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Add setinverse #25

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Sep 28, 2022
Merged

Add setinverse #25

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e6826aa
Add setinverse
oschulz Sep 23, 2022
c84aa36
Fix docstring of setinverse
oschulz Sep 23, 2022
f3c7053
Fix docstring of setinverse
oschulz Sep 23, 2022
c4c2c83
Fix docs gen
oschulz Sep 23, 2022
18051bd
Improve setinverse docs and implementation
oschulz Sep 24, 2022
62bca9b
Shorten definition of setinverse
oschulz Sep 25, 2022
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4 changes: 3 additions & 1 deletion docs/src/api.md
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Expand Up @@ -5,6 +5,7 @@
```@docs
inverse
NoInverse
setinverse
```

## Test utility
Expand All @@ -13,8 +14,9 @@ NoInverse
InverseFunctions.test_inverse
```

## Additional functions
## Additional functionality

```@docs
InverseFunctions.square
InverseFunctions.FunctionWithInverse
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Since it's not exported and not intended to be constructed directly, I wonder if it should be omitted from the docs?

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I thought people might want to have the option to dispatch on it, in low-level uses cases and so on, that's why I made it party of the official API.

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I assumed that this was the motivation. I wonder, however, how often one would actually want to dispatch on FunctionWithInverse. I assume for many cases it would be simpler to just use unwrap_f (or something equivalent of the same name) and inverse - similar to the setinverse case in this PR.

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@oschulz oschulz Sep 25, 2022 •
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I wonder, however, how often one would actually want to dispatch on FunctionWithInverse.

We may actually have occasion to do that in the pushforward measure in MeasureBase (in the context of JuliaMath/MeasureBase.jl#89, since PushforwardMeasure stores both forward and inverse function for performance reasons). Not sure yet - but it's an interesting option (we may want to extract forward and inverse from FunctionWithInverse). So there's at least one possible use case, so there may be more. And it doesn't cost us anything, I wouldn't expect FunctionWithInverse to change in breaking ways in the future.

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since PushforwardMeasure stores both forward and inverse function for performance reasons

To obtain these you don't have to specialize on FunctionWithInverse though. You could just store _unwrap_f(f) and inverse(f) if an arbitrary f is provided.

```
1 change: 1 addition & 0 deletions src/InverseFunctions.jl
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Expand Up @@ -10,6 +10,7 @@ using Test

include("functions.jl")
include("inverse.jl")
include("setinverse.jl")
include("test.jl")

end # module
54 changes: 54 additions & 0 deletions src/setinverse.jl
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@@ -0,0 +1,54 @@
# This file is a part of InverseFunctions.jl, licensed under the MIT License (MIT).


"""
struct FunctionWithInverse{F,InvF} <: Function

A function with an inverse.

Do not construct directly, use [`setinverse(f, invf)`](@ref) instead.
"""
struct FunctionWithInverse{F,InvF} <: Function
f::F
invf::InvF
end


(f::FunctionWithInverse)(x) = f.f(x)

inverse(f::FunctionWithInverse) = setinverse(f.invf, f.f)


"""
setinverse(f, invf)

Return a function that behaves like `f` and uses `invf` as its inverse.

Useful in cases where no inverse is defined for `f` or to set an inverse that
is only valid within a given context, e.g. only for a limited argument
range that is guaranteed by the use case but not in general.

For example, `asin` is not a valid inverse of `sin` for arbitrary arguments
of `sin`, but can be a valid inverse if the use case guarantees that the
argument of `sin` will always be within `-π` and `π`:

```jldoctest
julia> foo = setinverse(sin, asin);

julia> x = π/3;

julia> foo(x) == sin(x)
true

julia> inverse(foo)(foo(x)) ≈ x
true

julia> inverse(foo) === setinverse(asin, sin)
true
```
"""
setinverse(f, invf) = FunctionWithInverse(_unwrap_f(f), _unwrap_f(invf))
export setinverse

_unwrap_f(f) = f
_unwrap_f(f::FunctionWithInverse) = f.f
1 change: 1 addition & 0 deletions test/runtests.jl
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Expand Up @@ -7,6 +7,7 @@ import Documenter
Test.@testset "Package InverseFunctions" begin
include("test_functions.jl")
include("test_inverse.jl")
include("test_setinverse.jl")

# doctests
Documenter.DocMeta.setdocmeta!(
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15 changes: 15 additions & 0 deletions test/test_setinverse.jl
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# This file is a part of InverseFunctions.jl, licensed under the MIT License (MIT).

using Test
using InverseFunctions


@testset "setinverse" begin
@test @inferred(setinverse(sin, asin)) === InverseFunctions.FunctionWithInverse(sin, asin)
@test @inferred(setinverse(sin, setinverse(asin, sqrt))) === InverseFunctions.FunctionWithInverse(sin, asin)
@test @inferred(setinverse(setinverse(sin, sqrt), asin)) === InverseFunctions.FunctionWithInverse(sin, asin)
@test @inferred(setinverse(setinverse(sin, asin), setinverse(asin, sqrt))) === InverseFunctions.FunctionWithInverse(sin, asin)

InverseFunctions.test_inverse(setinverse(sin, asin), π/4)
InverseFunctions.test_inverse(setinverse(asin, sin), 0.5)
end