

In [1]:

    
using BasisFunctions
BA = BasisFunctions
using FrameFun
FE = FrameFun
using DomainSets
using Plots
using LinearAlgebra
gr()









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Plots.GRBackend()

Use AZ algorithm to solve using platform.

Platform implents matrix_A(...) and matrix_Zt(...) routines



In [2]:

    
function myFun(f::Function,P::Platform,i)
    AZS = AZSolver(matrix_A(P,i),matrix_Zt(P,i))
    F = DictFun(primal(P,i),AZS*f)
end









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myFun (generic function with 1 method)

Fourier Basis platform



In [3]:

    
P = BA.fourier_platform()









    Out[3]:





BasisFunctions.GenericPlatform(nothing, BasisFunctions.FourierBasis{Float64}, BasisFunctions.FourierBasis{Float64}, BasisFunctions.#513, BasisFunctions.#514, BasisFunctions.OddDoublingSequence(1), "Fourier series")

works for periodic functions



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f = x->cos(4*pi*x)
F = myFun(f,P,8)
plot(F)

but not for general functions



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f = x->exp(x)
F = myFun(f,P,8)
plot(F)

Singular value profile



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plot(svdvals(matrix(matrix_A(P,5)*matrix_Zt(P,5))),ylims=(-0.1,1.1))

Extension platform - from oversampled platform



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D = 0..0.5
P2a = BasisFunctions.fourier_platform(oversampling=4)
P2 = FrameFun.extension_frame_platform(P2a,D)



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f = x->exp(x)
F2 = myFun(f,P2,8)
plot(F2)

Singular value profile



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plot(svdvals(matrix(matrix_A(P2,5)*matrix_Zt(P2,5))),ylims=(-0.1,1.1))

Weighted Sum Platform based on extension platform

Square root type singularity



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WSP = FrameFun.WeightedSumPlatform([x->sqrt(x),x->1],P2)



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f = x->sqrt(x)*(1-x)-exp(x)
FSP = myFun(f,WSP,8)
plot(FSP,f)

This is much more accurate than the regular extension platform



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FSPb = myFun(f,P2,8)
plot(FSP,f)
plot!(FSPb,f)

Singular value profile



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plot(svdvals(matrix(matrix_A(WSP,7)*matrix_Zt(WSP,7))),ylims=(-0.1,4.1))



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