Compute loss

Numbers aren't obviously wrong

_code/notes/diffsim/main.cpp

@@ -23,11 +23,29 @@ struct LaunchObjective {
     }
 
     void operator()(VectorX<Scalar> const& velocity, Scalar& loss, VectorX<Scalar>& gradient) {
+        // prepare initial conditions
         initial_conditions_.segment<dim_>(3 * dim_) = velocity;
+
+        // run the simulation
         nbody_.initialize(dim_, masses_, initial_conditions_, delta_t_);
         for (uint32_t i = 0; i < n_steps_; ++i) {
             nbody_.step();
         }
+
+        // compute loss
+        Vector2<Scalar> const goal = Vector2<Scalar>(0, 1);
+        Vector2<Scalar> const difference = nbody_.state().segment<dim_>(dim_) - goal;
+        loss = difference.squaredNorm();
+
+        // compute gradient of loss
+        // loss = difference^T * difference
+        // d_loss = 2 * difference^T * d_difference
+        gradient = 2 * difference.transpose() * nbody_.state_jacobian().block<dim_, dim_>(dim_, 3 * dim_);
+
+        // print stuff
+        std::cout << "loss = " << loss << "\n";
+        std::cout << "loss gradient\n";
+        std::cout << gradient << '\n';
         std::cout << "state jacobian\n";
         std::cout << nbody_.state_jacobian() << '\n';
     }