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fix: CubicSpline's natural boundary conditions #235

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Mar 26, 2024
Merged

fix: CubicSpline's natural boundary conditions #235

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331c9c7
fix: CubicSpline's natural boundary conditions
sathvikbhagavan Mar 26, 2024
60ad06a
test: update CubicSpline tests
sathvikbhagavan Mar 26, 2024
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12 changes: 6 additions & 6 deletions src/interpolation_caches.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -268,10 +268,10 @@ function QuadraticSpline(u::uType, t; extrapolate = false) where {uType <: Abstr
end

"""
QuadraticSpline(u, t; extrapolate = false)
CubicSpline(u, t; extrapolate = false)

It is a spline interpolation using piecewise cubic polynomials between each pair of data points. Its first and second derivative is also continuous.
Extrapolation extends the last cubic polynomial on each side.
Second derivative on both ends are zero, which are also called "natural" boundary conditions. Extrapolation extends the last cubic polynomial on each side.

## Arguments

Expand Down Expand Up @@ -303,9 +303,9 @@ function CubicSpline(u::uType,
u, t = munge_data(u, t)
n = length(t) - 1
h = vcat(0, map(k -> t[k + 1] - t[k], 1:(length(t) - 1)), 0)
dl = h[2:(n + 1)]
dl = vcat(h[2:n], zero(eltype(h)))
d_tmp = 2 .* (h[1:(n + 1)] .+ h[2:(n + 2)])
du = h[2:(n + 1)]
du = vcat(zero(eltype(h)), h[3:(n + 1)])
tA = Tridiagonal(dl, d_tmp, du)

# zero for element type of d, which we don't know yet
Expand All @@ -324,9 +324,9 @@ function CubicSpline(u::uType, t; extrapolate = false) where {uType <: AbstractV
u, t = munge_data(u, t)
n = length(t) - 1
h = vcat(0, map(k -> t[k + 1] - t[k], 1:(length(t) - 1)), 0)
dl = h[2:(n + 1)]
dl = vcat(h[2:n], zero(eltype(h)))
d_tmp = 2 .* (h[1:(n + 1)] .+ h[2:(n + 2)])
du = h[2:(n + 1)]
du = vcat(zero(eltype(h)), h[3:(n + 1)])
tA = Tridiagonal(dl, d_tmp, du)
d_ = map(
i -> i == 1 || i == n + 1 ? zeros(eltype(t), size(u[1])) :
Expand Down
8 changes: 4 additions & 4 deletions test/interpolation_tests.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -498,8 +498,8 @@ end
A = CubicSpline(u, t; extrapolate = true)

# Solution
P₁ = x -> 1 + 1.5x + x^2 + 0.5x^3 # for x ∈ [-1.0, 0.0]
P₂ = x -> 1 + 1.5x + x^2 - 0.5x^3 # for x ∈ [0.0, 1.0]
P₁ = x -> 1 + 1.5x + 0.75 * x^2 + 0.25 * x^3 # for x ∈ [-1.0, 0.0]
P₂ = x -> 1 + 1.5x + 0.75 * x^2 - 0.25 * x^3 # for x ∈ [0.0, 1.0]

for (_t, _u) in zip(t, u)
@test A(_t) == _u
Expand Down Expand Up @@ -534,8 +534,8 @@ end
u = [0.0, 1.0, 3.0]
t = [-1.0, 0.0, 1.0]
A = CubicSpline(u, t; extrapolate = true)
@test A(-2.0) ≈ -2.0
@test A(2.0) ≈ 4.0
@test A(-2.0) ≈ -1.0
@test A(2.0) ≈ 5.0
A = CubicSpline(u, t)
@test_throws DataInterpolations.ExtrapolationError A(-2.0)
@test_throws DataInterpolations.ExtrapolationError A(2.0)
Expand Down
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