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A simple interface for solving systems of linear equations

Project description

Solving systems of linear equations

The purpose of this code 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.

The initial motivation for this tool was to solve economic models based on Stock Flow Consistent (SFC) models.

Installation

::
pip3 install pysolve

Usage

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', 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 o 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-3)

    prev_soln = model.solutions[-2]
    soln = model.solutions[-1]
    if is_close(prev_soln, soln, rtol=1e-3):
        break

print round_solution(model.solutions[-1], decimals=1)
For additional examples, view the iPython notebooks at
http://nbviewer.ipython.org/github/kennt/monetary-economics/tree/master/

Project details


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