The 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.
pysolve uses Gauss-Seidel/SOR to iterate to a solution.
It 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.
pip install pysolve- Define the variables used in the model.
- Define the parameters used in the model.
- Define the rules (equations)
- Solve
This example is taken Chapter 3 of the book "Monetary Economics 2e" by Lavoie and Godley, 2012.
from pysolve.model import Model
from pysolve.utils import round_solution, is_close
model = 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 convergence
for _ in xrange(100):
model.solve(iterations=100, threshold=1e-4)
prev_soln = model.solutions[-2]
soln = model.solutions[-1]
if is_close(prev_soln, soln, atol=1e-3):
break
print round_solution(model.solutions[-1], decimals=1)For more examples, please see the associated iPython notebooks.