Public API

Utils

Utility functions module for CTModels.

This module provides general-purpose utility functions used throughout CTModels, including interpolation, matrix operations, and function transformations.

Public API

The following functions are exported and accessible as CTModels.function_name():

• ctinterpolate: Linear interpolation for data
• ctinterpolate_constant: Piecewise-constant interpolation for data
• matrix2vec: Convert matrices to vectors

Private API

The following are internal utilities (accessible via Utils.function_name):

• to_out_of_place: Convert in-place functions to out-of-place
• @ensure: Validation macro for preconditions

See also: CTModels

ctinterpolate(
    x,
    f
) -> CTModels.Utils.var"#linear_interp#ctinterpolate##0"

Return a linear interpolation function for the data f defined at points x.

This function creates a one-dimensional linear interpolant with flat extrapolation beyond the bounds of x (returns f[1] for t < x[1] and f[end] for t >= x[end]).

Arguments

• x: A vector of points at which the values f are defined.
• f: A vector of values to interpolate.

Returns

A callable interpolation object that can be evaluated at new points.

Example

julia> x = [0.0, 1.0, 2.0]
julia> f = [1.0, 2.0, 3.0]
julia> interp = ctinterpolate(x, f)
julia> interp(0.5)  # Returns 1.5 (linear interpolation)
julia> interp(-1.0)  # Returns 1.0 (flat extrapolation)
julia> interp(3.0)  # Returns 3.0 (flat extrapolation)

ctinterpolate_constant(
    x,
    f
) -> CTModels.Utils.var"#steppost_interp#ctinterpolate_constant##0"

Return a piecewise-constant interpolation function for the data f defined at points x.

This function creates a right-continuous piecewise constant interpolant: the value at knot x[i] is held constant on the interval [x[i], x[i+1}).

This implements the standard steppost behavior for optimal control:

• u(t_i) = u_i (value at the knot)
• u(t) = u_i for all t ∈ [t_i, t_{i+1})
• Right-continuous: lim_{t→t_i^+} u(t) = u(t_i)

Arguments

• x: A vector of points at which the values f are defined.
• f: A vector of values to interpolate.

Returns

A callable interpolation object that can be evaluated at new points.

Example

julia> x = [0.0, 1.0, 2.0]
julia> f = [1.0, 2.0, 3.0]
julia> interp = ctinterpolate_constant(x, f)
julia> interp(0.0)  # Returns 1.0 (value at x[1])
julia> interp(0.5)  # Returns 1.0 (held from x[1] on [0.0, 1.0))
julia> interp(1.0)  # Returns 2.0 (value at x[2], right-continuous)
julia> interp(1.5)  # Returns 2.0 (held from x[2] on [1.0, 2.0))

matrix2vec(A::Matrix{<:Real}) -> Vector{<:Vector{<:Real}}
matrix2vec(
    A::Matrix{<:Real},
    dim::Int64
) -> Vector{<:Vector{<:Real}}

Transform a matrix into a vector of vectors along the specified dimension.

Each row or column of the matrix A is extracted and stored as an individual vector, depending on dim.

Arguments

• A: A matrix of elements of type <:ctNumber.
• dim: The dimension along which to split the matrix (1 for rows, 2 for columns). Defaults to 1.

Returns

A Vector of Vectors extracted from the rows or columns of A.

Note

This is useful when data needs to be represented as a sequence of state or control vectors in optimal control problems.

Example

julia> A = [1 2 3; 4 5 6]
julia> matrix2vec(A, 1)  # splits into rows: [[1, 2, 3], [4, 5, 6]]
julia> matrix2vec(A, 2)  # splits into columns: [[1, 4], [2, 5], [3, 6]]