[Lang] Raise an error for the semantic change of transpose() (#6813)

Issue: #5819

### Brief Summary

The background is that we would like to clearly distinguish vectors from
matrices. After #6528, `transpose()` of a vector makes no sense so we'd
better raise an error and guide users towards the current practice
(`outer_product()`).

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

python/taichi/lang/matrix_ops.py

@@ -4,7 +4,8 @@
 from taichi.lang.matrix import Matrix, Vector
 from taichi.lang.matrix_ops_utils import (arg_at, arg_foreach_check,
                                           assert_list, assert_tensor,
-                                          assert_vector, check_matmul, dim_lt,
+                                          assert_vector, check_matmul,
+                                          check_transpose, dim_lt,
                                           is_int_const, preconditions,
                                           same_shapes, square_matrix)
 from taichi.types.annotations import template
@@ -142,12 +143,10 @@ def inverse(mat):
     return None
 
 
-@preconditions(assert_tensor)
+@preconditions(check_transpose)
 @pyfunc
 def transpose(mat):
     shape = static(mat.get_shape())
-    if static(len(shape) == 1):
-        return Vector([mat[i] for i in static(range(shape[0]))])
     return Matrix([[mat[i, j] for i in static(range(shape[0]))]
                    for j in static(range(shape[1]))])
 

python/taichi/lang/matrix_ops_utils.py

@@ -172,3 +172,10 @@ def check_matmul(x, y):
         if x_shape[1] != y_shape[0]:
             return False, f'dimension mismatch between {x_shape} and {y_shape} for matrix multiplication'
     return True, None
+
+
+def check_transpose(x):
+    ok, msg = assert_tensor(x)
+    if ok and len(x.get_shape()) == 1:
+        return False, '`transpose()` cannot apply to a vector. If you want something like `a @ b.transpose()`, write `a.outer_product(b)` instead.'
+    return ok, msg

tests/python/test_matrix.py

@@ -1193,3 +1193,19 @@ def verify(x):
     field = ti.Vector.field(n=3, dtype=ti.f32, shape=10)
     ndarray = ti.Vector.ndarray(n=3, dtype=ti.f32, shape=(10))
     _test_field_and_ndarray(field, ndarray, func, verify)
+
+
+@test_utils.test()
+def test_vector_transpose():
+    @ti.kernel
+    def foo():
+        x = ti.Vector([1, 2])
+        y = ti.Vector([3, 4])
+        z = x @ y.transpose()
+
+    with pytest.raises(
+            TaichiCompilationError,
+            match=
+            r"`transpose\(\)` cannot apply to a vector. If you want something like `a @ b.transpose\(\)`, write `a.outer_product\(b\)` instead."
+    ):
+        foo()