Allow to differentiate expressions w.r.t. state derivatives to compute analytic Jacobian for daeMode

[Francesco Casella]

Give a system F(x, x_dot, t) = 0, solvers such as IDA require to compute the Jacobians dF/dx and dF/dx_dot.

The latter task cannot currently be carried out by the backend, because the backend has variables for the states, but not for the derivatives. The backend should then be enhanced to allow this.

[Francesco Casella]

As a first step, we could start computing dF/dx analytically, and only use colored numerical jacobians for dF/dx_dot. After all, in most models the states are only a tiny fraction of the variables, so this could already give a substantial performance improvement.

[Francesco Casella]

Another interim option is to add aliases for derivatives. The derivation of the jacobian for the equation der(x) = der_x is trivial, as it has two 1's in the corresponding columns, while all other partial derivatives would be carried out w.r.t. the algebraic variable der_x.

Of course this solution adds more unknowns to the DAE problem. However, as long as a sparse solver is used and the number of states is a small fraction of the total number of variables, this solution would add comparatively small an overhead.

[Francesco Casella]

Releasing 1.14.0 which is stable and has many improvements w.r.t. 1.13.2. This issue is rescheduled to 1.16.0

[Francesco Casella]

Retargeted to 1.17.0 after 1.16.0 release

[Francesco Casella]

Retargeted to 1.18.0 because of 1.17.0 timed release.

[Francesco Casella]

Ticket retargeted after milestone closed