fix and test transform_vector_cartesian_to_cylinder

src/utils/include/utils/math/coordinate_transformation.hpp

@@ -77,15 +77,14 @@ inline Vector3d transform_vector_cartesian_to_cylinder(Vector3d const &vec,
   std::tie(theta, rotation_axis) = rotation_params(axis, z_axis);
   auto const rotated_pos = vec_rotate(rotation_axis, theta, pos);
   auto const rotated_vec = vec_rotate(rotation_axis, theta, vec);
+  auto const r = std::sqrt(rotated_pos[0] * rotated_pos[0] +
+                           rotated_pos[1] * rotated_pos[1]);
   // v_r = (x * v_x + y * v_y) / sqrt(x^2 + y^2)
   auto const v_r =
-      (rotated_pos[0] * rotated_vec[0] + rotated_pos[1] * rotated_vec[1]) /
-      std::sqrt(rotated_pos[0] * rotated_pos[0] +
-                rotated_pos[1] * rotated_pos[1]);
-  // v_phi = (x * v_y - y * v_x ) / (x^2 + y^2)
+      (rotated_pos[0] * rotated_vec[0] + rotated_pos[1] * rotated_vec[1]) / r;
+  // v_phi = (x * v_y - y * v_x ) / sqrt(x^2 + y^2)
   auto const v_phi =
-      (rotated_pos[0] * rotated_vec[1] - rotated_pos[1] * rotated_vec[0]) /
-      (rotated_pos[0] * rotated_pos[0] + rotated_pos[1] * rotated_pos[1]);
+      (rotated_pos[0] * rotated_vec[1] - rotated_pos[1] * rotated_vec[0]) / r;
   return Vector3d{v_r, v_phi, rotated_vec[2]};
 }
 

src/utils/tests/coordinate_transformation.cpp

@@ -85,3 +85,21 @@ BOOST_AUTO_TEST_CASE(cylinder_to_cartesian_test) {
     BOOST_CHECK(transformed_z[i] == expected_z[i]);
   }
 }
+
+BOOST_AUTO_TEST_CASE(vector_cart_to_cyl_test) {
+  constexpr auto eps = 1e-13;
+  Vector3d const pos{{1.1, 2.2, 3.3}};
+  auto const axis = (Vector3d{{4.4, 5.5, 6.6}}).normalized();
+  Vector3d const vec{{7.7, 8.8, 9.9}};
+
+  auto const vec_cyl = transform_vector_cartesian_to_cylinder(vec, axis, pos);
+
+  // cylindrical basis vectors at pos
+  auto const e_z = axis;
+  auto const e_r = (pos - (pos * axis) * axis).normalized();
+  auto const e_phi = Utils::vector_product(e_z, e_r);
+
+  BOOST_CHECK_SMALL(vec_cyl[0] - vec * e_r, eps);
+  BOOST_CHECK_SMALL(vec_cyl[1] - vec * e_phi, eps);
+  BOOST_CHECK_SMALL(vec_cyl[2] - vec * e_z, eps);
+}