API

Splinter.BSplineBasis
Splinter.ISplineBasis
Splinter.MSplineBasis
Splinter.NSplineBasis
Splinter.bs
Splinter.is
Splinter.ms
Splinter.ns
Splinter.spline_args

Splinter.BSplineBasis — Method

BSplineBasis(x::AbstractVector{T};
             boundary_knots::Union{Tuple{T,T},Nothing}=nothing,
             interior_knots::Union{AbstractVector{T},Nothing}=nothing,
             order::Int=4,
             intercept::Bool=false,
             df::Int=order - 1 + Int(intercept),
             knots::Union{AbstractVector{T},Nothing}=nothing) where {T<:Real}

Calculate a basis for B-splines and return a callable type for evaluating points in that basis.

Keyword Arguments

boundary_knots: boundary knots
interior_knots: interior knots
order: order of the spline
intercept: bool for whether to include an intercept
df: degrees of freedom
knots: full set of knots (excluding repeats)

Keyword Arguments of Returned Callable

center: value to center the splines
derivs: derivatives of the splines

Examples

julia> spline = BSplineBasis(collect(0.0:0.2:1.0); df=3);
julia> spline(collect(0.0:0.2:1.0))
6×3 Array{Float64,2}:
 0.0    0.0    0.0
 0.384  0.096  0.008
 0.432  0.288  0.064
 0.288  0.432  0.216
 0.096  0.384  0.512
 0.0    0.0    1.0

source

Splinter.ISplineBasis — Method

ISplineBasis(x::AbstractVector{T};
             boundary_knots::Union{Tuple{T,T},Nothing}=nothing,
             interior_knots::Union{AbstractVector{T},Nothing}=nothing,
             order::Int=4,
             intercept::Bool=false,
             df::Int=order + Int(intercept),
             knots::Union{AbstractVector{T},Nothing}=nothing) where {T<:Real}

Calculate a basis for I-splines and return a callable type for evaluating points in that basis.

Keyword Arguments

boundary_knots: boundary knots
interior_knots: interior knots
order: order of the spline
intercept: bool for whether to include an intercept (column of ones). This behaviour is different to the splines2 package from R, where intercept=FALSE will drop the first spline term.
df: degrees of freedom
knots: full set of knots (excluding repeats)

Keyword Arguments of Returned Callable

derivs: derivatives of the splines

Examples

julia> spline = ISplineBasis(collect(0.0:0.2:1.0); df=3);
julia> spline(collect(0.0:0.2:1.0))
6×3 Array{Float64,2}:
 0.0     0.0     0.0
 0.1808  0.0272  0.0016
 0.5248  0.1792  0.0256
 0.8208  0.4752  0.1296
 0.9728  0.8192  0.4096
 1.0     1.0     1.0

source

Splinter.MSplineBasis — Method

MSplineBasis(x::AbstractVector{T};
             boundary_knots::Union{Tuple{T,T},Nothing}=nothing,
             interior_knots::Union{AbstractVector{T},Nothing}=nothing,
             order::Int=4,
             intercept::Bool=false,
             df::Int=order - 1 + Int(intercept),
             knots::Union{AbstractVector{T},Nothing}=nothing) where {T<:Real}

Calculate a basis for M-splines and return a callable type for evaluating points in that basis.

Keyword Arguments

boundary_knots: boundary knots
interior_knots: interior knots
order: order of the spline
intercept: bool for whether to include an intercept (column of ones). This behaviour is different to the Splinter package from R, where intercept=FALSE will drop the first spline term.
df: degrees of freedom
knots: full set of knots (excluding repeats)

Keyword Arguments of Returned Callable

center: value to center the splines
derivs: derivatives of the splines

Examples

julia> spline = MSplineBasis(collect(0.0:0.2:1.0); df=3);
julia> spline(collect(0.0:0.2:1.0))
6×3 Array{Float64,2}:
 0.0    0.0    0.0
 1.536  0.384  0.032
 1.728  1.152  0.256
 1.152  1.728  0.864
 0.384  1.536  2.048
 0.0    0.0    4.0

source

Splinter.NSplineBasis — Method

NSplineBasis(x::AbstractVector{T};              
             boundary_knots::Union{Tuple{T,T},Nothing}=nothing,
             interior_knots::Union{AbstractVector{T},Nothing}=nothing,
             order::Int=4,
             intercept::Bool=false,
             df::Int=order - 3 + Int(intercept),
             knots::Union{AbstractVector{T},Nothing}=nothing) where {T<:Real}

Calculate a basis for natural B-splines and return a callable type for evaluating points in that basis.

Keyword Arguments

boundary_knots: boundary knots
interior_knots: interior knots
order: order of the spline
intercept: bool for whether to include an intercept
df: degrees of freedom
knots: full set of knots (excluding repeats)

Keyword Arguments of Returned Callable

center: value to center the splines
derivs: derivatives of the splines

Examples

julia> spline = NSplineBasis(x; df=3);
julia> spline(0.0:0.2:1.0)
6×3 Matrix{Float64}:
  0.0       0.0        0.0     
 -0.100444  0.409332  -0.272888
  0.102383  0.540852  -0.359235
  0.501759  0.386722  -0.172481
  0.418872  0.327383   0.217745
 -0.142857  0.428571   0.714286

source

Splinter.bs — Method

bs(x::AbstractVector{T}; center::Union{T,Nothing}=nothing, derivs::Int=0, kwargs...) where {T <: Real}

Calculate a basis for B-splines and return x expressed in that basis.

Keyword arguments

center: value to center the splines
derivs: derivatives of the splines
Further keyword arguments are passed to BSplineBasis.

Arguments

boundary_knots :: Union{Tuple{T,T},Nothing} = nothing: boundary knots
interior_knots :: Union{Array{T,1},Nothing} = nothing: interior knots
order :: Int = 4: order of the spline
intercept :: Bool = false: bool for whether to include an intercept
df :: Int = order - 1 + Int(intercept): degrees of freedom
knots :: Union{Array{T,1}, Nothing} = nothing: full set of knots (excluding repeats)

Examples

julia> bs(collect(0.0:0.2:1.0), df=3)
6×3 Array{Float64,2}:
 0.0    0.0    0.0
 0.384  0.096  0.008
 0.432  0.288  0.064
 0.288  0.432  0.216
 0.096  0.384  0.512
 0.0    0.0    1.0

source

Splinter.is — Method

is(x::AbstractVector{T}; derivs::Int=0, kwargs...) where {T <: Real}

Calculate a basis for I-splines and return x expressed in that basis.

Keyword arguments

derivs: derivatives of the splines
Further keyword arguments are passed to ISplineBasis.

Arguments

boundary_knots :: Union{Tuple{T,T},Nothing} = nothing: boundary knots
interior_knots :: Union{Array{T,1},Nothing} = nothing: interior knots
order :: Int = 4: order of the spline
intercept :: Bool = false: bool for whether to include an intercept
df :: Int = order + Int(intercept): degrees of freedom
knots :: Union{Array{T,1}, Nothing} = nothing: full set of knots (excluding repeats)

Examples

julia> is(collect(0.0:0.2:1.0), df=3)
6×3 Array{Float64,2}:
 0.0     0.0     0.0
 0.1808  0.0272  0.0016
 0.5248  0.1792  0.0256
 0.8208  0.4752  0.1296
 0.9728  0.8192  0.4096
 1.0     1.0     1.0

source

Splinter.ms — Method

ms(x::AbstractVector{T}; center::Union{T,Nothing}=nothing, derivs::Int=0, kwargs...) where {T <: Real}

Calculate a basis for M-splines and return x expressed in that basis.

Keyword arguments

center: value to center the splines
derivs: derivatives of the splines
Further keyword arguments are passed to MSplineBasis.

Arguments

boundary_knots :: Union{Tuple{T,T},Nothing} = nothing: boundary knots
interior_knots :: Union{Array{T,1},Nothing} = nothing: interior knots
order :: Int = 4: order of the spline
intercept :: Bool = false: bool for whether to include an intercept
df :: Int = order - 1 + Int(intercept): degrees of freedom
knots :: Union{Array{T,1}, Nothing} = nothing: full set of knots (excluding repeats)

Examples

julia> ms(collect(0.0:0.2:1.0), df=3)
6×3 Array{Float64,2}:
 0.0    0.0    0.0
 1.536  0.384  0.032
 1.728  1.152  0.256
 1.152  1.728  0.864
 0.384  1.536  2.048
 0.0    0.0    4.0

source

Splinter.ns — Method

ns(x::AbstractVector{T}; center::Union{T,Nothing}=nothing, derivs::Int=0, kwargs...) where {T <: Real}

Calculate a basis for natural B-splines and return x expressed in that basis.

Keyword arguments

center: value to center the splines
derivs: derivatives of the splines
Further keyword arguments are passed to NSplineBasis.

Arguments

boundary_knots :: Union{Tuple{T,T},Nothing} = nothing: boundary knots
interior_knots :: Union{Array{T,1},Nothing} = nothing: interior knots
order :: Int = 4: order of the spline
intercept :: Bool = false: bool for whether to include an intercept
df :: Int = order - 1 + Int(intercept): degrees of freedom
knots :: Union{Array{T,1}, Nothing} = nothing: full set of knots (excluding repeats)

Examples

julia> ns(0.0:0.2:1.0; df=3)

6×3 Matrix{Float64}:
  0.0       0.0        0.0     
 -0.100444  0.409332  -0.272888
  0.102383  0.540852  -0.359235
  0.501759  0.386722  -0.172481
  0.418872  0.327383   0.217745
 -0.142857  0.428571   0.714286

source

Splinter.spline_args — Method

spline_args(x::AbstractVector{T};
            boundary_knots::Union{Tuple{T,T},Nothing}=nothing,
            interior_knots::Union{Vector{T},Nothing}=nothing,
            order::Int=4,
            intercept::Bool=false,
            df::Int=3 + Int(intercept),
            knots::Union{Vector{T},Nothing}=nothing,
            knots_offset::Int=0) where {T<:Real}

Utility function for processing the spline arguments.

Returns the computed boundary and interior knots. If these are already both computed (i.e. not nothing), then returns the passed values.

source