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July 26, 2019 14:40
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Interpolations on an irregular grid
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#= | |
The MIT License (MIT) | |
Copyright (c) 2015: Luke Stagner, Jens Adam | |
Permission is hereby granted, free of charge, to any person obtaining a copy of this software and | |
associated documentation files (the "Software"), to deal in the Software without restriction, | |
including without limitation the rights to use, copy, modify, merge, publish, distribute, | |
sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is | |
furnished to do so, subject to the following conditions: | |
The above copyright notice and this permission notice shall be included in all copies or substantial | |
portions of the Software. | |
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT | |
NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND | |
NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES | |
OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN | |
CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. | |
=# | |
module IrregularInterpolate | |
using LinearAlgebra | |
export PolyharmonicSpline, interpolate | |
struct PolyharmonicSpline{T} | |
dim::Int | |
order::Int | |
coeff::Vector{T} | |
centers::Matrix{T} | |
error::T | |
end | |
function polyharmonicK(r, K) | |
if iseven(K) | |
return r < 1 ? r^(K-1) * log(r^r) : (r^K) * log(r) | |
else | |
return r^K | |
end | |
end | |
function PolyharmonicSpline(K::Int, centers::Matrix{T}, values::Array{T}; s = zero(T)) where {T} | |
N, dim = size(centers) | |
N != length(values) && throw(DimensionMismatch()) | |
phK = Matrix{T}(undef, N, N) | |
for i in 1:N | |
for j in 1:N | |
dist = 0.0 | |
for d in 1:dim | |
dist += (centers[i, d] - centers[j, d])^2 | |
end | |
phK[i, j] = polyharmonicK(sqrt(dist), K) | |
end | |
end | |
A = copy(phK) | |
B = zeros(T, N, dim+1) | |
for i in 1:N | |
B[i, 1] = 1 | |
B[i, 2:end] = centers[i, :] | |
end | |
A .+= s .* Diagonal(I, N) | |
L = [A B; B' zeros(T, dim+1, dim+1)] | |
w = pinv(L) * [values; zeros(T, dim+1)] | |
ivalues = zeros(T, N) | |
for i in 1:N | |
tmp = 0.0 | |
for j in 1:N | |
tmp += w[j] * phK[i, j] | |
end | |
tmp += w[N+1] | |
for j in 2:dim+1 | |
tmp += w[N+j] * centers[i, j-1] | |
end | |
ivalues[i] = tmp | |
end | |
error = norm(values .- ivalues) | |
return PolyharmonicSpline(dim, K, w, centers, error) | |
end | |
function PolyharmonicSpline(K::Int, centers::Vector{T}, values::Vector{T}; s = zero(T)) where {T} | |
# PolyharmonicSpline(K, centers'', values, s = s) | |
PolyharmonicSpline(K, centers, values, s = s) | |
end | |
function interpolate(S::PolyharmonicSpline{T}, x::Matrix{T}) where {T} | |
m, n = size(x) | |
n != S.dim && throw(DimensionMismatch("$m != $(S.dim)")) | |
l = length(S.coeff) - (n+1) | |
interpolates = zeros(T, m) | |
for i in 1:m | |
tmp = 0.0 | |
for j in 1:l | |
dist = 0.0 | |
for d in 1:n | |
dist += (x[i, d] - S.centers[j, d])^2 | |
end | |
tmp += S.coeff[j] * polyharmonicK(sqrt(dist), S.order) | |
end | |
tmp += S.coeff[l+1] | |
for j in 2:n+1 | |
tmp += S.coeff[l+j] * x[i, j-1] | |
end | |
interpolates[i] = tmp | |
end | |
return interpolates | |
end | |
function interpolate(S::PolyharmonicSpline{T}, x::Vector{T}) where {T} | |
return interpolate(S, x) | |
end | |
function interpolate(S::PolyharmonicSpline{T}, x::Vector{T}, y::Vector{T}) where {T} | |
return interpolate(S, [x y]) | |
end | |
function interpolate(S::PolyharmonicSpline{T}, x::Vector{T}, y::Vector{T}, z::Vector{T}) where {T} | |
return interpolate(S, [x y z]) | |
end | |
end # module |
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Ported from this script.
Example usage: