^^^^^^^
#   CubicSpline may undershoot slightly here; PCHIP will be perfectly flat

So the short version:

Problem	Fix
Hump instead of plateau	Change the data — the input y-values must actually be flat
Undershoot/overshoot in flat region	Use monotone=True (PCHIP)

Both are needed together to get a clean rise-then-plateau output.

For your specific use case — drug dosing or experimental inputs to a biochemical model — yes, monotone=True should be your default. The reasoning:

• Dosing data typically has flat baselines, step-like rises, and plateaus — exactly the shapes PCHIP is designed to preserve
• You never want the spline to go negative between data points (e.g. a drug concentration dipping below zero between two positive measurements — physically meaningless)
• The C¹ vs C² smoothness difference is irrelevant for a forcing input; you're not differentiating it analytically
• Users entering a handful of (time, dose) points expect the curve to behave like the data looks — no surprise oscillations

The only case where you'd prefer monotone=False (natural cubic) is if the data represents something inherently smooth where the second derivative continuity matters — like a smoothly varying enzyme activity profile where you have dense, high-quality measurements. In that situation the extra smoothness of C² is a genuine benefit.

A practical default would be to simply make True the default in the function signature:

def antimony_piecewise(x, y, var_name="Input", time_var="time",
                       antimony_continuation=True,
                       monotone=True):   # ← changed default