Interpolation

The CTBase.Interpolation submodule provides lightweight, dependency-free interpolation for one-dimensional data. Two methods are available:

• Linear interpolation with flat extrapolation outside the node range.

• Piecewise-constant (right-continuous steppost) interpolation.

Both produce a callable Interpolant — a Function subtype whose evaluation rule is selected at compile time via a trait parameter.

Linear interpolation

ctinterpolate builds a linear interpolant from nodes x and values f. Outside [x[1], x[end]] the value is held flat (clamped to the nearest endpoint):

julia> using CTBase

julia> x = [0.0, 1.0, 2.0, 3.0]
4-element Vector{Float64}:
 0.0
 1.0
 2.0
 3.0

julia> f = [0.0, 1.0, 0.0, -1.0]
4-element Vector{Float64}:
  0.0
  1.0
  0.0
 -1.0

julia> interp = CTBase.Interpolation.ctinterpolate(x, f)
Interpolant (linear): 4 nodes

julia> interp(0.5)   # linear between x[1] and x[2]
0.5

julia> interp(2.5)   # linear between x[3] and x[4]
-0.5

julia> interp(-1.0)  # flat extrapolation → f[1]
0.0

julia> interp(5.0)   # flat extrapolation → f[end]
-1.0

Piecewise-constant interpolation

ctinterpolate_constant builds a right-continuous steppost interpolant: the value at node x[i] is held on [x[i], x[i+1]).

julia> const_interp = CTBase.Interpolation.ctinterpolate_constant(x, f)
Interpolant (piecewise-constant): 4 nodes

julia> const_interp(0.0)   # f[1]
0.0

julia> const_interp(0.5)   # still f[1] (held on [0, 1))
0.0

julia> const_interp(1.0)   # f[2] (right-continuous jump)
1.0

julia> const_interp(1.5)   # still f[2]
1.0

This is the standard representation for piecewise-constant control functions in optimal control.

The Interpolant type

An Interpolant is parametrised by its method trait (Linear or Constant), which makes the call type-stable:

julia> typeof(interp)
CTBase.Interpolation.Interpolant{CTBase.Interpolation.Linear, Vector{Float64}, Vector{Float64}}

The method can be recovered with method:

julia> CTBase.Interpolation.method(interp)
CTBase.Interpolation.Linear

julia> CTBase.Interpolation.method(const_interp)
CTBase.Interpolation.Constant

Display

julia> interp
Interpolant (linear): 4 nodes

julia> const_interp
Interpolant (piecewise-constant): 4 nodes

Function Reference

Function	Purpose
ctinterpolate	Linear interpolation with flat extrapolation
ctinterpolate_constant	Piecewise-constant (steppost) interpolation
method	Return the interpolation method trait of an Interpolant

See Also

• Traits guide — the trait-parameter pattern used by Interpolant.