# Parallel computing

If you have access to MATLAB Parallel Computing Toolbox, you can use parallel computing to speed up RECS. Parallel computing may matter a lot because models are solved on grids and, with most solution methods, the solution for each grid point can be solved independently from other grid points. It mostly matters in three steps: (i) the calculation of first guess through perfect foresight, (ii) the solution of stochastic rational expectations problems, and (iii) simulating models using equations solvers (rather than interpolation).

## Enabling parallel computing

For MATLAB versions before R2013b, parallel computation is enabled for MATLAB Parallel Computing Toolbox by the following call

matlabpool

After MATLAB R2013b, by default, parallel computation automatically starts when required or can be started using

parpool

## Parallel computing for computing first guess through perfect foresight

Solving for a first guess through perfect foresight can take as much time as solving for the stochastic rational expectations problem because a perfect-foresight solution has to be solved for each grid point independently.

As soon as MATLAB parallel computing features are enabled, parallel computing will be used automatically by recsFirstGuess by using each MATLAB worker to solve for one grid point.

## Parallel computing for solving for stochastic rational expectations equilibrium

Parallel computing can be used with recsSolveREE and recsSolveREEFiniteHorizon. By default, these functions solve for the rational expectations equilibrium by solving for all grid points at once the equilibrium equations for given expectations functions and by iterating through time. Grid points are solved all at once because it tends to be faster to solve a large system of equations than to solve many small systems. To benefit from parallel computing, the large system of equations has to be broken down in smaller systems that can be fed to the MATLAB workers. This is governed by the option loop_over_s.

By default loop_over_s is equal to 0, which implies that all grid points are solved at once; parallel computing will not be used in this case. Setting loop_over_s equal to 1 implies that each grid point is solved separately. This option can benefit from parallel computing, but it usually breaks down the problem in too many small systems of equations. For loop_over_s, any integer value n different from 0 and 1 implies that equations will be solved by n blocks of grid points. To keep each MATLAB worker occupied, a good rule is to set n equal to a multiple of the number of MATLAB workers.

It should also be noted that solving smaller systems of equations is easier than solving at once for all grid points (but if it may be slower). So increasing loop_over_s is, independently from parallel computing, useful to facilitate the solution process is the problem is difficult to solve.

In the case of recsSolveREE, parallel computing is not compatible with the option field reemethod equal to 1-step.

## Simulating models using equations solvers

There are two techniques to simulate models once the rational expectations solution has been found (see Simulate the model). The most precise and slowest technique simulates the model by solving equilibrium equations using approximated expectations (option field simulmethod set to solve). If several trajectories are simulated at the same time, the approach is similar to the one described above for recsSolveREE: by default, equilibrium equations for all trajectories are solved at once. To benefit from parallel computing, one needs to do as above: set loop_over_s to a non-zero integer value.