recsSolveREE finds the rational expectations equilibrium (REE) of a model
 
  recsSolveREE implementes various approximation schemes, and equation solvers to
  find the REE of a model.
 
  INTERP = recsSolveREE(INTERP,MODEL,S,X) tries to find the rational expectations
  equilibrium of the model defined in the object MODEL, by using the
  interpolation structure defined in the structure INTERP. The problem is solved
  on the grid of state variables provided in matrix S. Matrix X is used as a
  first guess of response variables on the grid. recsSolveREE returns the
  interpolation structure containing the coefficient matrices cx
  and cz, and ch if this field was initially included in INTERP.
  INTERP is a structure, which has to include the following field:
     fspace       : a definition structure for the interpolation family (created
                    by the function fundef)
  Optionally INTERP can also include first guess for the coefficients of
  approximation. If absent, an approximation is made from X.
     ch, cx or cz : a coefficient matrix providing a first guess of the
                    approximation of the expectations function for ch, of the
                    response variables for cx, or of the expectations for cz
  MODEL is an object created by recsmodel.
 
  INTERP = recsSolveREE(INTERP,MODEL,S,X,OPTIONS) solves the problem with the
  parameters defined by the structure OPTIONS. The fields of the structure are
     display          : 1 to show iterations (default: 1)
     eqsolver         : 'fsolve', 'lmmcp' (default), 'ncpsolve' or 'path'
     eqsolveroptions  : options structure to be passed to eqsolver
     extrapolate      : 1 or 2 if extrapolation is allowed outside the
                        interpolation space, 0 or -1 to forbid it (default: 1).
                        For -1 and 2, recsSolveREE displays a warning if state
                        variables exceed the interpolation space.
     funapprox        : 'expapprox', 'expfunapprox', or 'resapprox' (default)
     functional       : 1 if the equilibrium equations are a functional equation
                        problem (default: 0)
     loop_over_s      : 0 (default) to solve all grid points at once, 1 to loop
                        over each grid points, or n to loop over n blocks of
                        grid points
     reemethod        : 'iter' (default) or '1-step'
     reesolver        : 'krylov', 'mixed', 'SA' (default) or 'fsolve'
     reesolveroptions : options structure to be passed to reesolver
     useapprox        : (default: 1) behaviour dependent of the chosen function to
                        approximate. If 0 and funapprox is 'expapprox' then
                        next-period responses are calculated by equations solve and
                        not just interpolated. If 1 and funapprox is 'resapprox', the
                        guess of response variables is found with the new
                        approximation structure
   UseParallel        : 'always' (default) to use parallel calculation (require
                        Parallel Computing Toolbox)' or never'
 
  [INTERP,X] = recsSolveREE(INTERP,MODEL,S,X,...) returns the value of the response
  variables on the grid.
 
  [INTERP,X,Z] = recsSolveREE(INTERP,MODEL,S,X,...) returns the value of the
  expectations variables on the grid.
 
  [INTERP,X,Z,FVAL] = recsSolveREE(INTERP,MODEL,S,X,...) returns the value of the
  equilibrium equations on the grid.
 
  [INTERP,X,Z,FVAL,EXITFLAG] = recsSolveREE(INTERP,MODEL,S,X,...) returns EXITFLAG,
  which describes the exit conditions. Possible values are
     1 : recsSolveREE converges to the REE
     0 : Failure to converge
 
  [INTERP,X,Z,FVAL,EXITFLAG,OUTPUT] = recsSolveREE(INTERP,MODEL,S,X,...) returns
  OUTPUT, a structure containing the fields snextmin and snextmax, minimum and
  maximum of next-period state variables.