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RK4 unit-test for Luu doesn't pass with N different to zero

I have defined a general differential action LQR model in this PR !131 (merged), i.e.

l(\mathbf{x},\mathbf{u})=\frac{1}{2}\begin{pmatrix}1 \\ \mathbf{x} \\ \mathbf{u}\end{pmatrix}^T \begin{pmatrix}0 & \mathbf{lx}^T & \mathbf{lu}^T \\ \mathbf{lx} & \mathbf{Lxx} & \mathbf{Lxu} \\ \mathbf{lu} & \mathbf{Lxu}^T & \mathbf{Luu}\end{pmatrix} \begin{pmatrix}1 \\ \mathbf{x} \\ \mathbf{u}\end{pmatrix}

where

  • \mathbf{lx} and \mathbf{lu} describes the gradient of the quadratic cost, and
  • \mathbf{Lxx}, \mathbf{Luu} and \mathbf{Lxu} described the Hessian of the quadratic cost.

However when I defined \mathbf{0}\leq\mathbf{Lxu}\neq\mathbf{0}, then it's triggered an error in the comparison of \mathbf{L_{uu}} against NumDiff (last line of test_rk4). See !131 (merged).

@proyan could you have look on it?