pysolve - Solving systems of equations

Python3 update from pylinsolve. All credits and special thanks to Kenn Takara. Follow the updated version of the Readme file.

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.

The solver provides the following choices for solving:

• Gauss-Seidel
• Newton-Raphson
• Broyden

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.

Installation

pip install pysolve3

Usage

1. Define the variables used in the model.
2. Define the parameters used in the model.
3. Define the rules (equations)
4. Solve

Simple example

This example is taken Chapter 3 of the book "Monetary Economics 2e" by Lavoie and Godley, 2012.

from pysolve3.model import Model
from pysolve3.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', default=20)
model.param('W', desc='Wage rate', default=1)
model.param('alpha1', desc='Propensity to consume out of income', default=0.6)
model.param('alpha2', desc='Propensity to consume out of wealth', default=0.4)
model.param('theta', desc='Tax rate', default=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 range(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))

Tutorial

A short tutorial with more explanation is available here

More complex examples

For additional examples, view the iPython notebooks here

To do list

Data import features

Sparse matrix support (memory improvements for large systems)

Documentation

Changelog

Python3 Version

0.1.0

• Init commit