Minor fixes in code documentation

irlc/ex05/direct.py

@@ -131,14 +131,17 @@ def collocate(model : ControlModel, N=25, optimizer_options=None, guess : dict =
     timer = Timer(start=True)
     cost = model.get_cost()
     t0, tF = sym.symbols("t0"), sym.symbols("tF")
-    ts = t0 + np.linspace(0, 1, N) * (tF-t0)   # N points linearly spaced between [t0, tF] TODO: Convert this to a list.
+    ts = t0 + np.linspace(0, 1, N) * (tF-t0)   # N points linearly spaced between [t0, tF]
+    # ts is a list of length N representing the time points, i.e., t_0, t_1, ..., t_{N-1}. Notice these are symbolic
+    # objects that depend on t0 and tF.
+
+
     xs, us = [], []
     for i in range(N):
         xs.append(list(symv("x_%i_" % i, model.state_size)))
         us.append(list(symv("u_%i_" % i, model.action_size)))
 
     ''' (1) Construct guess z0, all simple bounds [z_lb, z_ub] for the problem and collect all symbolic variables as z '''
-    # sb = model.simple_bounds()  # get simple inequality boundaries in problem (v_lb <= v <= v_ub)
     z = []  # list of all *symbolic* variables in the problem
     # These lists contain the guess z0 and lower/upper bounds (list-of-numbers): z_lb[k] <= z0[k] <= z_ub[k].
     # They should be lists of *numbers*.
@@ -156,7 +159,6 @@ def collocate(model : ControlModel, N=25, optimizer_options=None, guess : dict =
         raise NotImplementedError("Updates for x_k, u_k")
 
     """ Update z, z0, z_lb, and z_ub with bounds/guesses corresponding to t0 and tF (same format as above). """
-    #         z, z0, z_lb, z_ub = z+[t0], z0+[guess['t0']], z_lb+[model.bounds['t0_low']], z_ub+[model.bounds['t0_high']]
     # TODO: 2 lines missing.
     raise NotImplementedError("Updates for t0, tF")
     assert len(z) == len(z0) == len(z_lb) == len(z_ub)