Package: pysolve
pysolve - Solving systems of equationsThe purpose of this tool is to aid in expressing and solving
sets of equations using Python.This tool will take a textual description of the equations,
and then run the solver iteratively until it converges to
a solution.The solver provides the following choices for solving:Gauss-SeidelNewton-RaphsonBroydenIt also uses parts of sympy to aid in parsing the equations and
evaluating the equations.The initial motivation for this tool was to solve economic
models based on Stock Flow Consistent (SFC) models.InstallationpipinstallpysolveUsageDefine the variables used in the model.Define the parameters used in the model.Define the rules (equations)SolveSimple exampleThis example is taken Chapter 3 of the book "Monetary Economics 2e" by
Lavoie and Godley, 2012.frompysolve.modelimportModelfrompysolve.utilsimportround_solution,is_closemodel=Model()model.set_var_default(0)model.var('Cd',desc='Consumption goods demand by households')model.var('Cs',desc='Consumption goods supply')model.var('Gs',desc='Government goods, supply')model.var('Hh',desc='Cash money held by households')model.var('Hs',desc='Cash money supplied by the government')model.var('Nd',desc='Demand for labor')model.var('Ns',desc='Supply of labor')model.var('Td',desc='Taxes, demand')model.var('Ts',desc='Taxes, supply')model.var('Y',desc='Income = GDP')model.var('YD',desc='Disposable income of households')# This is a shorter way to declare multiple variables# model.vars('Y', 'YD', 'Ts', 'Td', 'Hs', 'Hh', 'Gs', 'Cs',#            'Cd', 'Ns', 'Nd')model.param('Gd',desc='Government goods, demand',initial=20)model.param('W',desc='Wage rate',initial=1)model.param('alpha1',desc='Propensity to consume out of income',initial=0.6)model.param('alpha2',desc='Propensity to consume out of wealth',initial=0.4)model.param('theta',desc='Tax rate',initial=0.2)model.add('Cs = Cd')model.add('Gs = Gd')model.add('Ts = Td')model.add('Ns = Nd')model.add('YD = (W*Ns) - Ts')model.add('Td = theta * W * Ns')model.add('Cd = alpha1*YD + alpha2*Hh(-1)')model.add('Hs - Hs(-1) =  Gd - Td')model.add('Hh - Hh(-1) = YD - Cd')model.add('Y = Cs + Gs')model.add('Nd = Y/W')# solve until convergencefor_inrange(100):model.solve(iterations=100,threshold=1e-4)prev_soln=model.solutions[-2]soln=model.solutions[-1]ifis_close(prev_soln,soln,atol=1e-3):breakprint(round_solution(model.solutions[-1],decimals=1))TutorialA short tutorial with more explanation is available athttp://nbviewer.ipython.org/github/kennt/monetary-economics/blob/master/extra/pysolve%20tutorial.ipynbMore complex examplesFor additional examples, view the iPython notebooks athttp://nbviewer.ipython.org/github/kennt/monetary-economics/tree/master/To do listData import featuresSparse matrix support (memory improvements for large systems)DocumentationChangelog0.2.0Converted to Python 3.8Updated to pass pep8/pycodestyle and pylintrcFixes for usage with sympy 1.2Added requirements.txt0.1.7Tutorial0.1.6Added support for solving with Broyden's methodOptimized the code for Broyden and Newton-Raphson, should be much faster now.0.1.5Added the d() function.  Implements the difference between the current value
and the value from a previous iteration.  d(x) is equivalent to x - x(-1)Added support for the following sympy functions: abs, Min, Max, sign, sqrtAdded some helper functions to aid in debugging larger modelsAdded support for solving via Newton-Raphson0.1.4Improved error reporting when unable to solve an equation (due to variable
missing a value).Also, evaluate() used to require that all variables have a value, but that
may not be true on initialization, so this requirement has been removed.0.1.3 (and before)Added support for the exp() and log() functions.Fixed a bug where the usage of '>=' within an if_true() would cause an error.