diff --git a/examples/python/call-external.py b/examples/python/call-external.py
index 49b25d6e0..feb00e029 100644
--- a/examples/python/call-external.py
+++ b/examples/python/call-external.py
@@ -22,7 +22,7 @@ def with_types(self, arg_id_to_dtype, callables_table):
 
         if vec_dtype.numpy_dtype == np.float32:
             name_in_target = "cblas_sgemv"
-        elif vec_dtype. numpy_dtype == np.float64:
+        elif vec_dtype.numpy_dtype == np.float64:
             name_in_target = "cblas_dgemv"
         else:
             raise LoopyError("GEMV is only supported for float32 and float64 "
@@ -47,30 +47,37 @@ def with_descrs(self, arg_id_to_descr, callables_table):
         assert mat_descr.shape[0] == res_descr.shape[0]
         assert len(vec_descr.shape) == len(res_descr.shape) == 1
         # handling only the easy case when stride == 1
-        assert vec_descr.dim_tags[0].stride == 1
         assert mat_descr.dim_tags[1].stride == 1
-        assert res_descr.dim_tags[0].stride == 1
 
         return self.copy(arg_id_to_descr=arg_id_to_descr), callables_table
 
     def emit_call_insn(self, insn, target, expression_to_code_mapper):
         from pymbolic import var
+        from loopy.codegen import UnvectorizableError
         mat_descr = self.arg_id_to_descr[0]
+        vec_descr = self.arg_id_to_descr[1]
+        res_descr = self.arg_id_to_descr[-1]
         m, n = mat_descr.shape
         ecm = expression_to_code_mapper
+
+        if ecm.codegen_state.vectorization_info is not None:
+            raise UnvectorizableError("cannot vectorize BLAS-gemv.")
+
         mat, vec = insn.expression.parameters
         result, = insn.assignees
 
         c_parameters = [var("CblasRowMajor"),
                         var("CblasNoTrans"),
                         m, n,
-                        1,
+                        1,  # alpha
                         ecm(mat).expr,
-                        1,
+                        1,  # LDA
                         ecm(vec).expr,
-                        1,
+                        vec_descr.dim_tags[0].stride,  # INCX
+                        1,  # beta
                         ecm(result).expr,
-                        1]
+                        res_descr.dim_tags[0].stride  # INCY
+                        ]
         return (var(self.name_in_target)(*c_parameters),
                 False  # cblas_gemv does not return anything
                 )
@@ -83,17 +90,66 @@ def generate_preambles(self, target):
 # }}}
 
 
-n = 10
+def transform_1(knl):
+    return knl
+
+
+def transform_2(knl):
+    # A similar transformation is applied to kernels containing
+    # SLATE <https://www.firedrakeproject.org/firedrake.slate.html>
+    # callables.
+    knl = lp.split_iname(knl, "e", 4, inner_iname="e_inner", slabs=(0, 1))
+    knl = lp.privatize_temporaries_with_inames(knl, "e_inner")
+    knl = lp.tag_inames(knl, {"e_inner": "vec"})
+    if 0:
+        # Easy codegen exercise, but misses vectorizing certain instructions.
+        knl = lp.tag_array_axes(knl, "tmp3", "c,vec")
+    else:
+        knl = lp.tag_array_axes(knl, "tmp3,tmp2", "c,vec")
+    return knl
+
+
+def main():
 
-knl = lp.make_kernel(
-        "{:}",
+    knl = lp.make_kernel(
+        "{[e,i1,i2]: 0<=e<n and 0<=i1,i2<4}",
         """
-        y[:] = gemv(A[:, :], x[:])
-        """, [
-            lp.GlobalArg("A", dtype=np.float64, shape=(n, n)),
-            lp.GlobalArg("x", dtype=np.float64, shape=(n, )),
-            lp.GlobalArg("y", shape=(n, )), ...],
-        target=CTarget())
-
-knl = lp.register_callable(knl, "gemv", CBLASGEMV(name="gemv"))
-print(lp.generate_code_v2(knl).device_code())
+        for e
+            for i1
+                tmp1[i1] = 3*x[e, i1]
+            end
+            tmp2[:] = matvec(A[:, :], tmp1[:])
+            for i2
+                <> tmp3[i2] = 2 * tmp2[i2]
+                out[e, i2] = tmp3[i2]
+            end
+        end
+        """,
+        kernel_data=[
+            lp.TemporaryVariable("tmp1",
+                                 shape=(4, ),
+                                 dtype=None),
+            lp.TemporaryVariable("tmp2",
+                                 shape=(4, ),
+                                 dtype=None),
+            lp.GlobalArg("A",
+                         shape=(4, 4),
+                         dtype="float64"),
+            lp.GlobalArg("x",
+                         shape=lp.auto,
+                         dtype="float64"),
+            ...],
+        target=lp.CVectorExtensionsTarget(),
+        lang_version=(2018, 2))
+
+    knl = lp.register_callable(knl, "matvec", CBLASGEMV("matvec"))
+
+    for transform_func in [transform_1, transform_2]:
+        knl = transform_func(knl)
+        print("Generated code from '{transform_func.__name__} -----'")
+        print(lp.generate_code_v2(knl).device_code())
+        print(75 * "-")
+
+
+if __name__ == "__main__":
+    main()