pyperfectforesight.process_model

pyperfectforesight.process_model(equations, vars_dyn, vars_exo=None, vars_aux=None, aux_method='auto', eliminate_static_vars=True, compiler='lambdify')

Process model equations and compile to numeric functions

Parameters:

equationslist

List of model equations

vars_dynlist

List of endogenous (dynamic) variable names

vars_exolist, optional

List of exogenous variable names (default: None)

vars_auxlist, optional

List of auxiliary variable names - static variables to be determined from dynamic and exogenous variables (default: None).

aux_methodstr, optional

Method for handling auxiliary variables (default: 'auto'):

• 'auto': Try analytical first; if SymPy can’t solve, treat as dynamic. Best default — fast when possible, robust when needed. (Similar to Dynare: eliminate if possible, else keep in system.)

• 'analytical': Force analytical method only. Faster but will fail if SymPy cannot solve the auxiliary equations symbolically.

• 'nested': Force post-solve numerical solving of auxiliary equations. After the main solver converges, auxiliary variables are solved period-by-period using scipy.optimize.root with warm starting. Requires a square auxiliary system and auxiliary variables appearing only in auxiliary equations; raises ValueError otherwise. Use when analytical solve fails and these structural conditions hold; otherwise prefer 'dynamic'.

• 'dynamic': Treat auxiliary variables as dynamic. Auxiliary equations included in main system. Single optimization, higher dimension.

eliminate_static_varsbool

Whether to eliminate non-auxiliary static variables (default: True)

compilerstr

Compilation method: ‘lambdify’ (default), or other backends

Returns:

dictDictionary containing:

• ‘dynamic_eqs’: Processed dynamic equations

• ‘blocks’: Symbolic Jacobian blocks

• ‘all_syms’: Sorted list of all symbols

• ‘block_funcs’: Compiled Jacobian block functions (lag → matrix lambda)

• ‘block_elem_funcs’: Per-element scalar lambdas for each Jacobian block (lag → neq×n list of scalar-valued lambdas); broadcast correctly over numpy array inputs, unlike the matrix lambda in block_funcs

• ‘residual_funcs’: Compiled residual functions

• ‘incidence’: Lead/lag incidence information

• ‘vars_dyn’: List of dynamic variable names

• ‘vars_exo’: List of exogenous variable names

• ‘vars_aux’: List of auxiliary variable names

• ‘aux_method’: Method used for auxiliary variables

• ‘aux_eqs’: Symbolic auxiliary equations

• ‘aux_eqs_funcs’: Compiled residual functions for auxiliary equations (nested method)

• ‘aux_eqs_syms’: Sorted list of all free symbols appearing in auxiliary equations (nested method)

• ‘aux_sols’: Analytical solutions for auxiliary variables (analytical method)

• ‘aux_funcs’: Compiled evaluation functions (analytical method)

Notes:

Recommended usage:

• 'auto' (default): Best for most cases — tries analytical, falls back to dynamic. Like Dynare: eliminate if possible, else keep in system.

• 'analytical': When equations are simple (e.g. i = y - c - g) and guaranteed fast performance with no fallback is desired.

• 'nested': When nested post-solve optimization is explicitly preferred (rare).

• 'dynamic': To skip the analytical attempt and treat aux vars as dynamic.

The analytical method solves equations symbolically then evaluates (fastest). The dynamic method includes auxiliary equations in main system (Dynare-style). The nested method solves auxiliary variables post-solve, period-by-period.