test_solve_random_cone_prob.py

from __future__ import print_function, division
import scs
import numpy as np
from scipy import sparse
import gen_random_cone_prob as tools

#############################################
#  Uses scs to solve a random cone problem  #
#############################################


def import_error(msg):
    print()
    print("## IMPORT ERROR:" + msg)
    print()


try:
    import pytest
except ImportError:
    import_error("Please install pytest to run tests.")
    raise

flags = [(False, False), (True, False)]
try:
    import _scs_gpu

    flags += [(True, True)]
except ImportError:
    pass

np.random.seed(1)

# cone:
K = {
    "z": 10,
    "l": 15,
    "q": [5, 10, 0, 1],
    "s": [3, 4, 0, 0, 1, 10],
    "ep": 10,
    "ed": 10,
    "p": [-0.25, 0.5, 0.75, -0.33],
}
m = tools.get_scs_cone_dims(K)
params = {"verbose": True, "eps_abs": 1e-5, "eps_rel": 1e-5, "eps_infeas": 1e-5}


@pytest.mark.parametrize("use_indirect,gpu", flags)
def test_solve_feasible(use_indirect, gpu):
    data, p_star = tools.gen_feasible(K, n=m // 3, density=0.1)
    solver = scs.SCS(data, K, use_indirect=use_indirect, gpu=gpu, **params)
    sol = solver.solve()
    x = sol["x"]
    y = sol["y"]
    s = sol["s"]
    np.testing.assert_almost_equal(np.dot(data["c"], x), p_star, decimal=3)
    np.testing.assert_almost_equal(np.dot(data["c"], x), p_star, decimal=3)
    np.testing.assert_array_less(
        np.linalg.norm(data["A"] @ x - data["b"] + s), 1e-3
    )
    np.testing.assert_array_less(
        np.linalg.norm(data["A"].T @ y + data["c"]), 1e-3
    )
    np.testing.assert_almost_equal(s.T @ y, 0.0)
    np.testing.assert_almost_equal(s, tools.proj_cone(s, K), decimal=4)
    np.testing.assert_almost_equal(y, tools.proj_dual_cone(y, K), decimal=3)


@pytest.mark.parametrize("use_indirect,gpu", flags)
def test_solve_infeasible(use_indirect, gpu):
    data = tools.gen_infeasible(K, n=m // 2)
    solver = scs.SCS(data, K, use_indirect=use_indirect, gpu=gpu, **params)
    sol = solver.solve()
    y = sol["y"]
    np.testing.assert_array_less(np.linalg.norm(data["A"].T @ y), 1e-3)
    np.testing.assert_array_less(data["b"].T @ y, -0.1)
    np.testing.assert_almost_equal(y, tools.proj_dual_cone(y, K), decimal=4)


# TODO: indirect solver has trouble in this test, so disable for now
@pytest.mark.parametrize("use_indirect,gpu", [(False, False)])
def test_solve_unbounded(use_indirect, gpu):
    data = tools.gen_unbounded(K, n=m // 2)
    solver = scs.SCS(data, K, use_indirect=use_indirect, gpu=gpu, **params)
    sol = solver.solve()
    x = sol["x"]
    s = sol["s"]
    np.testing.assert_array_less(np.linalg.norm(data["A"] @ x + s), 1e-3)
    np.testing.assert_array_less(data["c"].T @ x, -0.1)
    np.testing.assert_almost_equal(s, tools.proj_cone(s, K), decimal=4)