Add support for distributions with monotonically increasing bijector

Project.toml

@@ -1,6 +1,6 @@
 name = "Bijectors"
 uuid = "76274a88-744f-5084-9051-94815aaf08c4"
-version = "0.13.7"
+version = "0.13.8"
 
 [deps]
 ArgCheck = "dce04be8-c92d-5529-be00-80e4d2c0e197"

src/bijectors/ordered.jl

@@ -17,14 +17,21 @@ Return a `Distribution` whose support are ordered vectors, i.e., vectors with in
 This transformation is currently only supported for otherwise unconstrained distributions.
 """
 function ordered(d::ContinuousMultivariateDistribution)
-    if bijector(d) !== identity
+    # We're good if the map from unconstrained (in which we apply the ordered bijector)
+    # to constrained is monotonically increasing, i.e. order-preserving. In that case,
+    # we can form the ordered transformation as `binv ∘ OrderedBijector() ∘ b`.
+    # TODO: Add support for monotonically _decreasing_ transformations. This will be the
+    # the same as above, but the ordering will be reversed by `binv` so we need to handle this.
+    b = bijector(d)
+    binv = inverse(b)
+    if !is_monotonically_increasing(binv)
         throw(
             ArgumentError(
-                "ordered transform is currently only supported for unconstrained distributions.",
+                "ordered transform is not supported for $d.",
             ),
         )
     end
-    return transformed(d, OrderedBijector())
+    return transformed(d, binv ∘ OrderedBijector() ∘ b)
 end
 
 with_logabsdet_jacobian(b::OrderedBijector, x) = transform(b, x), logabsdetjac(b, x)

src/interface.jl

@@ -230,6 +230,23 @@ transform!(::typeof(identity), x, y) = copy!(y, x)
 logabsdetjac(::typeof(identity), x) = zero(eltype(x))
 logabsdetjac!(::typeof(identity), x, logjac) = logjac
 
+###################
+# Other utilities #
+###################
+"""
+    is_monotonically_increasing(f)
+
+Returns `true` if `f` is monotonically increasing.
+"""
+is_monotonically_increasing(f) = false
+is_monotonically_increasing(::typeof(identity)) = true
+function is_monotonically_increasing(cf::ComposedFunction)
+    return is_monotonically_increasing(cf.inner) && is_monotonically_increasing(cf.outer)
+end
+is_monotonically_increasing(::typeof(exp)) = true
+is_monotonically_increasing(ef::Elementwise) = is_monotonically_increasing(ef.x)
+
+
 ######################
 # Bijectors includes #
 ######################

test/bijectors/ordered.jl

@@ -22,11 +22,13 @@ end
         MvTDist(1, collect(1.0:5), Matrix(I(5))),
         product_distribution(fill(Normal(), 5)),
         product_distribution(fill(TDist(1), 5)),
+        product_distribution(fill(LogNormal(), 5)),
+        product_distribution(fill(InverseGamma(2, 3), 5)),
     ]
         d_ordered = ordered(d)
         @test d_ordered isa Bijectors.TransformedDistribution
         @test d_ordered.dist === d
-        @test d_ordered.transform isa OrderedBijector
+        # @test d_ordered.transform isa OrderedBijector
         y = randn(5)
         x = inverse(bijector(d_ordered))(y)
         @test issorted(x)