Skip to content

Ultraspherical conversion in Jacobi #190

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Merged
merged 4 commits into from
Feb 18, 2023
Merged

Ultraspherical conversion in Jacobi #190

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
4 commits
Select commit Hold shift + click to select a range
e76efa8
Ultraspherical conversion in Jacobi
jishnub Feb 18, 2023
0fd1b9f
Specialize Chebyshev cases
jishnub Feb 18, 2023
a57a074
change equality to approx
jishnub Feb 18, 2023
f89ac6d
Add Legendre conversion tests
jishnub Feb 18, 2023
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
2 changes: 1 addition & 1 deletion Project.toml
View file
Open in desktop
Original file line number Diff line number Diff line change
@@ -1,6 +1,6 @@
name = "ApproxFunOrthogonalPolynomials"
uuid = "b70543e2-c0d9-56b8-a290-0d4d6d4de211"
version = "0.6.9"
version = "0.6.10"

[deps]
ApproxFunBase = "fbd15aa5-315a-5a7d-a8a4-24992e37be05"
Expand Down
44 changes: 27 additions & 17 deletions src/Spaces/Jacobi/JacobiOperators.jl
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -142,14 +142,22 @@ function Conversion(L::Jacobi,M::Jacobi)
domain(L) == domain(M) || domain(L) == reverseorientation(domain(M)) ||
throw(ArgumentError("Domains must be the same"))

if isapproxinteger(L.a-M.a) && isapproxinteger(L.b-M.b)
dm=domain(M)
if isapprox(M.a,L.a) && isapprox(M.b,L.b)
ConversionWrapper(Operator(I,L))
elseif (isapprox(M.b,L.b+1) && isapprox(M.a,L.a)) ||
(isapprox(M.b,L.b) && isapprox(M.a,L.a+1))
ConcreteConversion(L,M)
elseif M.b >= L.b && M.a >= L.a
dm=domain(M)
dl=domain(L)

if isapproxinteger(L.a-M.a) && isapproxinteger(L.b-M.b) && M.b >= L.b && M.a >= L.a
if isapprox(L.a,M.a) && isapprox(L.b,M.b)
return ConversionWrapper(Operator(I,L))
elseif (isapprox(L.b+1,M.b) && isapprox(L.a,M.a)) ||
(isapprox(L.b,M.b) && isapprox(L.a+1,M.a))
return ConcreteConversion(L,M)
elseif L.a ≈ L.b ≈ -0.5 && M.a ≈ M.b
return Conversion(L,Chebyshev(dl),Ultraspherical(M),M)
elseif L.a ≈ L.b && M.a ≈ M.b ≈ -0.5
return Conversion(L,Ultraspherical(L),Chebyshev(dm),M)
elseif L.a ≈ L.b && M.a ≈ M.b
return Conversion(L,Ultraspherical(L),Ultraspherical(M),M)
else
# We split this into steps where a and b are changed by 1:
# Define the intermediate space J = Jacobi(M.b, L.a, dm)
# Conversion(L, M) == Conversion(J, M) * Conversion(L, J)
Expand All @@ -158,17 +166,19 @@ function Conversion(L::Jacobi,M::Jacobi)
CLJ = [ConcreteConversion(Jacobi(b-1,L.a,dm), Jacobi(b, L.a, dm)) for b in M.b:-1:L.b+1]
CJM = [ConcreteConversion(Jacobi(M.b,a-1,dm), Jacobi(M.b, a, dm)) for a in M.a:-1:L.a+1]
C = [CJM; CLJ]
ConversionWrapper(TimesOperator(C))
else
error("Implement for $L → $M")
return ConversionWrapper(TimesOperator(C))
end
elseif isapproxinteger_addhalf(L.a - M.a) && isapproxinteger_addhalf(L.b - M.b)
if L.a ≈ L.b && M.a ≈ M.b ≈ -0.5
return Conversion(L,Ultraspherical(L),Chebyshev(dm),M)
elseif L.a ≈ L.b ≈ -0.5 && M.a ≈ M.b && M.a >= L.a
return Conversion(L,Chebyshev(dl),Ultraspherical(M),M)
elseif L.a ≈ L.b && M.a ≈ M.b && M.a >= L.a
return Conversion(L,Ultraspherical(L),Ultraspherical(M),M)
end
elseif L.a ≈ L.b ≈ 0 && M.a ≈ M.b ≈ 0.5
Conversion(L,Ultraspherical(L),Ultraspherical(M),M)
elseif L.a ≈ L.b ≈ 0 && M.a ≈ M.b ≈ -0.5
Conversion(L,Ultraspherical(L),Chebyshev(M),M)
else # L.a - M.a ≈ L.b - M.b
error("Implement for $L → $M")
end

error("Implement for $L → $M")
end

bandwidths(::ConcreteConversion{<:Jacobi,<:Jacobi}) = (0,1)
Expand Down
64 changes: 55 additions & 9 deletions test/JacobiTest.jl
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -48,18 +48,64 @@ using Static
testtransforms(Jacobi(-0.5,-0.5))
@test norm(Fun(Fun(exp),Jacobi(-.5,-.5))-Fun(exp,Jacobi(-.5,-.5))) < 300eps()

@testset for d in [-1..1, 0..1]
f = Fun(x->x^2, Chebyshev(d))
C = space(f)
for J1 in (Jacobi(-0.5, -0.5, d), Legendre(d),
Jacobi(0.5, 0.5, d), Jacobi(2.5, 1.5, d))
for J in (J1, NormalizedPolynomialSpace(J1))
g = Fun(f, J)
if !any(isnan, coefficients(g))
@test Conversion(C, J) * f ≈ g
@testset for d in (-1..1, 0..1, ChebyshevInterval())
@testset "Chebyshev" begin
f = Fun(x->x^2, Chebyshev(d))
C = space(f)
for J1 in (Jacobi(-0.5, -0.5, d), Legendre(d),
Jacobi(0.5, 0.5, d), Jacobi(2.5, 1.5, d))
@testset for J in (J1, NormalizedPolynomialSpace(J1))
g = Fun(f, J)
if !any(isnan, coefficients(g))
@test Conversion(C, J) * f ≈ g
end
end
end
end
@testset "legendre" begin
f = Fun(x->x^2, Legendre(d))
C = space(f)
for J1 in (Jacobi(-0.5, -0.5, d), Legendre(d),
Jacobi(0.5, 0.5, d), Jacobi(1, 1, d))
@testset for J in (J1, NormalizedPolynomialSpace(J1))
g = Fun(f, J)
if !any(isnan, coefficients(g))
@test Conversion(C, J) * f ≈ g
end
end
end
end
@testset "Ultraspherical(0.5)" begin
f = Fun(x->x^2, Ultraspherical(0.5,d))
U = space(f)
for J1 in (Jacobi(-0.5, -0.5, d), Legendre(d),
Jacobi(0.5, 0.5, d))
@testset for J in (J1, NormalizedPolynomialSpace(J1))
g = Fun(f, J)
if !any(isnan, coefficients(g))
@test Conversion(U, J) * f ≈ g
end
end
end
end
@testset "Ultraspherical(1)" begin
f = Fun(x->x^2, Ultraspherical(1,d))
U = space(f)
for J1 in (Legendre(d), Jacobi(0.5, 0.5, d), Jacobi(1.5, 0.5, d),
Jacobi(0.5, 1.5, d))
@testset for J in (J1,)
g = Fun(f, J)
if !any(isnan, coefficients(g))
@test Conversion(U, J) * f ≈ g
end
end
end
end
end

@testset for (S1, S2) in ((Legendre(), Jacobi(-0.5, -0.5)), (Jacobi(-0.5, -0.5), Legendre()),
(Legendre(), Jacobi(1.5, 1.5)))
@test Conversion(S1, S2) * Fun(x->x^4, S1) ≈ Fun(x->x^4, S2)
end

@testset "inference tests" begin
Expand Down