A Moonbit library for defining and solving linear programming problems

/** how to define a linear-program */
(1) general step

1. define variables_array
2. define object_func
3. define eq_constraint
4. define ineq_constraint
5. define linear-program

let arr = [
    Variable::new("x1", 0.0, 100.0),
    Variable::new("x2", 0.0, 100.0),
    Variable::new("x3", 0.0, 100.0),
  ]
let obj_func = Obj_func::from_array("max", [1.0, 2.0, 3.0], arr)
let eqarr = [([2.0, 2.0, 3.0], 100.0)]
let ineqarr = [([2.5, 0.0, 4.7], ">=", 0.0), ([-1.7, 2.5, 12], "<=", 0.0)]
let lp2 = Lp::new(obj_func, arr).cons_from_Array(
    eq_array=eqarr,
    ineq_array=ineqarr,
)

(2) matrix to linear-program
only contain Eq-constraint, don't contain Ineq-constraint

let vars = [
  Variable::new("x1", 0.0, @double.max_value),
  Variable::new("x2", 0.0, @double.max_value),
  Variable::new("x3", 0.0, @double.max_value),
  Variable::new("x4", 0.0, @double.max_value),
]

let matrix = Matrix::from_2d_array([
  [1, 2, 3, 4, 0],
  [4, 1, 0, 6, 1],
  [1, 3, 1, 0, 0],
  [-1, 4, 7, 1, 2]
])

let lp = Lp::from_matrix(matrix, vars, "min")

/** solve linear-program by two_stage method */
(1) define linear-program

let vars = [
  Variable::new("x1", 0.0, @double.max_value),
  Variable::new("x2", 0.0, @double.max_value),
  Variable::new("x3", 0.0, @double.max_value),
]
  let matrix: Matrix[Double] = Matrix::from_2d_array([
    [-1, -2, -3, 0],
    [1, 2, 3, 10],
    [2, 1, 1, 8],
  ])

(2) make program standardization and call two-stage function

let lp = Lp::from_matrix(matrix, vars, "min").to_standard()
let res = lp.two_stage()

(3) Result (vars, best_base_solve, object_function_value)

[x1, x2, x3]  //(lp.vars)
[1.9999999999999991, 4.000000000000001, 0] //(res.0)
-10 //(res.1)