Solving Linear Programs

class cdd.LinProg(mat)

A class for solving linear programs.

Bases: NumberTypeable

Parameters:

• mat (Matrix) – The matrix to load the linear program from.

Methods and Attributes

LinProg.solve(solver=cdd.LPSolverType.DUAL_SIMPLEX)

Solve linear program.

Parameters:

• solver (int) – The method of solution (see LPSolverType).

LinProg.dual_solution

A tuple containing the dual solution.

LinProg.obj_type

Whether we are minimizing or maximizing (see LPObjType).

LinProg.obj_value

The optimal value of the objective function.

LinProg.primal_solution

A tuple containing the primal solution.

LinProg.solver

The type of solver to use (see LPSolverType).

LinProg.status

The status of the linear program (see LPStatusType).

Examples

Note that the following examples presume:

>>> import cdd

Fractions

This is the testlp2.c example that comes with cddlib.

>>> mat = cdd.Matrix([['4/3',-2,-1],['2/3',0,-1],[0,1,0],[0,0,1]], number_type='fraction')
>>> mat.obj_type = cdd.LPObjType.MAX
>>> mat.obj_func = (0,3,4)
>>> print(mat)
begin
 4 3 rational
 4/3 -2 -1
 2/3 0 -1
 0 1 0
 0 0 1
end
maximize
 0 3 4
>>> print(mat.obj_func)
(0, 3, 4)
>>> lp = cdd.LinProg(mat)
>>> lp.solve()
>>> lp.status == cdd.LPStatusType.OPTIMAL
True
>>> print(lp.obj_value)
11/3
>>> print(" ".join("{0}".format(val) for val in lp.primal_solution))
1/3 2/3
>>> print(" ".join("{0}".format(val) for val in lp.dual_solution))
3/2 5/2

Another example.

>>> mat = cdd.Matrix([[1,-1,-1,-1],[-1,1,1,1],[0,1,0,0],[0,0,1,0],[0,0,0,1]], number_type='fraction')
>>> mat.obj_type = cdd.LPObjType.MIN
>>> mat.obj_func = (0,1,2,3)
>>> lp = cdd.LinProg(mat)
>>> lp.solve()
>>> print(lp.obj_value)
1
>>> mat.obj_func = (0,-1,-2,-3)
>>> lp = cdd.LinProg(mat)
>>> lp.solve()
>>> print(lp.obj_value)
-3
>>> mat.obj_func = (0,'1.12','1.2','1.3')
>>> lp = cdd.LinProg(mat)
>>> lp.solve()
>>> print(lp.obj_value) # 28/25 is 1.12
28/25
>>> print(lp.primal_solution) # extreme point in simplex
(1, 0, 0)

Floats

This is the testlp2.c example that comes with cddlib.

>>> mat = cdd.Matrix([['4/3',-2,-1],['2/3',0,-1],[0,1,0],[0,0,1]])
>>> mat.obj_type = cdd.LPObjType.MAX
>>> mat.obj_func = (0,3,4)
>>> print(mat) 
begin
 4 3 real
 1.333333333E+00 -2 -1
 6.666666667E-01 0 -1
 0 1 0
 0 0 1
end
maximize
 0 3 4
>>> print(mat.obj_func)
(0.0, 3.0, 4.0)
>>> lp = cdd.LinProg(mat)
>>> lp.solve()
>>> lp.status == cdd.LPStatusType.OPTIMAL
True
>>> print(lp.obj_value) 
3.66666...
>>> print(" ".join("{0}".format(val) for val in lp.primal_solution)) 
0.33333... 0.66666...
>>> print(" ".join("{0}".format(val) for val in lp.dual_solution))
1.5 2.5

Another example.

>>> mat = cdd.Matrix([[1,-1,-1,-1],[-1,1,1,1],[0,1,0,0],[0,0,1,0],[0,0,0,1]])
>>> mat.obj_type = cdd.LPObjType.MIN
>>> mat.obj_func = (0,1,2,3)
>>> lp = cdd.LinProg(mat)
>>> lp.solve()
>>> print(lp.obj_value)
1.0
>>> mat.obj_func = (0,-1,-2,-3)
>>> lp = cdd.LinProg(mat)
>>> lp.solve()
>>> print(lp.obj_value)
-3.0
>>> mat.obj_func = (0,'1.12','1.2','1.3')
>>> lp = cdd.LinProg(mat)
>>> lp.solve()
>>> print(lp.obj_value) # 28/25 is 1.12
1.12