Constant Interpolation

Step function interpolation that returns values from neighboring data points without blending.

Key Feature: The side keyword controls which neighbor to sample using AbstractSide types.

Usage

using FastInterpolations

x = [0.0, 1.0, 2.5, 4.0, 5.0]
y = [1.0, 3.0, 2.0, 4.0, 1.5]

# One-shot evaluation
constant_interp(x, y, 1.5)              # → 3.0 (nearest neighbor)
constant_interp(x, y, 1.5; side=LeftSide())  # → 3.0 (left neighbor)
constant_interp(x, y, 1.5; side=RightSide()) # → 2.0 (right neighbor)

# Create reusable interpolant
itp = constant_interp(x, y; side=NearestSide())
itp(1.5)           # single point
itp([1.0, 2.0])    # multiple points

# In-place evaluation (zero allocation)
xq = range(x[1], x[end], 100)
out = similar(xq)
constant_interp!(out, x, y, xq)

# Derivatives (always 0 for step function)
constant_interp(x, y, 1.5; deriv=DerivOp(1))  # → 0.0
d1 = deriv1(itp); d1(1.5)            # → 0.0

Side Modes Comparison

using FastInterpolations
using Plots

x = [0.0, 1.0, 2.5, 4.0, 5.0]
y = [1.0, 3.0, 2.0, 4.0, 1.5]
xq = range(x[1], x[end], 100)

sides = [NearestSide(), LeftSide(), RightSide()]
labels = ["NearestSide()", "LeftSide()", "RightSide()"]
p = plot(layout=(1,3), size=(900, 280), legend=:topright)
for (i, (side, lbl)) in enumerate(zip(sides, labels))
    yq = constant_interp(x, y, xq; side=side)
    plot!(p[i], xq, yq, label="spline", linewidth=2)
    scatter!(p[i], x, y, label="data", markersize=7, color=:black)
    title!(p[i], "side=$lbl")
end
p

When to Use

• Discrete states or categories
• Sharp transitions must be preserved
• Monotonicity preservation is critical
• Lookup table behavior

Need smooth curves? → Linear or Cubic