MMatrix.hs

#!/usr/bin/env stack
-- stack --resolver lts-3.11 --install-ghc runghc --package hmatrix-glpk-0.4.1.0

module Main where

import Numeric.LinearProgramming

constraints :: [Bound [Double]]
constraints =
  -- first vector is valid
  [ [ 1, 1, 1,   0, 0, 0,   0, 0, 0 ] :>=: 0
  , [ 1, 0, 0,   0, 0, 0,   0, 0, 0 ] :>=: 1
  , [ 0, 1, 0,   0, 0, 0,   0, 0, 0 ] :<=: 0
  , [ 0, 0, 1,   0, 0, 0,   0, 0, 0 ] :<=: 0

  -- second vector is valid
  , [ 0, 0, 0,   1, 1, 1,   0, 0, 0 ] :>=: 0
  , [ 0, 0, 0,   0, 1, 0,   0, 0, 0 ] :>=: 1
  , [ 0, 0, 0,   1, 0, 0,   0, 0, 0 ] :<=: 0
  , [ 0, 0, 0,   0, 0, 1,   0, 0, 0 ] :<=: 0

  -- third vector is valid
  , [ 0, 0, 0,   0, 0, 0,   1, 1, 1 ] :>=: 0
  , [ 0, 0, 0,   0, 0, 0,   0, 0, 1 ] :>=: 1
  , [ 0, 0, 0,   0, 0, 0,   1, 0, 0 ] :<=: 0
  , [ 0, 0, 0,   0, 0, 0,   0, 1, 0 ] :<=: 0

  -- at least one vector is strictly positive
  --, [ 1, 1, 1,   1, 1, 1,   1, 1, 1 ] :>=: 1

  -- the third vector is a combination of the first two
  , [ 1, 0, 0,   -1, 0, 0,  1, 0, 0 ] :==: 0
  , [ 0, 1, 0,   0, -1, 0,  0, 1, 0 ] :==: 0
  , [ 0, 0, 1,   0, 0, -1,  0, 0, 1 ] :==: 0 
  ]

main :: IO ()
main = print $ simplex opt (Dense constraints) []
  where opt = Minimize [1,1,1,1,1,1,1,1,1]