Refactor inverse_eltype calculations to use types.

src/aggregation.jl

@@ -141,7 +141,10 @@ function _domain_label(transformation::ViewTransformation, index::Int)
     _array_domain_label(asℝ, dims, index)
 end
 
-inverse_eltype(transformation::ViewTransformation, y) = eltype(y)
+function inverse_eltype(transformation::ViewTransformation,
+                        ::Type{T}) where T <: AbstractArray
+    _ensure_float(eltype(T))
+end
 
 function inverse_at!(x::AbstractVector, index, transformation::ViewTransformation,
                      y::AbstractArray)
@@ -210,8 +213,9 @@ function transform_with(flag::LogJacFlag, transformation::StaticArrayTransformat
 end
 
 function inverse_eltype(transformation::Union{ArrayTransformation,StaticArrayTransformation},
-                        x::AbstractArray)
-    inverse_eltype(transformation.inner_transformation, first(x)) # FIXME shortcut
+                        ::Type{T}) where T <: AbstractArray
+    inverse_eltype(transformation.inner_transformation,
+                   _ensure_float(eltype(T)))
 end
 
 function inverse_at!(x::AbstractVector, index,
@@ -341,12 +345,17 @@ internally.
 
 *Performs no argument validation, caller should do this.*
 """
-_inverse_eltype_tuple(ts::NTransforms, ys::Tuple) =
-    reduce(promote_type, map(inverse_eltype, ts, ys))
-# NOTE: See https://github.com/tpapp/TransformVariables.jl/pull/80
-#       `map` and `reduce` both have specializations on `Tuple`s that make them type stable
-#       even when the `Tuple` is heterogenous, but that is not currently the case with
-#       `mapreduce`, therefore separate `reduce` and `map` are preferred as a workaround.
+function _inverse_eltype_tuple(ts::NTransforms{N}, ::Type{T}) where {N,T<:Tuple}
+    @argcheck T <: NTuple{N,Any} "Incompatible input length."
+    __inverse_eltype_tuple(ts, T)
+end
+function __inverse_eltype_tuple(ts::NTransforms, ::Type{Tuple{}})
+    Union{}
+end
+function __inverse_eltype_tuple(ts::NTransforms, ::Type{T}) where {T<:Tuple}
+    promote_type(inverse_eltype(Base.first(ts), fieldtype(T, 1)),
+                 __inverse_eltype_tuple(Base.tail(ts), Tuple{Base.tail(fieldtypes(T))...}))
+end
 
 """
 $(SIGNATURES)
@@ -366,10 +375,9 @@ function transform_with(flag::LogJacFlag, tt::TransformTuple{<:Tuple}, x, index)
     transform_tuple(flag, tt.transformations, x, index)
 end
 
-function inverse_eltype(tt::TransformTuple{<:Tuple}, y::Tuple)
+function inverse_eltype(tt::TransformTuple{<:Tuple}, ::Type{T}) where T <: Tuple
     (; transformations) = tt
-    @argcheck length(transformations) == length(y)
-    _inverse_eltype_tuple(transformations, y)
+    _inverse_eltype_tuple(transformations, T)
 end
 
 function inverse_at!(x::AbstractVector, index, tt::TransformTuple{<:Tuple}, y::Tuple)
@@ -378,19 +386,19 @@ function inverse_at!(x::AbstractVector, index, tt::TransformTuple{<:Tuple}, y::T
     _inverse!_tuple(x, index, tt.transformations, y)
 end
 
-as(transformations::NamedTuple{N,<:NTransforms}) where N =
+function as(transformations::NamedTuple{N,<:NTransforms}) where N
     TransformTuple(transformations)
+end
 
 function transform_with(flag::LogJacFlag, tt::TransformTuple{<:NamedTuple}, x, index)
     (; transformations) = tt
     y, ℓ, index′ = transform_tuple(flag, values(transformations), x, index)
     NamedTuple{keys(transformations)}(y), ℓ, index′
 end
 
-function inverse_eltype(tt::TransformTuple{<:NamedTuple}, y::NamedTuple)
+function inverse_eltype(tt::TransformTuple{<:NamedTuple}, ::Type{NamedTuple{N,T}}) where {N,T}
     (; transformations) = tt
-    @argcheck _same_set_of_names(transformations, y)
-    _inverse_eltype_tuple(values(transformations), values(NamedTuple{keys(transformations)}(y)))
+    _inverse_eltype_tuple(values(transformations), T)
 end
 
 function inverse_at!(x::AbstractVector, index, tt::TransformTuple{<:NamedTuple}, y::NamedTuple)

src/constant.jl

@@ -19,7 +19,7 @@ function transform_with(logjac_flag::LogJacFlag, t::Constant, x::AbstractVector,
     t.value, logjac_zero(logjac_flag, eltype(x)), index
 end
 
-inverse_eltype(t::Constant, _) = Union{}
+inverse_eltype(t::Constant, ::Type) = Union{}
 
 function inverse_at!(x::AbstractVector, index, t::Constant, y)
     @argcheck t.value == y

src/generic.jl

@@ -181,16 +181,31 @@
 inverse(f::CallableInverse) = Base.Fix1(transform, f.x)
 
 """
-    $(FUNCTIONNAME)(t::AbstractTransform, y)
+```
+$(FUNCTIONNAME)(t::AbstractTransform, y)
+$(FUNCTIONNAME)(t::AbstractTransform, ::Type{T})
+```
 
-The element type for vector `x` so that `inverse!(x, t, y)` works.
+The element type for vector `x` so that `inverse!(x, t, y::T)` works.
 
-!!! note
-    It is not guaranteed that the result is the narrowest possible type, and may change
-    without warning between versions. Some effort is made to come up with a reasonable
-    concrete type even in corner cases.
+# Notes
+
+1. It is not guaranteed that the result is the narrowest possible type, and may change
+   without warning between versions. Some effort is made to come up with a reasonable
+   concrete type even in corner cases.
+
+2. Transformations should provide a method for *types*, not values.
+
+3. No dimension or input compatibility checks are guaranteed to be performed, even for
+   values.
 """
-function inverse_eltype end
+function inverse_eltype(t::AbstractTransform, y::T) where T
+    inverse_eltype(t, T)
+end
+
+function inverse_eltype(t::AbstractTransform, T::Type)
+    throw(MethodError(inverse_eltype, (t, T)))
+end
 
 """
 $(SIGNATURES)
@@ -283,15 +298,8 @@
 
 # We want to avoid vectors with non-numerical element types
 # Ref https://github.com/tpapp/TransformVariables.jl/issues/132
-function inverse(t::VectorTransform, y)
-    inverse!(Vector{_float_or_Float64(inverse_eltype(t, y))}(undef, dimension(t)), t, y)
-end
-function _float_or_Float64(::Type{T}) where T
-    if T !== Union{} && T <: Number # heuristic: it is assumed that every `Number` type defines `float`
-        return float(T)
-    else
-        return Float64
-    end
+function inverse(t::VectorTransform, y::T) where T
+    inverse!(Vector{_ensure_float(inverse_eltype(t, T))}(undef, dimension(t)), t, y)
 end
 
 """

src/scalar.jl

@@ -30,10 +30,10 @@ function inverse_at!(x::AbstractVector, index::Int, t::ScalarTransform, y::Real)
     index + 1
 end
 
-function inverse_eltype(t::ScalarTransform, y::Real)
+function inverse_eltype(t::ScalarTransform, ::Type{T}) where T <: Real
     # NOTE this is a shortcut to get sensible types for all subtypes of ScalarTransform, which
     # we test for. If it breaks it should be extended accordingly.
-    return Base.promote_typejoin_union(Base.promote_op(inverse, typeof(t), typeof(y)))
+    return Base.promote_typejoin_union(Base.promote_op(inverse, typeof(t), T))
 end
 
 _domain_label(::ScalarTransform, index::Int) = ()
@@ -66,43 +66,50 @@ $(TYPEDEF)
 
 Exponential transformation `x ↦ eˣ`. Maps from all reals to the positive reals.
 """
-struct TVExp <: ScalarTransform 
-end
+struct TVExp <: ScalarTransform end
+
 transform(::TVExp, x::Real) = exp(x)
+
 transform_and_logjac(t::TVExp, x::Real) = transform(t, x), x
 
 function inverse(::TVExp, x::Number)
     log(x)
 end
+
 inverse_and_logjac(t::TVExp, x::Number) = inverse(t, x), -log(x)
 
 """
 $(TYPEDEF)
 
 Logistic transformation `x ↦ logit(x)`. Maps from all reals to (0, 1).
 """
-struct TVLogistic <: ScalarTransform
-end
+struct TVLogistic <: ScalarTransform end
+
 transform(::TVLogistic, x::Real) = logistic(x)
+
 transform_and_logjac(t::TVLogistic, x::Real) = transform(t, x), logistic_logjac(x)
 
 function inverse(::TVLogistic, x::Number)
     logit(x)
 end
+
 inverse_and_logjac(t::TVLogistic, x::Number) = inverse(t, x), logit_logjac(x)
 
 """
 $(TYPEDEF)
 
-Shift transformation `x ↦ x + shift`. 
+Shift transformation `x ↦ x + shift`.
 """
 struct TVShift{T <: Real} <: ScalarTransform
     shift::T
 end
+
 transform(t::TVShift, x::Real) = x + t.shift
+
 transform_and_logjac(t::TVShift, x::Real) = transform(t, x), logjac_zero(LogJac(), typeof(x))
 
 inverse(t::TVShift, x::Number) = x - t.shift
+
 inverse_and_logjac(t::TVShift, x::Number) = inverse(t, x), logjac_zero(LogJac(), typeof(x))
 
 """
@@ -117,12 +124,15 @@ struct TVScale{T} <: ScalarTransform
         new(scale)
     end
 end
+
 TVScale(scale::T) where {T} = TVScale{T}(scale)
 
 transform(t::TVScale, x::Real) = t.scale * x
-transform_and_logjac(t::TVScale{<:Real}, x::Real) = transform(t, x), log(t.scale) 
+
+transform_and_logjac(t::TVScale{<:Real}, x::Real) = transform(t, x), log(t.scale)
 
 inverse(t::TVScale, x::Number) = x / t.scale
+
 inverse_and_logjac(t::TVScale{<:Real}, x::Number) = inverse(t, x), -log(t.scale)
 
 """
@@ -155,15 +165,15 @@ struct CompositeScalarTransform{Ts <: Tuple} <: ScalarTransform
 end
 
 transform(t::CompositeScalarTransform, x) = foldr(transform, t.transforms, init=x)
-function transform_and_logjac(ts::CompositeScalarTransform, x) 
+function transform_and_logjac(ts::CompositeScalarTransform, x)
     foldr(ts.transforms, init=(x, logjac_zero(LogJac(), typeof(x)))) do t, (x, logjac)
         nx, nlogjac = transform_and_logjac(t, x)
         (nx, logjac + nlogjac)
     end
 end
 
 inverse(ts::CompositeScalarTransform, x) = foldl((y, t) -> inverse(t, y), ts.transforms, init=x)
-function inverse_and_logjac(ts::CompositeScalarTransform, x) 
+function inverse_and_logjac(ts::CompositeScalarTransform, x)
     foldl(ts.transforms, init=(x, logjac_zero(LogJac(), typeof(x)))) do (x, logjac), t
         nx, nlogjac = inverse_and_logjac(t, x)
         (nx, logjac + nlogjac)
@@ -283,7 +293,7 @@ function Base.show(io::IO, ct::CompositeScalarTransform{Tuple{TVShift{T}, TVNeg,
     print(io, "as(Real, -∞, ", ct.transforms[1].shift, ")")
 end
 function Base.show(io::IO, ct::CompositeScalarTransform{Tuple{TVShift{T1}, TVScale{T2}, TVLogistic}}) where {T1, T2}
-    print(io, "as(Real, ", ct.transforms[1].shift, ", ", ct.transforms[1].shift + 
+    print(io, "as(Real, ", ct.transforms[1].shift, ", ", ct.transforms[1].shift +
     ct.transforms[2].scale, ")")
 end
 

src/special_arrays.jl

@@ -95,7 +95,10 @@ function transform_with(flag::LogJacFlag, t::UnitVector, x::AbstractVector, inde
     y, ℓ, index
 end
 
-inverse_eltype(t::UnitVector, y::AbstractVector) = robust_eltype(y)
+function inverse_eltype(t::UnitVector,
+                        ::Type{T}) where T <: AbstractVector
+    _ensure_float(eltype(T))
+end
 
 function inverse_at!(x::AbstractVector, index, t::UnitVector, y::AbstractVector)
     (; n) = t
@@ -157,7 +160,10 @@ function transform_with(flag::LogJacFlag, t::UnitSimplex, x::AbstractVector, ind
     y, ℓ, index
 end
 
-inverse_eltype(t::UnitSimplex, y::AbstractVector) = robust_eltype(y)
+function inverse_eltype(t::UnitSimplex,
+                        ::Type{T}) where T <: AbstractVector
+    _ensure_float(eltype(T))
+end
 
 function inverse_at!(x::AbstractVector, index, t::UnitSimplex, y::AbstractVector)
     (; n) = t
@@ -297,7 +303,10 @@ function transform_with(flag::LogJacFlag, transformation::StaticCorrCholeskyFact
     UpperTriangular(SMatrix{S,S}(U)), ℓ, index′
 end
 
-inverse_eltype(t::Union{CorrCholeskyFactor,StaticCorrCholeskyFactor}, U::UpperTriangular) = robust_eltype(U)
+function inverse_eltype(t::Union{CorrCholeskyFactor,StaticCorrCholeskyFactor},
+                        ::Type{T}) where {T<:UpperTriangular}
+    _ensure_float(eltype(T))
+end
 
 function inverse_at!(x::AbstractVector, index,
                      t::Union{CorrCholeskyFactor,StaticCorrCholeskyFactor}, U::UpperTriangular)

src/utilities.jl

@@ -37,3 +37,31 @@
 end
 
 robust_eltype(x::T) where T = robust_eltype(T)
+
+"""
+$(SIGNATURES)
+
+Regularize input type, preferring a floating point, falling back to `Float64`.
+
+Internal, not exported.
+
+# Motivation
+
+Type calculations occasionally give types that are too narrow (eg `Union{}` for empty
+vectors) or broad. Since this package is primarily intended for *numerical*
+calculations, we fall back to something sensible. This function implements the
+heuristics for this, and is currently used in inverse element type calculations.
+"""
+function _ensure_float(::Type{T}) where T
+    if T <: Number # heuristic: it is assumed that every `Number` type defines `float`
+        return float(T)
+    else
+        return Float64
+    end
+end
+
+# pass through containers
+_ensure_float(::Type{T}) where {T<:AbstractArray} = T
+
+# special case Union{}
+_ensure_float(::Type{Union{}}) = Float64

test/Project.toml

@@ -4,6 +4,7 @@ DocStringExtensions = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
 Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 InverseFunctions = "3587e190-3f89-42d0-90ee-14403ec27112"
+JET = "c3a54625-cd67-489e-a8e7-0a5a0ff4e31b"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 LogDensityProblems = "6fdf6af0-433a-55f7-b3ed-c6c6e0b8df7c"
 LogDensityProblemsAD = "996a588d-648d-4e1f-a8f0-a84b347e47b1"