fix signature, add infer_shape

Author: jessegrabowski

pytensor/tensor/slinalg.py

@@ -1704,7 +1704,7 @@ def _to_banded_form(A, kl, ku):
 
 class BandedDot(Op):
     __props__ = ("lower_diags", "upper_diags")
-    gufunc_signature = "(m,n),(n)->(n)"
+    gufunc_signature = "(m,n),(n)->(m)"
 
     def __init__(self, lower_diags, upper_diags):
         self.lower_diags = lower_diags
@@ -1719,6 +1719,9 @@ def make_node(self, A, b):
 
         return pytensor.graph.basic.Apply(self, [A, B], [output])
 
+    def infer_shape(self, fgraph, nodes, shapes):
+        return [shapes[0][:-1]]
+
     def perform(self, node, inputs, outputs_storage):
         A, b = inputs
         m, n = A.shape