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Merged
merged 5 commits into from
Aug 21, 2022
Merged

ConcreteConversion in Chebyshev-Jacobi #89

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08673ab
ConcreteConversion in Chebyshev-Jacobi
jishnub Aug 16, 2022
fe2eb0a
add tests for deriv
jishnub Aug 20, 2022
e9cd8e1
tests for Chebyshev->Jacobi conversions
jishnub Aug 20, 2022
8d85941
tests for different domains
jishnub Aug 20, 2022
6301e4c
Merge branch 'master' into concreteconversionjacobi
jishnub Aug 20, 2022
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26 changes: 14 additions & 12 deletions src/Spaces/Jacobi/JacobiOperators.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -300,14 +300,14 @@ function Conversion(A::Jacobi,B::Chebyshev)
elseif A.a == A.b == 0
ConversionWrapper(
SpaceOperator(
Conversion(Ultraspherical(1//2),B),
ConcreteConversion(Ultraspherical(1//2),B),
A,B))
elseif A.a == A.b
US = Ultraspherical(A)
ConversionWrapper(Conversion(US,B)*Conversion(A,US))
ConversionWrapper(Conversion(US,B)*ConcreteConversion(A,US))
else
J = Jacobi(B)
Conversion(J,B)*Conversion(A,J)
ConcreteConversion(J,B)*Conversion(A,J)
end
end

Expand All @@ -317,21 +317,22 @@ function Conversion(A::Chebyshev,B::Jacobi)
elseif B.a == B.b == 0
ConversionWrapper(
SpaceOperator(
Conversion(A,Ultraspherical(1//2,domain(B))),
ConcreteConversion(A,Ultraspherical(1//2,domain(B))),
A,B))
elseif B.a == B.b
US = Ultraspherical(B)
ConversionWrapper(Conversion(US,B)*Conversion(A,US))
ConcreteConversion(US,B) * Conversion(A,US)
else
J = Jacobi(A)
Conversion(J,B)*Conversion(A,J)
Conversion(J,B)*ConcreteConversion(A,J)
end
end


function Conversion(A::Jacobi,B::Ultraspherical)
if A.a == A.b == -0.5
ConversionWrapper(Conversion(Chebyshev(domain(A)),B)*Conversion(A,Chebyshev(domain(A))))
ConversionWrapper(Conversion(Chebyshev(domain(A)),B)*
ConcreteConversion(A,Chebyshev(domain(A))))
elseif A.a == A.b == order(B)-0.5
ConcreteConversion(A,B)
elseif A.a == A.b == 0
Expand All @@ -341,16 +342,17 @@ function Conversion(A::Jacobi,B::Ultraspherical)
A,B))
elseif A.a == A.b
US = Ultraspherical(A)
ConversionWrapper(Conversion(US,B)*Conversion(A,US))
ConversionWrapper(Conversion(US,B)*ConcreteConversion(A,US))
else
J = Jacobi(B)
Conversion(J,B)*Conversion(A,J)
ConcreteConversion(J,B)*Conversion(A,J)
end
end

function Conversion(A::Ultraspherical,B::Jacobi)
if B.a == B.b == -0.5
ConversionWrapper(Conversion(Chebyshev(domain(A)),B)*Conversion(A,Chebyshev(domain(A))))
ConversionWrapper(ConcreteConversion(Chebyshev(domain(A)),B)*
Conversion(A,Chebyshev(domain(A))))
elseif B.a == B.b == order(A)-0.5
ConcreteConversion(A,B)
elseif B.a == B.b == 0
Expand All @@ -360,10 +362,10 @@ function Conversion(A::Ultraspherical,B::Jacobi)
A,B))
elseif B.a == B.b
US = Ultraspherical(B)
ConversionWrapper(Conversion(US,B)*Conversion(A,US))
ConversionWrapper(ConcreteConversion(US,B)*Conversion(A,US))
else
J = Jacobi(A)
Conversion(J,B)*Conversion(A,J)
Conversion(J,B)*ConcreteConversion(A,J)
end
end

Expand Down
9 changes: 5 additions & 4 deletions src/Spaces/Ultraspherical/UltrasphericalOperators.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -123,8 +123,8 @@ function Conversion(A::Chebyshev,B::Ultraspherical)
else
d=domain(A)
US=Ultraspherical(order(B)-1,d)
ConversionWrapper(TimesOperator(ConcreteConversion(US,B),
Conversion(Chebyshev(d),US)))
ConversionWrapper(TimesOperator(
ConcreteConversion(US,B), Conversion(A,US)))
end
end

Expand All @@ -148,8 +148,9 @@ function Conversion(A::Ultraspherical,B::Ultraspherical)
ConcreteConversion(A,B)
elseif b-a > 1
d=domain(A)
ConversionWrapper(TimesOperator(ConcreteConversion(Ultraspherical(b-1,d),B),
Conversion(A,Ultraspherical(b-1,d))))
US=Ultraspherical(b-1,d)
ConversionWrapper(TimesOperator(
ConcreteConversion(US,B), Conversion(A,US)))
else
throw(ArgumentError("Cannot convert from $A to $B"))
end
Expand Down
28 changes: 28 additions & 0 deletions test/JacobiTest.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -55,12 +55,40 @@ import ApproxFunOrthogonalPolynomials: jacobip
end
end
end

@testset for d in [-1..1, 0..1]
f = Fun(x->x^2, Chebyshev(d))
C = space(f)
for J1 = Any[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
end
end
end
end
end

@testset "Derivative" begin
D=Derivative(Jacobi(0.,1.,Segment(1.,0.)))
@time testbandedoperator(D)


@testset for d in [-1..1, 0..1]
f = Fun(x->x^2, Chebyshev(d))
C = space(f)
for J = Any[Jacobi(-0.5, -0.5, d), Legendre(d)]
g = (Derivative(J) * Conversion(C, J)) * f
h = Derivative(C) * f
@test g ≈ h

g = (Derivative(C) * Conversion(J, C)) * f
h = Derivative(J) * f
@test g ≈ h
end
end
@testset for S1 in Any[Jacobi(0,0),
Jacobi(0,0,1..2), Jacobi(2,2,1..2), Jacobi(0.5,2.5,1..2)],
S in Any[S1, NormalizedPolynomialSpace(S1)]
Expand Down