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Add explanation of requirements for spline parameters in RQSpline docs #27

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Jan 2, 2025
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Add explanation of requirements for spline parameters in RQSpline docs #27

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15 changes: 10 additions & 5 deletions src/rqspline.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -31,9 +31,16 @@ Fields:
- three-dimensional arrays of the shape `K+1 x n_dims x n_samples`, representing a set of splines for different
dimensions and input samples.

The spline is continued with a linear function of slope one beyond the first
and last knot, so the first and last entry of dYdX should be one if the spline
is indended to be used at this extended range.
Requirements for the fields:

Each spline is continued with the identity function beyond its first and last knot.
So to ensure the continuity and differentiability of the splines, the first and last knots must lie on the
diagonal through 0, and the derivatives at these knots must be 1.
Formally:
For parameter vectors `pX[1] == pY[1]` and `pX[end] == pY[end]` and `dYdX[1] == dYdX[end] == 1` must hold.
For 3 dimensional parameter arrays `pX[1,:,:] == pY[1,:,:]` and `pX[end,:,:] == pY[end,:,:]` and
`dYdX[1,:,:] .== dYdX[end,:,:] .== 1` must be true.


`RQSpline` supports the InverseFunctions, ChangesOfVariables, and Functors
APIs.
Expand Down Expand Up @@ -215,7 +222,6 @@ end
pY::AbstractArray{<:Real},
dYdX::AbstractArray{<:Real}
)

i, j = @index(Global, NTuple)

K = size(pX, 1) - 1
Expand Down Expand Up @@ -321,7 +327,6 @@ function rqs_inverse(
pY::AbstractArray{<:Real,3},
dYdX::AbstractArray{<:Real,3}
)

compute_unit = get_compute_unit(x)
backend = ka_backend(compute_unit)
kernel! = rqs_inverse_kernel!(backend, _ka_threads(backend)...)
Expand Down
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