Stability | experimental |
---|---|
Maintainer | erkokl@gmail.com |
Safe Haskell | None |
(The linear equation solver library is hosted at http://github.com/LeventErkok/linearEqSolver. Comments, bug reports, and patches are always welcome.)
Solvers for linear equations over integers. Both single solution and all solution variants are supported.
Finding a solution
solveIntegerLinearEqs :: [[Integer]] -> [Integer] -> IO (Maybe [Integer])Source
Solve a system of linear integer equations. The first argument is
the matrix of coefficients, known as A
, of size mxn
. The second argument
is the vector of results, known as B
, of size mx1
. The result will be
either Nothing
, if there is no solution, or Just x
-- such that Ax = B
holds.
(Naturally, the result x
will be a vector of size nx1
in this case.)
Here's an example call, to solve the following system of equations:
2x + 3y + 4z = 20 6x - 3y + 9z = -6 2x + z = 8
>>>
solveIntegerLinearEqs [[2,3,4],[6,-3,9],[2,0,1]] [20,-6,8]
Just [5,6,-2]
In case there are no solutions, we will get Nothing
:
>>>
solveIntegerLinearEqs [[1], [1]] [2,3]
Nothing
Note that there are no solutions to this second system as it stipulates the unknown is equal to both 2 and 3. (Overspecified.)
Finding all solutions
solveIntegerLinearEqsAll :: [[Integer]] -> [Integer] -> IO [[Integer]]Source
Similar to solveIntegerLinearEqs
, except returns all possible solutions.
Note that there might be an infinite number of solutions if the system
is underspecified, in which case the result will be a lazy list of solutions
that the caller can consume as much as needed.
Here's an example call, where we underspecify the system and hence there are multiple (in this case an infinite number of) solutions. Here, we only take the first 3 elements, for testing purposes, but all such results can be computed lazily. Our system is:
2x + 3y + 4z = 20 6x - 3y + 9z = -6
We have:
>>>
take 3 `fmap` solveIntegerLinearEqsAll [[2,3,4],[6,-3,9]] [20,-6]
[[5,6,-2],[-8,4,6],[18,8,-10]]