A simple interface for solving systems of equations

## Project description

==========

pysolve

==========

Solving systems of 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

--------------

pip install pysolve

Usage

-------------

.. code::

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 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/

Tutorial

--------

A short tutorial with more explanation is available at

http://nbviewer.ipython.org/github/kennt/monetary-economics/blob/master/extra/pysolve%20tutorial.ipynb

TODO list

---------

- Sparse matrix support (memory improvements for large systems)

- Documentation

Changelog

---------

0.2.0 (in progress)

-------------------

- Tutorial

- 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.

pysolve

==========

Solving systems of 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

--------------

pip install pysolve

Usage

-------------

.. code::

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 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/

Tutorial

--------

A short tutorial with more explanation is available at

http://nbviewer.ipython.org/github/kennt/monetary-economics/blob/master/extra/pysolve%20tutorial.ipynb

TODO list

---------

- Sparse matrix support (memory improvements for large systems)

- Documentation

Changelog

---------

0.2.0 (in progress)

-------------------

- Tutorial

- 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.

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