Breaking-up dr1.m

The changes decribed below have been merged into the master branch on March 15, 2012.

Currently the function dr1.m contains most of the code for computing first, second and third order approximation of stochastic model. Current shortcomings:

• This code is messy
• It contains parts that could be advantageously factorized so as to be computed only once per model and not repeatedly every time that one calls the solution.
• Since we limited the model to have leads and lags on one period only and added necessary auxilary variables, some part of the code can be greatly simplified.

Branch dr1break

• dr1.m is replaced by stochastic_solvers.m, but the parent function resol.m keeps calling dr_block.m separately.

• stochastic_solvers.m calls in turn

  • dyn_first_order_solver.m

  • AIM_first_order_solver.m

  • dyn_second_order_solver.m

  • k_order_pert.m

  • dyn_risky_steadystate_solver.m

• stochastic_solvers.m performs the following inside the function itself:

  • obtains first and second derivatives from <modfile>_dynamic() or bytecode()

  • solves for first order approximation of purely backward for purely forward directly
  • transforms the solution for log-linear option
  • computes the first-order coefficients of deterministic shocks

Still to be done to meet goals described below

• 2nd and 3rd order approximation of purely backward and purely forward models (making separate functions for purely backward and purely forward models) (72)

• factorizing code for description of state space

• integrating dr_block.m in the new organization of code (separating evaluation of the Jacobian blocks and computation of the solution) (148)

• implementing better storage of results

Proposed re-organization of the code

Factorized code

• computation of the elements of the state space and the number of different types of variables (static, forward, predetermined, both). This code should return list of variable indices.

Solution code

• replace dr1.m by stochastic_solvers.

• if k_order algorithm || 3rd order

  • k_order_perturbation

• else if 1st order

  • first_order_solvers

    • if purely backward
      • inversion of Jacobian matrix
    • if purely forward
      • algorithm to be developed (not urgent)
    • general case
      • Generalized Schur decomposition (current algorithm by default)
        • will use Sims qz routines
      • Generalized Schur decomposition for several model blocks
      • Generalized Schur decomposition (DLL version)
        • will be new default
      • Generalized Schur decomposition (DLL version) for several blocks
      • AIM algorithm
      • Partial Information
    • solution for deterministic exogenous variables
• else if 2nd order

  • second order solvers

    • current algorithm
    • approximation around the stochastic steady state (to be developed by Michel)
• Create a separate function for computing the eigenvalues of a model using only the Generalized Schur decomposition algorithm (not necessarily a separate function after all)

Storing results

• The code must keep storing results in the current format to keep compatibility with existing Dynare code and user code
• However, the current ordering of variables in stored matrices was a very bad idea, inefficient and source of many confusion. We should also save

  • matrices of derivatives of the solution function (declared variables x state variables). The variables should be ordered in declaration order (i.e. as in the VAR statement). I don't think that we need the solution function for the auxiliary variables for forward expression, but I may be wrong.

  • matrices of derivatives of the solution function for state variables (state variables x state variables). Also in variable declaration order. This is duplicate saving, but I think it is more efficient than having to reform these matrices from the previous ones over and over again.
• Systematize order_var in internal storage of matrix (let think more)

Open questions

• Shall we reorder the Jacobian to permit block copy in forming D and E