robabsmith / pylinsolve

A simple interface for solving systems of equations

pysolve - Solving systems of equations

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 pysolve

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 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)

Tutorial

A short tutorial with more explanation is available at http://nbviewer.ipython.org/github/kennt/monetary-economics/blob/master/extra/pysolve%20tutorial.ipynb

More complex examples

For additional examples, view the iPython notebooks at http://nbviewer.ipython.org/github/kennt/monetary-economics/tree/master/

To do list

Data import features

Sparse matrix support (memory improvements for large systems)

Documentation

Changelog

0.2.0 (in progress)

• Improved documentation

0.1.7

• Tutorial

0.1.6

• Added support for solving with Broyden's method
• Optimized the code for Broyden and Newton-Raphson, should be much faster now.

0.1.5

• Added 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, sqrt
• Added some helper functions to aid in debugging larger models
• Added support for solving via Newton-Raphson

0.1.4

• Improved 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.