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recsSolveREE

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.