jprockbelly - 2 months ago 21

Python Question

I have a set of a few hundred simple sum equations. For example here are 3:

`w1 - u1 - u2 = 0`

w1 + w2 - w3 - u3 = 0

w1 - w2 - w4 = 0

I am trying to find a way to solve as many as possible given only a few of the values. For example, in the above equation set if I have

`u1`

`u2`

`w1`

Given

`u1`

`u2`

`w2`

`w1`

`w4`

Currently I'm approaching this in a fairly straight forward way (psudo code):

`while there are new results:`

for each equation:

try to solve equation:

if solved update result set

This works but feels clunky and inefficient.

Is there a better way? (using Python if that is relevant)

`from sympy import linsolve, symbols, linear_eq_to_matrix`

def my_solver(known_vals):

w1, w2, w3, w4, u1, u2, u3 = symbols("w1, w2, w3, w4, u1, u2, u3", integer=True)

variables = [w1, w2, w3, w4, u1, u2, u3]

eqns = [w1 - u1 - u2,

w1 + w2 - w3 - u3,

w1 - w2 - w4]

A, b = linear_eq_to_matrix(eqns, variables)

solution = linsolve((A, B), variables)

e= next(iter(answer))

for idx, x in enumerate(e):

print(variables[idx], x.subs(known_vals)) #this has a bug see comment below

my_solver({w1:2, u2:-2})

I noticed a bug in the approach, if I pass

`{w1:2, u1: -10, u2:-2}`

Answer

Just get SymPy and stuff the whole system of linear equations into `sympy.solvers.solveset.linsolve`

. It'll give you the whole solution space, including the values of variables with determined values, in a form dependent on whether the system has 0, 1, or infinite solutions.

There's probably also a NumPy/SciPy way to get the solution set of an underdetermined system, but whatever that way is, I don't know it. Google suggests a singular value decomposition would be useful, but I haven't figured out how you'd get a basis for the solution set out of that.