PiecewiseLinearFunctions.jl

PiecewiseLinearFunctions.jl is a small package for creating and manipulating piecewise linear (continuous) functions

One can instantiate a piecewise linear function by providing the x and y coordinates of the breakpoints, as well as the slopes of the function to the left of the first breakpoint and to the right of the last breakpoint.

using PiecewiseLinearFunctions
f = PiecewiseLinearFunction([0.0, 1.0, 2.0], [0.0, 2.0, 1.0], -1.0, 0.5)

PiecewiseLinearFunction{Float64}([0.0, 1.0, 2.0], [0.0, 2.0, 1.0], -1.0, 0.5)

We can visualize it with Plots:

using Plots
g = PiecewiseLinearFunction([0.0, 1.5, 2.1], [1.0, 3.0, 0.5], 1.0, 3.0)
plot(f; label="f")
plot!(g; label="g")

Basic operations

We can perform basic operations on piecewise linear functions, such as addition, subtraction.

plot(-f; label="-f")
plot!(f + g; label="f + g")
plot!(f - g; label="f - g")
plot!(2f - 3; label="2f - 3")

Min and max

Minimum and maximum operations are also supported.

plot(min(f, g); label="min(f, g)")
plot!(max(f, g); label="max(f, g)")

Composition

We can also compose piecewise linear functions.

plot(f ∘ g; label="f ∘ g")

Convexity

We can check if a piecewise linear function is convex.

is_convex(f)

false

We can also ompute the convex lower bound of a piecewise linear function.

plot(f; label="f")
plot!(convex_lower_bound(f); label="convex_lower_bound(f)")

And compute the convex meet between two convex functions, i.e. the tightest convex lower bound.

f = PiecewiseLinearFunction([-0.5, 0.0, 0.5], [0.5, 0.25, 0.5], -1.0, 1.0)
g = PiecewiseLinearFunction([0.0, 0.5, 1.0], [0.5, 0.4, 0.5], -0.5, 2.0)

PiecewiseLinearFunction{Float64}([0.0, 0.5, 1.0], [0.5, 0.4, 0.5], -0.5, 2.0)

is_convex(f), is_convex(g)

(true, true)

h = convex_meet(f, g)
plot(f; label="f")
plot!(g; label="g")
plot!(h; label="convex_meet(f, g)")

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