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complete chebyshev_filter
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@yuehhua
yuehhua committed Aug 31, 2022
1 parent a5d756f commit 4e244b1
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36 changes: 17 additions & 19 deletions src/Transform/polynomials.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -165,25 +165,23 @@ function chebyshev_filter(k)
Φ1 = zeros(k, k)
ϕ, ψ1, ψ2 = chebyshev_ϕ_ψ(k)

# ----------------------------------------------------------

# x = Symbol('x')
# kUse = 2*k
# roots = Poly(chebyshevt(kUse, 2*x-1)).all_roots()
# x_m = np.array([rt.evalf(20) for rt in roots]).astype(np.float64)
# # x_m[x_m==0.5] = 0.5 + 1e-8 # add small noise to avoid the case of 0.5 belonging to both phi(2x) and phi(2x-1)
# # not needed for our purpose here, we use even k always to avoid
# wm = np.pi / kUse / 2

# for ki in range(k):
# for kpi in range(k):
# H0[ki, kpi] = 1/np.sqrt(2) * (wm * phi[ki](x_m/2) * phi[kpi](x_m)).sum()
# G0[ki, kpi] = 1/np.sqrt(2) * (wm * psi(psi1, psi2, ki, x_m/2) * phi[kpi](x_m)).sum()
# H1[ki, kpi] = 1/np.sqrt(2) * (wm * phi[ki]((x_m+1)/2) * phi[kpi](x_m)).sum()
# G1[ki, kpi] = 1/np.sqrt(2) * (wm * psi(psi1, psi2, ki, (x_m+1)/2) * phi[kpi](x_m)).sum()

# PHI0[ki, kpi] = (wm * phi[ki](2*x_m) * phi[kpi](2*x_m)).sum() * 2
# PHI1[ki, kpi] = (wm * phi[ki](2*x_m-1) * phi[kpi](2*x_m-1)).sum() * 2
k_use = 2k
c = convert(Polynomial, gen_poly(Chebyshev, k_use))
x_m = roots(c(Polynomial([-1, 2]))) # 2x-1
# x_m[x_m==0.5] = 0.5 + 1e-8 # add small noise to avoid the case of 0.5 belonging to both phi(2x) and phi(2x-1)
# not needed for our purpose here, we use even k always to avoid
wm = π / k_use / 2

for ki in 0:(k-1)
for kpi in 0:(k-1)
H0[ki+1, kpi+1] = 1/sqrt(2) * sum(wm .* ϕ[ki+1].(x_m/2) .* ϕ[kpi+1].(x_m))
H1[ki+1, kpi+1] = 1/sqrt(2) * sum(wm .* ϕ[ki+1].((x_m.+1)/2) .* ϕ[kpi+1].(x_m))
G0[ki+1, kpi+1] = 1/sqrt(2) * sum(wm .* ψ(ψ1, ψ2, ki, x_m/2) .* ϕ[kpi+1].(x_m))
G1[ki+1, kpi+1] = 1/sqrt(2) * sum(wm .* ψ(ψ1, ψ2, ki, (x_m.+1)/2) .* ϕ[kpi+1].(x_m))
Φ0[ki+1, kpi+1] = 2*sum(wm .* ϕ[ki+1].(2x_m) .* ϕ[kpi+1].(2x_m))
Φ1[ki+1, kpi+1] = 2*sum(wm .* ϕ[ki+1].(2 .* x_m .- 1) .* ϕ[kpi+1].(2 .* x_m .- 1))
end
end

zero_out!(H0)
zero_out!(H1)
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38 changes: 19 additions & 19 deletions test/polynomials.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -85,25 +85,25 @@
end

@testset "chebyshev_filter" begin
# H0, H1, G0, G1, Φ1, Φ2 = NeuralOperators.chebyshev_filter(3)
H0, H1, G0, G1, Φ0, Φ1 = NeuralOperators.chebyshev_filter(3)

# @test H0 ≈ [0.70710678 0. 0. ;
# -0.5 0.35355339 0. ;
# -0.25 -0.70710678 0.1767767]
# @test H1 ≈ [0.70710678 0. 0. ;
# 0.5 0.35355339 0. ;
# -0.25 0.70710678 0.1767767]
# @test G0 ≈ [0.60944614 0.77940383 0. ;
# 0.66325172 1.02726613 1.14270252;
# 0.61723435 0.90708619 1.1562954 ]
# @test G1 ≈ [-0.60944614 0.77940383 0. ;
# 0.66325172 -1.02726613 1.14270252;
# -0.61723435 0.90708619 -1.1562954 ]
# @test Φ1 ≈ [1. -0.40715364 -0.21440101;
# -0.40715364 0.84839559 -0.44820615;
# -0.21440101 -0.44820615 0.84002127]
# @test Φ2 ≈ [1. 0.40715364 -0.21440101;
# 0.40715364 0.84839559 0.44820615;
# -0.21440101 0.44820615 0.84002127]
@test H0 ≈ [0.70710678 0. 0. ;
-0.5 0.35355339 0. ;
-0.25 -0.70710678 0.1767767]
@test H1 ≈ [0.70710678 0. 0. ;
0.5 0.35355339 0. ;
-0.25 0.70710678 0.1767767]
@test G0 ≈ [0.60944614 0.77940383 0. ;
0.66325172 1.02726613 1.14270252;
0.61723435 0.90708619 1.1562954 ]
@test G1 ≈ [-0.60944614 0.77940383 0. ;
0.66325172 -1.02726613 1.14270252;
-0.61723435 0.90708619 -1.1562954 ]
@test Φ0 ≈ [1. -0.40715364 -0.21440101;
-0.40715364 0.84839559 -0.44820615;
-0.21440101 -0.44820615 0.84002127]
@test Φ1 ≈ [1. 0.40715364 -0.21440101;
0.40715364 0.84839559 0.44820615;
-0.21440101 0.44820615 0.84002127]
end
end

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