Fix missing out_axes for transpose-of-vprim.

In particular this resulted in a trace error here: patrick-kidger/lineax#101

equinox/internal/_primitive.py

@@ -6,6 +6,7 @@
 import jax.interpreters.ad as ad
 import jax.interpreters.batching as batching
 import jax.interpreters.mlir as mlir
+import jax.numpy as jnp
 import jax.tree_util as jtu
 from jaxtyping import PyTree
 
@@ -404,20 +405,41 @@ def _resolve_undefined_b(input, batch_axis):
 def _vprim_transpose(
     cts, *inputs, prim, __axis_size, __axis_name, __batch_axes, params
 ):
-    inputs = [_resolve_undefined_i(i, b) for i, b in zip(inputs, __batch_axes)]
+    mapped_inputs = [_resolve_undefined_i(i, b) for i, b in zip(inputs, __batch_axes)]
     batch_axes = [_resolve_undefined_b(i, b) for i, b in zip(inputs, __batch_axes)]
-    transpose = ft.partial(_vprim_transpose_registry[prim], **params)
+
+    def _transpose(*_inputs):
+        _outputs = _vprim_transpose_registry[prim](*_inputs, **params)
+        # `Zero` is not a JAX type -- it's an internal AD thing -- so we shouldn't pass
+        # it across the `vmap` boundary. In particular JAX won't apply the out batch
+        # axis to it.
+        # JAX allows for returning `None` to indicate no cotangent, so we use that
+        # instead, which is compatible with both `vmap` and `out_axes`.
+        return tuple(None if type(o) is ad.Zero else o for o in _outputs)
+
     transpose = jax.vmap(
-        transpose,
+        _transpose,
         in_axes=(0, *batch_axes),
+        out_axes=__batch_axes,
         axis_size=__axis_size,
         axis_name=__axis_name,
     )
     if prim.multiple_results:
         cts = tuple(None if type(c) is ad.Zero else c for c in cts)
     else:
         cts = None if type(cts) is ad.Zero else cts
-    return transpose(cts, *inputs)
+    outputs = transpose(cts, *mapped_inputs)
+    assert len(inputs) == len(outputs)
+    for i, o in zip(inputs, outputs):
+        if o is not None:
+            # Can't have cotangents on defined variables I think? The point of an
+            # `UndefinedPrimal` is to declare what you want cotangents with respect to.
+            assert type(i) is ad.UndefinedPrimal
+            # We've filtered out all other avals above, with a `NotImplementedError` if
+            # required.
+            assert isinstance(i.aval, jax.core.ShapedArray)
+            assert i.aval.shape == jnp.shape(o)
+    return outputs
 
 
 # _vprim_p is itself a vprim!