-
Notifications
You must be signed in to change notification settings - Fork 112
/
Copy pathconvolution.jl
139 lines (121 loc) · 6.22 KB
/
convolution.jl
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
export ConvolutionInterpolation, FastConvolutionInterpolation, ConvolutionMethod, convolution_interpolation
# for type stability of specialized interpolation functions
struct HigherDimension{N} end
HigherDimension(::Val{N}) where N = HigherDimension{N}()
struct ConvolutionKernel{DG} end
ConvolutionKernel(::Val{DG}) where {DG} = ConvolutionKernel{DG}()
struct GaussianConvolutionKernel{B} end
GaussianConvolutionKernel(::Val{B}) where B = GaussianConvolutionKernel{B}()
struct ConvolutionInterpolation{T,N,TCoefs<:AbstractArray,IT<:NTuple{N,ConvolutionMethod},
Axs<:Tuple,KA,DT,DG,EQ} <: AbstractConvolutionInterpolation{T,N,TCoefs,IT,Axs,KA,DT,DG,EQ}
coefs::TCoefs
knots::Axs
it::IT
h::NTuple{N,Float64}
kernel::KA
dimension::DT
deg::DG
eqs::EQ
end
struct FastConvolutionInterpolation{T,N,TCoefs<:AbstractArray,IT<:NTuple{N,ConvolutionMethod},
Axs<:Tuple,KA,DT,DG,EQ,PR,KP} <: AbstractConvolutionInterpolation{T,N,TCoefs,IT,Axs,KA,DT,DG,EQ}
coefs::TCoefs
knots::Axs
it::IT
h::NTuple{N,Float64}
kernel::KA
dimension::DT
deg::DG
eqs::EQ
pre_range::PR
kernel_pre::KP
end
include("convolution_extrapolation.jl")
include("convolution_coefs.jl")
include("convolution_fast_interpolation.jl")
include("convolution_kernel_interpolation.jl")
include("convolution_kernels.jl")
function ConvolutionInterpolation(knots::NTuple{N,AbstractVector}, vs::AbstractArray{T,N};
degree::Int=3, B=nothing) where {T,N}
eqs = B === nothing ? get_equations_for_degree(degree) : 50
h = map(k -> k[2] - k[1], knots)
it = ntuple(_ -> ConvolutionMethod(), N)
knots_new = expand_knots(knots, eqs-1) # expand boundaries
coefs = create_convolutional_coefs(vs, h, eqs) # create boundaries
kernel = B === nothing ? ConvolutionKernel(Val(degree)) : GaussianConvolutionKernel(Val(B))
dimension = N <= 3 ? Val(N) : HigherDimension(Val(N))
degree = Val(degree)
ConvolutionInterpolation{T,N,typeof(coefs),typeof(it),typeof(knots_new),typeof(kernel),typeof(dimension),typeof(degree),typeof(eqs)}(
coefs, knots_new, it, h, kernel, dimension, degree, eqs
)
end
function FastConvolutionInterpolation(knots::NTuple{N,AbstractVector}, vs::AbstractArray{T,N};
degree::Int=3, precompute::Int=1000, B=nothing) where {T,N}
eqs = B === nothing ? get_equations_for_degree(degree) : 50
h = map(k -> k[2] - k[1], knots)
it = ntuple(_ -> ConvolutionMethod(), N)
knots_new = expand_knots(knots, eqs-1) # expand boundaries
coefs = create_convolutional_coefs(vs, h, eqs) # create boundaries
kernel = B === nothing ? ConvolutionKernel(Val(degree)) : GaussianConvolutionKernel(Val(B))
dimension = N <= 3 ? Val(N) : HigherDimension(Val(N))
pre_range = range(0.0, 1.0, length=precompute)
kernel_pre = zeros(T, precompute, 2*eqs)
for i = 1:2*eqs
kernel_pre[:,i] .= kernel.(pre_range .- eqs .+ i .- 1)
end
degree = Val(degree)
FastConvolutionInterpolation{T,N,typeof(coefs),typeof(it),typeof(knots_new),typeof(kernel),typeof(dimension),typeof(degree),typeof(eqs),typeof(pre_range),typeof(kernel_pre)}(
coefs, knots_new, it, h, kernel, dimension, degree, eqs, pre_range, kernel_pre
)
end
function extend_vector(x::AbstractVector, n_extra::Integer)
step_start = x[2] - x[1]
step_end = x[end] - x[end-1]
start_extension = range(x[1] - n_extra * step_start, step=step_start, length=n_extra)
end_extension = range(x[end] + step_end, step=step_end, length=n_extra)
return vcat(start_extension, x, end_extension)
end
function expand_knots(knots::NTuple{N,AbstractVector}, n_extra::Integer) where N
knots_new = ntuple(i -> extend_vector(knots[i], n_extra), N)
return knots_new
end
getknots(itp::ConvolutionInterpolation) = itp.knots
Base.axes(itp::ConvolutionInterpolation) = axes(itp.coefs)
Base.size(itp::ConvolutionInterpolation) = size(itp.coefs)
lbounds(itp::ConvolutionInterpolation) = first.(itp.knots)
ubounds(itp::ConvolutionInterpolation) = last.(itp.knots)
itpflag(::Type{<:ConvolutionInterpolation{T,N,TCoefs,IT}}) where {T,N,TCoefs,IT} = IT()
coefficients(itp::ConvolutionInterpolation) = itp.coefs
Base.length(itp::ConvolutionInterpolation) = length(itp.coefs)
Base.iterate(itp::ConvolutionInterpolation, state=1) = state > length(itp) ? nothing : (itp[state], state+1)
itpflag(itp::ConvolutionInterpolation) = itp.it
getknots(itp::FastConvolutionInterpolation) = itp.knots
Base.axes(itp::FastConvolutionInterpolation) = axes(itp.coefs)
Base.size(itp::FastConvolutionInterpolation) = size(itp.coefs)
lbounds(itp::FastConvolutionInterpolation) = first.(itp.knots)
ubounds(itp::FastConvolutionInterpolation) = last.(itp.knots)
itpflag(::Type{<:FastConvolutionInterpolation{T,N,TCoefs,IT}}) where {T,N,TCoefs,IT} = IT()
coefficients(itp::FastConvolutionInterpolation) = itp.coefs
Base.length(itp::FastConvolutionInterpolation) = length(itp.coefs)
Base.iterate(itp::FastConvolutionInterpolation, state=1) = state > length(itp) ? nothing : (itp[state], state+1)
itpflag(itp::FastConvolutionInterpolation) = itp.it
lbound(ax::AbstractRange, itp::ConvolutionMethod) = lbound(ax, itpflag(itp))
# accessing the coefficients
function Base.getindex(itp::ConvolutionInterpolation{T,N,TCoefs,IT,Axs,ConvolutionKernel{DG},DT}, I::Vararg{Integer,N}) where {T,N,TCoefs,IT,Axs,DT,DG}
return itp.coefs[I...]
end
function (itp::ConvolutionInterpolation{T,1,TCoefs,IT,Axs,ConvolutionKernel{DG},Val{1}})(i::Integer) where {T,TCoefs,IT,Axs,DG}
return itp.coefs[i]
end
function (itp::ConvolutionInterpolation{T,N,TCoefs,IT,Axs,ConvolutionKernel{DG},DT})(I::Vararg{Integer,N}) where {T,N,TCoefs,IT,Axs,DT,DG}
return itp.coefs[I...]
end
function Base.getindex(itp::FastConvolutionInterpolation{T,N,TCoefs,IT,Axs,ConvolutionKernel{DG},DT}, I::Vararg{Integer,N}) where {T,N,TCoefs,IT,Axs,DT,DG}
return itp.coefs[I...]
end
function (itp::FastConvolutionInterpolation{T,1,TCoefs,IT,Axs,ConvolutionKernel{DG},Val{1}})(i::Integer) where {T,TCoefs,IT,Axs,DG}
return itp.coefs[i]
end
function (itp::FastConvolutionInterpolation{T,N,TCoefs,IT,Axs,ConvolutionKernel{DG},DT})(I::Vararg{Integer,N}) where {T,N,TCoefs,IT,Axs,DT,DG}
return itp.coefs[I...]
end