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runtests.jl
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runtests.jl
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using Smolyak
using Test
# make a linear function to predict
global slopes = rand(4)
for basis_fun_type in [:chebyshev, :spread], mu_ in 1:4
@testset "testing interpolation on grid with mu=$mu_ with basis fun = $(basis_fun_type)" begin
println("1D")
truefun1(x) = 1.1 + x[1]^3
mu = [mu_]
xbnds = [[-2., rand()] for i in 1:length(mu)]
# Smolyak Components
sk = SmolyakKernel(mu, xbnds)
sg = SmolyakGrid(sk)
sb = SmolyakBasis(basis_fun_type, sk; NumDeriv=0)
sp = SmolyakPoly(sb; NumDeriv=0)
# Get true values of function at grid points
W = truefun1.(xgrid(sg))
# Generate corresponding Smolyak Basis Functions
BF = VVtoMatrix(BasisFunctions(xgrid(sg), sb));
# Solve for the coefficients
θ = BF\W
# Update the coefficients
coef!(θ, sp) # Update coefficient in Smolyak Polynomial
# Evaluate Smolayk poly on Smolyak Grid
What = value(xgrid(sg) , sp)
# Check maximum difference
@test maximum(abs, W-What) < 1e-12
println("2D")
truefun2(x) = 1.1 + (x[1]-x[2]^2)^2
mu = [mu_,mu_]
xbnds = [[-2., rand()] for i in 1:length(mu)]
# Smolyak Components
sk = SmolyakKernel(mu, xbnds)
sg = SmolyakGrid(sk)
sb = SmolyakBasis(basis_fun_type, sk; NumDeriv=0)
sp = SmolyakPoly(sb; NumDeriv=0)
# Get true values of function at grid points
W = truefun2.(xgrid(sg))
# Generate corresponding Smolyak Basis Functions
BF = VVtoMatrix(BasisFunctions(xgrid(sg), sb));
# Solve for the coefficients
θ = BF\W
# Update the coefficients
coef!(θ, sp) # Update coefficient in Smolyak Polynomial
# Evaluate Smolayk poly on Smolyak Grid
What = value(xgrid(sg) , sp)
# Check maximum difference
@test maximum(abs, W-What) <1e-12
println("3D")
truefun3(x) = 1.1 + (x[1]-x[2]^2)^2 + x[3]^2
mu = [mu_,mu_,mu_]
xbnds = [[-2., rand()] for i in 1:length(mu)]
# Smolyak Components
sk = SmolyakKernel(mu, xbnds)
sg = SmolyakGrid(sk)
sb = SmolyakBasis(basis_fun_type, sk; NumDeriv=0)
sp = SmolyakPoly(sb; NumDeriv=0)
# Get true values of function at grid points
W = truefun3.(xgrid(sg))
# Generate corresponding Smolyak Basis Functions
BF = VVtoMatrix(BasisFunctions(xgrid(sg), sb));
# Solve for the coefficients
θ = BF\W
# Update the coefficients
coef!(θ, sp) # Update coefficient in Smolyak Polynomial
# Evaluate Smolayk poly on Smolyak Grid
What = value(xgrid(sg) , sp)
# Check maximum difference
@test maximum(abs, W-What) <1e-12
println("4D")
truefun4(x) = 1.1 + (x[1]-x[2]^2)^2 + x[3]^2 - (x[3]+x[4])^2
mu = [mu_,mu_,mu_,mu_]
xbnds = [[-2., rand()] for i in 1:length(mu)]
# Smolyak Components
sk = SmolyakKernel(mu, xbnds)
sg = SmolyakGrid(sk)
sb = SmolyakBasis(basis_fun_type, sk; NumDeriv=0)
sp = SmolyakPoly(sb; NumDeriv=0)
# Get true values of function at grid points
W = truefun4.(xgrid(sg))
# Generate corresponding Smolyak Basis Functions
BF = VVtoMatrix(BasisFunctions(xgrid(sg), sb));
# Solve for the coefficients
θ = BF\W
# Update the coefficients
coef!(θ, sp) # Update coefficient in Smolyak Polynomial
# Evaluate Smolayk poly on Smolyak Grid
What = value(xgrid(sg) , sp)
# Check maximum difference
@test maximum(abs, W-What) <1e-12
end
end
for basis_fun_type in [:chebyshev, :spread], mu_ in 1:4
@testset "testing interpolation off grid with mu=$(mu_)" begin
# random point picker
rpoint(lb,ub) = (ub - lb)*rand() + lb
rpoint(bounds) = rpoint(bounds...)
println("one dimension")
function truefun1(x)
return 1.1 + slopes[1]*x[1]
end
mu = [mu_]
xbnds = [[-2., 12.] for i in 1:length(mu)]
# Smolyak Components
sk = SmolyakKernel(mu, xbnds)
sg = SmolyakGrid(sk)
sb = SmolyakBasis(basis_fun_type, sk; NumDeriv=0)
sp = SmolyakPoly(sb; NumDeriv=0)
# Get true values of function at grid points
W = truefun1.(xgrid(sg))
# Solve for the coefficients
BF = VVtoMatrix(BasisFunctions(xgrid(sg), sb));
θ = BF\W
# Update coefficient in Smolyak Polynomial
coef!(θ, sp)
# make basis on random point
NumObs = 10
xx = [rpoint.(xbnds) for n in 1:NumObs]
What = value(xx , sp)
@test isapprox(What, truefun1.(xx), atol=1e-6)
println("2D")
function truefun2(x)
return 1.1 + slopes[1]*x[1] - slopes[2]*x[2]
end
mu = [mu_,mu_]
xbnds = [[-2., 12.] for i in 1:length(mu)]
# Smolyak Components
sk = SmolyakKernel(mu, xbnds)
sg = SmolyakGrid(sk)
sb = SmolyakBasis(basis_fun_type, sk; NumDeriv=0)
sp = SmolyakPoly(sb; NumDeriv=0)
# Solve for the coefficients
BF = VVtoMatrix(BasisFunctions(xgrid(sg), sb));
θ = BF\truefun2.(xgrid(sg))
# Update coefficient in Smolyak Polynomial
coef!(θ, sp)
# make basis on random point
NumObs = 10
xx = [rpoint.(xbnds) for n in 1:NumObs]
What = value(xx , sp)
@test isapprox(What, truefun2.(xx), atol=1e-6)
println("3D")
function truefun3(x)
return 1.1 + slopes[1]*x[1] - slopes[2]*x[2] + slopes[3]*x[3]
end
mu = [mu_,mu_,mu_]
xbnds = [[-2., 12.] for i in 1:length(mu)]
# Smolyak Components
sk = SmolyakKernel(mu, xbnds)
sg = SmolyakGrid(sk)
sb = SmolyakBasis(basis_fun_type, sk; NumDeriv=0)
sp = SmolyakPoly(sb; NumDeriv=0)
# Solve for the coefficients
BF = VVtoMatrix(BasisFunctions(xgrid(sg), sb));
θ = BF\truefun3.(xgrid(sg))
# Update coefficient in Smolyak Polynomial
coef!(θ, sp)
# make basis on random point
NumObs = 10
xx = [rpoint.(xbnds) for n in 1:NumObs]
What = value(xx , sp)
@test isapprox(What, truefun3.(xx), atol=1e-6)
println("4D")
function truefun4(x)
return 1.1 + slopes[1]*x[1] - slopes[2]*x[2] + slopes[3]*x[3] * slopes[4] * x[4]
end
mu = [mu_,mu_,mu_,mu_]
xbnds = [[-2., 12.] for i in 1:length(mu)]
# Smolyak Components
sk = SmolyakKernel(mu, xbnds)
sg = SmolyakGrid(sk)
sb = SmolyakBasis(basis_fun_type, sk; NumDeriv=0)
sp = SmolyakPoly(sb; NumDeriv=0)
# Solve for the coefficients
BF = VVtoMatrix(BasisFunctions(xgrid(sg), sb));
θ = BF\truefun4.(xgrid(sg))
# Update coefficient in Smolyak Polynomial
coef!(θ, sp)
# make basis on random point
NumObs = 10
xx = [rpoint.(xbnds) for n in 1:NumObs]
What = value(xx , sp)
if mu_ == 1
println("approximation level mu=1 is too low in 4D with multiplicative component.")
for i in 1:NumObs
#@test !isapprox(What, truefun.(xx), atol=1e-6)
end
else
for i in 1:NumObs
@test isapprox(What, truefun4.(xx), atol=1e-6)
end
end
end
end