linprog.jl

using Base.Test
using MathProgBase

function linprogtest(solver; objtol = 1e-7, primaltol = 1e-6)
    println("Testing linprog and subfunctions with solver ", string(typeof(solver)))
    # min -x
    # s.t. 2x + y <= 1.5
    # x,y >= 0
    # solution is (0.75,0) with objval -0.75

    # test buildlp and solvelp
    m = buildlp([-1,0],[2 1],'<',1.5,solver)
    sol = solvelp(m)
    @test sol.status == :Optimal
    @test isapprox(sol.objval, -0.75, atol=objtol)
    @test isapprox(norm(sol.sol - [0.75,0.0]), 0.0, atol=primaltol)

    # test linprog
    sol = linprog([-1,0],[2 1],'<',1.5,solver)
    @test sol.status == :Optimal
    @test isapprox(sol.objval, -0.75, atol=objtol)
    @test isapprox(norm(sol.sol - [0.75,0.0]), 0.0, atol=primaltol)

    # test buildlp and solvelp
    m = buildlp([-1,0],[2 1],'<',1.5,solver)
    sol = solvelp(m)
    @test sol.status == :Optimal
    @test isapprox(sol.objval, -0.75, atol=objtol)
    @test isapprox(norm(sol.sol - [0.75,0.0]), 0.0, atol=primaltol)

    # test linprog
    sol = linprog([-1,0],sparse([2 1]),'<',1.5,solver)
    @test sol.status == :Optimal
    @test isapprox(sol.objval, -0.75, atol=objtol)
    @test isapprox(norm(sol.sol - [0.75,0.0]), 0.0, atol=primaltol)

    # test infeasible problem:
    # min x
    # s.t. 2x+y <= -1
    # x,y >= 0

    # test buildlp and solvelp
    m = buildlp([1,0],[2 1],'<',-1,solver)
    sol = solvelp(m)
    @test sol.status == :Infeasible

    r = sol.attrs[:infeasibilityray][1]
    @test isapprox(r/abs(r), -1.0)

    # test linprog
    sol = linprog([1,0],[2 1],'<',-1,solver)
    @test sol.status == :Infeasible

    r = sol.attrs[:infeasibilityray][1]
    @test isapprox(r/abs(r), -1.0)

    # test unbounded problem:
    # min -x-y
    # s.t. -x+2y <= 0
    # x,y >= 0

    # test buildlp and solvelp
    m = buildlp([-1,-1],[-1 2],'<',[0],solver)
    sol = solvelp(m)
    @test sol.status == :Unbounded

    # test linprog
    sol = linprog([-1,-1],[-1 2],'<',[0],solver)
    @test sol.status == :Unbounded

    # unbounded problem with unique ray:
    # min -x-y
    # s.t. x-y == 0
    # x,y >= 0

    # test buildlp and solvelp
    m = buildlp([-1,-1],[1 -1],'=',0,solver)
    sol = solvelp(m)
    @test sol.status == :Unbounded
    @test sol.attrs[:unboundedray][1] > 1e-7
    @test isapprox(sol.attrs[:unboundedray][1], sol.attrs[:unboundedray][2])

    # test linprog
    sol = linprog([-1,-1],[1 -1],'=',0,solver)
    @test sol.status == :Unbounded
    @test sol.attrs[:unboundedray][1] > 1e-7
    @test isapprox(sol.attrs[:unboundedray][1], sol.attrs[:unboundedray][2])


    println("Passed")
end