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Basis Function Expansions for Julia

License: Other

Julia 100.00%

approximation linear-regression time-series-analysis function-expansion function-approximation julia-package

basisfunctionexpansions.jl's People

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tkelman fargolo mleprovost valentinkaisermayer standardgalactic tangwang-ustc

basisfunctionexpansions.jl's Issues

New ambiguity on Julia 1.3

While running the package tests for the upcoming 1.3, a new ambiguity in this package was detected:

ERROR: LoadError: LoadError: MethodError: LPVSS(::MultiRBFE{BasisFunctionExpansions.var"##21#25"{Array{Float64,2},Array{Array{Float64,2},1}},Array{Float64,2},Array{Float64,2}}, ::Array{Float64,2}, ::Array{Float64,2}, ::Array{Float64,1}) is ambiguous. Candidates:
  LPVSS(bfe::BasisFunctionExpansion, params, cov, σ) in BasisFunctionExpansions at /root/.julia/packages/BasisFunctionExpansions/tggwO/src/dynamics.jl:81
  LPVSS(x, u, v::Union{AbstractArray{T,1}, AbstractArray{T,2}} where T, nc) in BasisFunctionExpansions at /root/.julia/packages/BasisFunctionExpansions/tggwO/src/dynamics.jl:154
Possible fix, define
  LPVSS(::BasisFunctionExpansion, ::Any, ::Union{AbstractArray{T,1}, AbstractArray{T,2}} where T, ::Any)
Stacktrace:
 [1] #LPVSS#62(::Bool, ::Float64, ::Type{LPVSS}, ::Adjoint{Float64,Array{Float64,2}}, ::Adjoint{Float64,Array{Float64,2}}, ::Int64) at /root/.julia/packages/BasisFunctionExpansions/tggwO/src/dynamics.jl:120
 [2] (::Core.var"#kw#Type")(::NamedTuple{(:normalize, :λ),Tuple{Bool,Float64}}, ::Type{LPVSS}, ::Adjoint{Float64,Array{Float64,2}}, ::Adjoint{Float64,Array{Float64,2}}, ::Int64) at ./none:0
 [3] top-level scope at /root/.julia/packages/BasisFunctionExpansions/tggwO/test/test_LPVSS.jl:25
 [4] include at ./boot.jl:328 [inlined]
 [5] include_relative(::Module, ::String) at ./loading.jl:1105
 [6] include(::Module, ::String) at ./Base.jl:31
 [7] include(::String) at ./client.jl:432
 [8] top-level scope at /root/.julia/packages/BasisFunctionExpansions/tggwO/test/runtests.jl:123
 [9] include at ./boot.jl:328 [inlined]
 [10] include_relative(::Module, ::String) at ./loading.jl:1105
 [11] include(::Module, ::String) at ./Base.jl:31
 [12] include(::String) at ./client.jl:432
 [13] top-level scope at none:6
in expression starting at /root/.julia/packages/BasisFunctionExpansions/tggwO/test/test_LPVSS.jl:25
in expression starting at /root/.julia/packages/BasisFunctionExpansions/tggwO/test/runtests.jl:123

We believe this is a real ambiguity that got detected due to improvements in the Julia type system and thus needs to be fixed in this package.

How to get basis coefficients?

First off, thanks for this package!

Is there an API to retrieve basis coefficients and reconstruct approximation objects? I need to retrieve coefficients of approximation, do some calculations with them, generate new coefficients and reconstruct a signal with the updated coefficients using the same radial basis.

Please let me know how I can achieve this. If there is no exposed API yet, is it safe to lookup bfa.linear_combinations?

Is there an option to have the input and output be for different dimensions?

For example, consider the problem y=Mx, where M is mxn dimension and a set of basis functions. Is there a way that we can estimate the basis functions in M here?

plotrecipes dep

Hi,
this package depends on PlotRecipes, but you don't seem to be using it. I'm guessing it's a mistake and the REQUIRE file should hold RecipesBase instead?
BTW very pretty graphs. I believe that the color bar issue with the Plotly surface should be solved on current Plots.

TODO

Initialization by clustering
Support also full covariance matrix using the clustering initialization
Additional basis functions
Parameter covariance
Output covariance

Plot recipe for rbf is broken

Copying/pasting the example in the docs:

N   = 200
v   = linspace(0,10,N)
y   = 0.1*(v-2).*(v-7) + 0.2randn(N)
rbf = UniformRBFE(v, 5, normalize = true)
bfa = BasisFunctionApproximation(y,v,rbf)

scatter(v,y,lab="Signal",c=:orange, subplot=1, xlabel="\$v\$", size=(600,300))
plot!(rbf) # this is broken
plot!(v,bfa(v),lab="Reconstruction",c=:blue,linewidth=2)

UndefVarError: HSV not defined

function normalized_squared_exponential(v, vc, gamma::Number)
    r = squared_exponential(v, vc, gamma)
    r ./= (sum(r, dims=2) .+ 1e-8)  
end

Which yields the incorrect extrapolation behaviour:

The correct implementation would be

function normalized_squared_exponential(v, vc, gamma::Number)
    r = squared_exponential(v, vc, gamma)
    r ./= (sum(r, dims=2))  
end

Which yields:

However, for points that are really far outside of the support of the RBF this does not work either.
I have a somewhat hacked solution:

function normalized_squared_exponential(v, vc, gamma::Number)
    r = squared_exponential(v, vc, gamma)
    s = vec(sum(r, dims=2))
    r ./= s
    r[isnan.(r)] .= 0.
    r[(s .<= eps()) .& (v .< vc[1]), 1] .= 1.
    r[(s .<= eps()) .& (v .> vc[end]), end] .= 1.
    r
end

This assumes that vc is ordered increasingly.

baggepinnen / basisfunctionexpansions.jl Goto Github PK

basisfunctionexpansions.jl's People

Contributors

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basisfunctionexpansions.jl's Issues

New ambiguity on Julia 1.3

How to get basis coefficients?

Is there an option to have the input and output be for different dimensions?

plotrecipes dep

TODO

Plot recipe for rbf is broken

Register

Derivatives

Wrong Normalization

Run femtocleaner

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