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A Lift of a Function is a Function #211

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Aug 5, 2024
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A Lift of a Function is a Function #211

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23 changes: 13 additions & 10 deletions src/differential_geometry.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -29,7 +29,7 @@ end
"""
$(TYPEDSIGNATURES)

Return the HamiltonianLift of a function.
Return the Lift of a function.
Dependencies are specified with boolean : autonomous and variable.

# Example
Expand All @@ -42,16 +42,19 @@ julia> H(1, 1, 1, 1)
2
```
"""
function Lift(X::Function; autonomous::Bool=true, variable::Bool=false)::HamiltonianLift
time_dependence = autonomous ? Autonomous : NonAutonomous
variable_dependence = variable ? NonFixed : Fixed
return Lift(VectorField(X, time_dependence, variable_dependence))
function Lift(X::Function; autonomous::Bool=true, variable::Bool=false)::Function
return @match (autonomous, variable) begin
(true , false) => ( x, p ) -> p' * X( x )
(true , true ) => ( x, p, v) -> p' * X( x, v)
(false, false) => (t, x, p ) -> p' * X(t, x )
_ => (t, x, p, v) -> p' * X(t, x, v)
end
end

"""
$(TYPEDSIGNATURES)

Return the HamiltonianLift of a VectorField or a function.
Return the Lift of a function.
Dependencies are specified with DataType : Autonomous, NonAutonomous and Fixed, NonFixed.

# Example
Expand All @@ -64,11 +67,11 @@ julia> H(1, 1, 1, 1)
2
```
"""
function Lift(X::Function, dependences::DataType...)::HamiltonianLift
function Lift(X::Function, dependences::DataType...)::Function
__check_dependencies(dependences)
variable_dependence = NonFixed ∈ dependences ? NonFixed : Fixed
time_dependence = NonAutonomous ∈ dependences ? NonAutonomous : Autonomous
return Lift(VectorField(X, time_dependence, variable_dependence))
autonomous = NonAutonomous ∈ dependences ? false : true
variable = NonFixed ∈ dependences ? true : false
return Lift(X; autonomous=autonomous, variable=variable)
end

# ---------------------------------------------------------------------------
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26 changes: 16 additions & 10 deletions test/test_differential_geometry.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -101,6 +101,12 @@ function test_differential_geometry()
Test.@test H(1, 1, 1, 1) == 2
Test.@test H(1, [1, 2], [3, 4], 1) == 22

# overload
F::Function = x -> 2x
H_F(x, p) = Lift(F)(x, p)
H_F(y) = H_F(y, y)
Test.@test H_F(1) == 2

# exceptions
Test.@test_throws IncorrectArgument Lift(X, Int64)

Expand Down Expand Up @@ -386,12 +392,12 @@ function test_differential_geometry()
@testset "nonautonomous case" begin
f = (t, x) -> [t*x[1] + x[2]^2, x[1], 0]
g = (t, x) -> [0, x[2], t*x[1]^2 + 4*x[2]]
F = Lift(f,NonAutonomous)
G = Lift(g,NonAutonomous)
F = Lift(f, NonAutonomous)
G = Lift(g, NonAutonomous)
F_ = (t, x, p) -> p' * f(t, x)
G_ = (t, x, p) -> p' * g(t, x)
Test.@test Poisson(F, G)(2, [1, 2, 3], [4, 0, 4]) ≈ Poisson(F_, G_, NonAutonomous)(2, [1, 2, 3], [4, 0, 4]) atol=1e-6
Test.@test Poisson(F, G_)(2, [1, 2, 3], [4, 0, 4]) ≈ Poisson(F_, G)(2, [1, 2, 3], [4, 0, 4]) atol=1e-6
Test.@test Poisson(F, G, NonAutonomous)(2, [1, 2, 3], [4, 0, 4]) ≈ Poisson(F_, G_, NonAutonomous)(2, [1, 2, 3], [4, 0, 4]) atol=1e-6
Test.@test Poisson(F, G_, NonAutonomous)(2, [1, 2, 3], [4, 0, 4]) ≈ Poisson(F_, G, NonAutonomous)(2, [1, 2, 3], [4, 0, 4]) atol=1e-6
end

@testset "autonomous nonfixed case" begin
Expand All @@ -401,19 +407,19 @@ function test_differential_geometry()
G = Lift(g, NonFixed)
F_ = (x, p, v) -> p' * f(x, v)
G_ = (x, p, v) -> p' * g(x, v)
Test.@test Poisson(F, G)([1, 2, 3], [4, 0, 4], 1) ≈ Poisson(F_, G_, NonFixed)([1, 2, 3], [4, 0, 4], 1) atol=1e-6
Test.@test Poisson(F, G_)([1, 2, 3],[4, 0, 4], 1) ≈ Poisson(F_, G)([1, 2, 3],[4, 0, 4], 1) atol=1e-6
Test.@test Poisson(F, G, NonFixed)([1, 2, 3], [4, 0, 4], 1) ≈ Poisson(F_, G_, NonFixed)([1, 2, 3], [4, 0, 4], 1) atol=1e-6
Test.@test Poisson(F, G_, NonFixed)([1, 2, 3],[4, 0, 4], 1) ≈ Poisson(F_, G, NonFixed)([1, 2, 3],[4, 0, 4], 1) atol=1e-6
end

@testset "nonautonomous nonfixed case" begin
f = (t, x, v) -> [t*x[1] + v*x[2]^2, x[1], 0]
g = (t, x, v) -> [0, x[2], t*x[1]^2 + v*4*x[2]]
F = Lift(f,NonAutonomous, NonFixed)
G = Lift(g,NonAutonomous, NonFixed)
F = Lift(f, NonAutonomous, NonFixed)
G = Lift(g, NonAutonomous, NonFixed)
F_ = (t, x, p, v) -> p' * f(t, x, v)
G_ = (t, x, p, v) -> p' * g(t, x, v)
Test.@test Poisson(F, G)(2, [1, 2, 3], [4, 0, 4], 1) ≈ Poisson(F_, G_, NonAutonomous, NonFixed)(2, [1, 2, 3], [4, 0, 4], 1) atol=1e-6
Test.@test Poisson(F, G_)(2, [1, 2, 3], [4, 0, 4], 1) ≈ Poisson(F_, G)(2, [1, 2, 3], [4, 0, 4], 1) atol=1e-6
Test.@test Poisson(F, G, NonAutonomous, NonFixed)(2, [1, 2, 3], [4, 0, 4], 1) ≈ Poisson(F_, G_, NonAutonomous, NonFixed)(2, [1, 2, 3], [4, 0, 4], 1) atol=1e-6
Test.@test Poisson(F, G_, NonAutonomous, NonFixed)(2, [1, 2, 3], [4, 0, 4], 1) ≈ Poisson(F_, G, NonAutonomous, NonFixed)(2, [1, 2, 3], [4, 0, 4], 1) atol=1e-6
end

end
Expand Down
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