Description

general_cartesian_product extends the existing functionality of itertools.product by variable limits. It's possible to create cartesian products like:

   i1           i2             i3
[1, 2, 3] x [1, ..., i1] x [0, ..., i2] = 
[
    [1, 1, 0]
    [1, 1, 1]
    [2, 1, 0]
    [2, 1, 1]
    [2, 2, 0]
    [2, 2, 1]
    [2, 2, 2]
    [3, 1, 0]
    [3, 1, 1]
    [3, 2, 0]
    [3, 2, 1]
    [3, 2, 2]
    [3, 3, 0]
    [3, 3, 1]
    [3, 3, 2]
    [3, 3, 3]
]

via this config file:

rules = {
    'i1': { 'start': 1, 'end': 3, },
    'i2': { 'start': 1, 'end': i1, },
    'i3': { 'end': i2, },
}

Obviously this example is quite useless, because its the same as [1,2,3]x[1,2,3]x[0,1,2,3] The whole thing becomes interesting if we have problems like this:

[1, 2, 3] x [1, ..., 3-i1] x [0, ..., 3-i2] = 
[
    [1, 1, 0]
    [1, 1, 1]
    [1, 1, 2]
    [1, 2, 0]
    [1, 2, 1]
    [2, 1, 0]
    [2, 1, 1]
    [2, 1, 2]
]

which is generated by this configuration:

rules = {
    'i1': {'start': 1, 'end': 3, },
    'i2': {'start': 1, 'end': 3-i1, },
    'i3': {'end': 3-i2, },
}

Limitations

Currently the only known limitation is that there must be always at least one constant limit. This means that the output of the cartesian product function will always be finite. To create 'infinite' generator like cartesian products a complete rewrite of this package is probably needed.

Installation

This package depends on sympy (or sage symbolic variables e.g.:i = var('i'))

pip install generalcartesianproduct sympy

Usage

sympy Example:

from sympy import symbols
from generalcartesianproduct.general_cartesian_product import *
i1, i2, u, v = symbols('i1,i2,u,v')

general_cartesian_product([i1, i2, i3])

sage Example:

from generalcartesianproduct.general_cartesian_product import *
m = 4
i1, i2, u, v = var('i1,i2,u,v')
rules = {
    'i1': { 'end': m, },
    'i2': { 'end': m, },
    'u':  { 'end': min_symbolic(m-i1, m-i2), },
    'v':  { 'end': min_symbolic(m-i1, m-i2)-u, }
}
cp = general_cartesian_product([i1, i2, i3], rules)
print(cp)

How to use the rules dictionary.

# simple example with only one dependency
rules = {
    'i1': { 'end': m, },
    'i2': { 'end': m-i1, },
}

TODO

• better logging
• add exceptions
• make start, end accesable via kargs