Lagrange Interpolation

lagrange_interpolation.jl

using PyPlot
using PyCall


function generate_Lᵢ(xs, ys, i)
    function Lᵢ(x)
        n, d = 1, 1
        for (j, xⱼ) in enumerate(xs)
            if i == j
                continue
            end

            n *= (x-xⱼ)
            d *= (xs[i]-xⱼ)
        end
        return n / d
    end
    return Lᵢ
end


function generate_pₙ(xs, ys)
    function pₙ(x)
        v = 0
        for (i, y) in enumerate(ys)
            Lᵢ = generate_Lᵢ(xs, ys, i)
            v += Lᵢ(x) * y
        end
        return v
    end
    return pₙ
end


xs = 0.5:0.5:2.5
ys = [
    0.479425539,
    0.841470985,
    0.997494987,
    0.909297427,
    0.598472144
]

pₙ = generate_pₙ(xs, ys)


xs = collect(0.0:0.1:3.0)

fig, ax = subplots()
ax[:plot](xs, [pₙ(x) for x in xs], label=L"$p_n(x)$")
ax[:plot](xs, [sin(x) for x in xs], label=L"$sin(x)$")
ax[:legend](loc="lower center")
show()

result.png