Vehicle-cpp/hkpc/software/scipy/optimize/tests/test__shgo.py

import logging
import numpy
from numpy.testing import assert_allclose
import pytest
from pytest import raises as assert_raises, warns
from scipy.optimize import shgo, Bounds, minimize
from scipy.optimize._shgo import SHGO


class StructTestFunction:
    def __init__(self, bounds, expected_x, expected_fun=None,
                 expected_xl=None, expected_funl=None):
        self.bounds = bounds
        self.expected_x = expected_x
        self.expected_fun = expected_fun
        self.expected_xl = expected_xl
        self.expected_funl = expected_funl


def wrap_constraints(g):
    cons = []
    if g is not None:
        if (type(g) is not tuple) and (type(g) is not list):
            g = (g,)
        else:
            pass
        for g in g:
            cons.append({'type': 'ineq',
                         'fun': g})
        cons = tuple(cons)
    else:
        cons = None
    return cons


class StructTest1(StructTestFunction):
    def f(self, x):
        return x[0] ** 2 + x[1] ** 2

    def g(x):
        return -(numpy.sum(x, axis=0) - 6.0)

    cons = wrap_constraints(g)


test1_1 = StructTest1(bounds=[(-1, 6), (-1, 6)],
                      expected_x=[0, 0])
test1_2 = StructTest1(bounds=[(0, 1), (0, 1)],
                      expected_x=[0, 0])
test1_3 = StructTest1(bounds=[(None, None), (None, None)],
                      expected_x=[0, 0])


class StructTest2(StructTestFunction):
    """
    Scalar function with several minima to test all minimizer retrievals
    """

    def f(self, x):
        return (x - 30) * numpy.sin(x)

    def g(x):
        return 58 - numpy.sum(x, axis=0)

    cons = wrap_constraints(g)


test2_1 = StructTest2(bounds=[(0, 60)],
                      expected_x=[1.53567906],
                      expected_fun=-28.44677132,
                      # Important: test that funl return is in the correct order
                      expected_xl=numpy.array([[1.53567906],
                                               [55.01782167],
                                               [7.80894889],
                                               [48.74797493],
                                               [14.07445705],
                                               [42.4913859],
                                               [20.31743841],
                                               [36.28607535],
                                               [26.43039605],
                                               [30.76371366]]),

                      expected_funl=numpy.array([-28.44677132, -24.99785984,
                                                 -22.16855376, -18.72136195,
                                                 -15.89423937, -12.45154942,
                                                 -9.63133158, -6.20801301,
                                                 -3.43727232, -0.46353338])
                      )

test2_2 = StructTest2(bounds=[(0, 4.5)],
                      expected_x=[1.53567906],
                      expected_fun=[-28.44677132],
                      expected_xl=numpy.array([[1.53567906]]),
                      expected_funl=numpy.array([-28.44677132])
                      )


class StructTest3(StructTestFunction):
    """
    Hock and Schittkowski 18 problem (HS18). Hoch and Schittkowski (1981)
    http://www.ai7.uni-bayreuth.de/test_problem_coll.pdf
    Minimize: f = 0.01 * (x_1)**2 + (x_2)**2

    Subject to: x_1 * x_2 - 25.0 >= 0,
                (x_1)**2 + (x_2)**2 - 25.0 >= 0,
                2 <= x_1 <= 50,
                0 <= x_2 <= 50.

    Approx. Answer:
        f([(250)**0.5 , (2.5)**0.5]) = 5.0


    """

    def f(self, x):
        return 0.01 * (x[0]) ** 2 + (x[1]) ** 2

    def g1(x):
        return x[0] * x[1] - 25.0

    def g2(x):
        return x[0] ** 2 + x[1] ** 2 - 25.0

    g = (g1, g2)

    cons = wrap_constraints(g)


test3_1 = StructTest3(bounds=[(2, 50), (0, 50)],
                      expected_x=[250 ** 0.5, 2.5 ** 0.5],
                      expected_fun=5.0
                      )


class StructTest4(StructTestFunction):
    """
    Hock and Schittkowski 11 problem (HS11). Hoch and Schittkowski (1981)

    NOTE: Did not find in original reference to HS collection, refer to
          Henderson (2015) problem 7 instead. 02.03.2016
    """

    def f(self, x):
        return ((x[0] - 10) ** 2 + 5 * (x[1] - 12) ** 2 + x[2] ** 4
                + 3 * (x[3] - 11) ** 2 + 10 * x[4] ** 6 + 7 * x[5] ** 2 + x[
                    6] ** 4
                - 4 * x[5] * x[6] - 10 * x[5] - 8 * x[6]
                )

    def g1(x):
        return -(2 * x[0] ** 2 + 3 * x[1] ** 4 + x[2] + 4 * x[3] ** 2
                 + 5 * x[4] - 127)

    def g2(x):
        return -(7 * x[0] + 3 * x[1] + 10 * x[2] ** 2 + x[3] - x[4] - 282.0)

    def g3(x):
        return -(23 * x[0] + x[1] ** 2 + 6 * x[5] ** 2 - 8 * x[6] - 196)

    def g4(x):
        return -(4 * x[0] ** 2 + x[1] ** 2 - 3 * x[0] * x[1] + 2 * x[2] ** 2
                 + 5 * x[5] - 11 * x[6])

    g = (g1, g2, g3, g4)

    cons = wrap_constraints(g)


test4_1 = StructTest4(bounds=[(-10, 10), ] * 7,
                      expected_x=[2.330499, 1.951372, -0.4775414,
                                  4.365726, -0.6244870, 1.038131, 1.594227],
                      expected_fun=680.6300573
                      )


class StructTest5(StructTestFunction):
    def f(self, x):
        return (-(x[1] + 47.0)
                * numpy.sin(numpy.sqrt(abs(x[0] / 2.0 + (x[1] + 47.0))))
                - x[0] * numpy.sin(numpy.sqrt(abs(x[0] - (x[1] + 47.0))))
                )

    g = None
    cons = wrap_constraints(g)


test5_1 = StructTest5(bounds=[(-512, 512), (-512, 512)],
                      expected_fun=[-959.64066272085051],
                      expected_x=[512., 404.23180542])


class StructTestLJ(StructTestFunction):
    """
    LennardJones objective function. Used to test symmetry constraints settings.
    """

    def f(self, x, *args):
        self.N = args[0]
        k = int(self.N / 3)
        s = 0.0

        for i in range(k - 1):
            for j in range(i + 1, k):
                a = 3 * i
                b = 3 * j
                xd = x[a] - x[b]
                yd = x[a + 1] - x[b + 1]
                zd = x[a + 2] - x[b + 2]
                ed = xd * xd + yd * yd + zd * zd
                ud = ed * ed * ed
                if ed > 0.0:
                    s += (1.0 / ud - 2.0) / ud

        return s

    g = None
    cons = wrap_constraints(g)


N = 6
boundsLJ = list(zip([-4.0] * 6, [4.0] * 6))

testLJ = StructTestLJ(bounds=boundsLJ,
                      expected_fun=[-1.0],
                      expected_x=[-2.71247337e-08,
                                  -2.71247337e-08,
                                  -2.50000222e+00,
                                  -2.71247337e-08,
                                  -2.71247337e-08,
                                  -1.50000222e+00]
                      )


class StructTestTable(StructTestFunction):
    def f(self, x):
        if x[0] == 3.0 and x[1] == 3.0:
            return 50
        else:
            return 100

    g = None
    cons = wrap_constraints(g)


test_table = StructTestTable(bounds=[(-10, 10), (-10, 10)],
                             expected_fun=[50],
                             expected_x=[3.0, 3.0])


class StructTestInfeasible(StructTestFunction):
    """
    Test function with no feasible domain.
    """

    def f(self, x, *args):
        return x[0] ** 2 + x[1] ** 2

    def g1(x):
        return x[0] + x[1] - 1

    def g2(x):
        return -(x[0] + x[1] - 1)

    def g3(x):
        return -x[0] + x[1] - 1

    def g4(x):
        return -(-x[0] + x[1] - 1)

    g = (g1, g2, g3, g4)
    cons = wrap_constraints(g)


test_infeasible = StructTestInfeasible(bounds=[(2, 50), (-1, 1)],
                                       expected_fun=None,
                                       expected_x=None
                                       )


def run_test(test, args=(), test_atol=1e-5, n=128, iters=None,
             callback=None, minimizer_kwargs=None, options=None,
             sampling_method='sobol'):
    res = shgo(test.f, test.bounds, args=args, constraints=test.cons,
               n=n, iters=iters, callback=callback,
               minimizer_kwargs=minimizer_kwargs, options=options,
               sampling_method=sampling_method)

    logging.info(res)

    if test.expected_x is not None:
        numpy.testing.assert_allclose(res.x, test.expected_x,
                                      rtol=test_atol,
                                      atol=test_atol)

    # (Optional tests)
    if test.expected_fun is not None:
        numpy.testing.assert_allclose(res.fun,
                                      test.expected_fun,
                                      atol=test_atol)

    if test.expected_xl is not None:
        numpy.testing.assert_allclose(res.xl,
                                      test.expected_xl,
                                      atol=test_atol)

    if test.expected_funl is not None:
        numpy.testing.assert_allclose(res.funl,
                                      test.expected_funl,
                                      atol=test_atol)
    return


# Base test functions:
class TestShgoSobolTestFunctions:
    """
    Global optimization tests with Sobol sampling:
    """

    # Sobol algorithm
    def test_f1_1_sobol(self):
        """Multivariate test function 1:
        x[0]**2 + x[1]**2 with bounds=[(-1, 6), (-1, 6)]"""
        run_test(test1_1)

    def test_f1_2_sobol(self):
        """Multivariate test function 1:
         x[0]**2 + x[1]**2 with bounds=[(0, 1), (0, 1)]"""
        run_test(test1_2)

    def test_f1_3_sobol(self):
        """Multivariate test function 1:
        x[0]**2 + x[1]**2 with bounds=[(None, None),(None, None)]"""
        run_test(test1_3)

    def test_f2_1_sobol(self):
        """Univariate test function on
        f(x) = (x - 30) * sin(x) with bounds=[(0, 60)]"""
        run_test(test2_1)

    def test_f2_2_sobol(self):
        """Univariate test function on
        f(x) = (x - 30) * sin(x) bounds=[(0, 4.5)]"""
        run_test(test2_2)

    def test_f3_sobol(self):
        """NLP: Hock and Schittkowski problem 18"""
        run_test(test3_1)

    @pytest.mark.slow
    def test_f4_sobol(self):
        """NLP: (High-dimensional) Hock and Schittkowski 11 problem (HS11)"""
        # run_test(test4_1, n=500)
        # run_test(test4_1, n=800)
        options = {'infty_constraints': False}
        run_test(test4_1, n=2048, options=options)

    def test_f5_1_sobol(self):
        """NLP: Eggholder, multimodal"""
        run_test(test5_1, n=64)

    def test_f5_2_sobol(self):
        """NLP: Eggholder, multimodal"""
        # run_test(test5_1, n=60, iters=5)
        run_test(test5_1, n=128, iters=5)

        # def test_t911(self):
        #    """1-D tabletop function"""
        #    run_test(test11_1)


class TestShgoSimplicialTestFunctions:
    """
    Global optimization tests with Simplicial sampling:
    """

    def test_f1_1_simplicial(self):
        """Multivariate test function 1:
        x[0]**2 + x[1]**2 with bounds=[(-1, 6), (-1, 6)]"""
        run_test(test1_1, n=1, sampling_method='simplicial')

    def test_f1_2_simplicial(self):
        """Multivariate test function 1:
        x[0]**2 + x[1]**2 with bounds=[(0, 1), (0, 1)]"""
        run_test(test1_2, n=1, sampling_method='simplicial')

    def test_f1_3_simplicial(self):
        """Multivariate test function 1: x[0]**2 + x[1]**2
        with bounds=[(None, None),(None, None)]"""
        run_test(test1_3, n=1, sampling_method='simplicial')

    def test_f2_1_simplicial(self):
        """Univariate test function on
        f(x) = (x - 30) * sin(x) with bounds=[(0, 60)]"""
        options = {'minimize_every_iter': False}
        run_test(test2_1, iters=7, options=options,
                 sampling_method='simplicial')

    def test_f2_2_simplicial(self):
        """Univariate test function on
        f(x) = (x - 30) * sin(x) bounds=[(0, 4.5)]"""
        run_test(test2_2, n=1, sampling_method='simplicial')

    def test_f3_simplicial(self):
        """NLP: Hock and Schittkowski problem 18"""
        run_test(test3_1, n=1, sampling_method='simplicial')

    @pytest.mark.slow
    def test_f4_simplicial(self):
        """NLP: (High-dimensional) Hock and Schittkowski 11 problem (HS11)"""
        run_test(test4_1, n=1, sampling_method='simplicial')

    def test_lj_symmetry(self):
        """LJ: Symmetry-constrained test function"""
        options = {'symmetry': True,
                   'disp': True}
        args = (6,)  # Number of atoms
        run_test(testLJ, args=args, n=None,
                 options=options, iters=4,
                 sampling_method='simplicial')


# Argument test functions
class TestShgoArguments:
    def test_1_1_simpl_iter(self):
        """Iterative simplicial sampling on TestFunction 1 (multivariate)"""
        run_test(test1_2, n=None, iters=2, sampling_method='simplicial')

    def test_1_2_simpl_iter(self):
        """Iterative simplicial on TestFunction 2 (univariate)"""
        options = {'minimize_every_iter': False}
        run_test(test2_1, n=None, iters=7, options=options,
                 sampling_method='simplicial')

    def test_2_1_sobol_iter(self):
        """Iterative Sobol sampling on TestFunction 1 (multivariate)"""
        run_test(test1_2, n=None, iters=1, sampling_method='sobol')

    def test_2_2_sobol_iter(self):
        """Iterative Sobol sampling on TestFunction 2 (univariate)"""
        res = shgo(test2_1.f, test2_1.bounds, constraints=test2_1.cons,
                   n=None, iters=1, sampling_method='sobol')

        numpy.testing.assert_allclose(res.x, test2_1.expected_x, rtol=1e-5,
                                      atol=1e-5)
        numpy.testing.assert_allclose(res.fun, test2_1.expected_fun, atol=1e-5)

    def test_3_1_disp_simplicial(self):
        """Iterative sampling on TestFunction 1 and 2  (multi- and univariate)"""

        def callback_func(x):
            print("Local minimization callback test")

        for test in [test1_1, test2_1]:
            shgo(test.f, test.bounds, iters=1,
                 sampling_method='simplicial',
                 callback=callback_func, options={'disp': True})
            shgo(test.f, test.bounds, n=1, sampling_method='simplicial',
                 callback=callback_func, options={'disp': True})

    def test_3_2_disp_sobol(self):
        """Iterative sampling on TestFunction 1 and 2 (multi- and univariate)"""

        def callback_func(x):
            print("Local minimization callback test")

        for test in [test1_1, test2_1]:
            shgo(test.f, test.bounds, iters=1, sampling_method='sobol',
                 callback=callback_func, options={'disp': True})

            shgo(test.f, test.bounds, n=1, sampling_method='simplicial',
                 callback=callback_func, options={'disp': True})

    def test_args_gh14589(self):
        # Using `args` used to cause `shgo` to fail; see #14589, #15986, #16506
        res = shgo(func=lambda x, y, z: x*z + y, bounds=[(0, 3)], args=(1, 2))
        ref = shgo(func=lambda x: 2*x + 1, bounds=[(0, 3)])
        assert_allclose(res.fun, ref.fun)
        assert_allclose(res.x, ref.x)

    @pytest.mark.slow
    def test_4_1_known_f_min(self):
        """Test known function minima stopping criteria"""
        # Specify known function value
        options = {'f_min': test4_1.expected_fun,
                   'f_tol': 1e-6,
                   'minimize_every_iter': True}
        # TODO: Make default n higher for faster tests
        run_test(test4_1, n=None, test_atol=1e-5, options=options,
                 sampling_method='simplicial')

    @pytest.mark.slow
    def test_4_2_known_f_min(self):
        """Test Global mode limiting local evalutions"""
        options = {  # Specify known function value
            'f_min': test4_1.expected_fun,
            'f_tol': 1e-6,
            # Specify number of local iterations to perform
            'minimize_every_iter': True,
            'local_iter': 1}

        run_test(test4_1, n=None, test_atol=1e-5, options=options,
                 sampling_method='simplicial')

    @pytest.mark.slow
    def test_4_3_known_f_min(self):
        """Test Global mode limiting local evalutions"""
        options = {  # Specify known function value
            'f_min': test4_1.expected_fun,
            'f_tol': 1e-6,
            # Specify number of local iterations to perform+
            'minimize_every_iter': True,
            'local_iter': 1,
            'infty_constraints': False}

        run_test(test4_1, n=1024, test_atol=1e-5, options=options,
                 sampling_method='sobol')

    def test_4_4_known_f_min(self):
        """Test Global mode limiting local evalutions for 1-D functions"""
        options = {  # Specify known function value
            'f_min': test2_1.expected_fun,
            'f_tol': 1e-6,
            # Specify number of local iterations to perform+
            'minimize_every_iter': True,
            'local_iter': 1,
            'infty_constraints': False}

        res = shgo(test2_1.f, test2_1.bounds, constraints=test2_1.cons,
                   n=None, iters=None, options=options,
                   sampling_method='sobol')
        numpy.testing.assert_allclose(res.x, test2_1.expected_x, rtol=1e-5,
                                      atol=1e-5)

    def test_5_1_simplicial_argless(self):
        """Test Default simplicial sampling settings on TestFunction 1"""
        res = shgo(test1_1.f, test1_1.bounds, constraints=test1_1.cons)
        numpy.testing.assert_allclose(res.x, test1_1.expected_x, rtol=1e-5,
                                      atol=1e-5)

    def test_5_2_sobol_argless(self):
        """Test Default sobol sampling settings on TestFunction 1"""
        res = shgo(test1_1.f, test1_1.bounds, constraints=test1_1.cons,
                   sampling_method='sobol')
        numpy.testing.assert_allclose(res.x, test1_1.expected_x, rtol=1e-5,
                                      atol=1e-5)

    def test_6_1_simplicial_max_iter(self):
        """Test that maximum iteration option works on TestFunction 3"""
        options = {'max_iter': 2}
        res = shgo(test3_1.f, test3_1.bounds, constraints=test3_1.cons,
                   options=options, sampling_method='simplicial')
        numpy.testing.assert_allclose(res.x, test3_1.expected_x, rtol=1e-5,
                                      atol=1e-5)
        numpy.testing.assert_allclose(res.fun, test3_1.expected_fun, atol=1e-5)

    def test_6_2_simplicial_min_iter(self):
        """Test that maximum iteration option works on TestFunction 3"""
        options = {'min_iter': 2}
        res = shgo(test3_1.f, test3_1.bounds, constraints=test3_1.cons,
                   options=options, sampling_method='simplicial')
        numpy.testing.assert_allclose(res.x, test3_1.expected_x, rtol=1e-5,
                                      atol=1e-5)
        numpy.testing.assert_allclose(res.fun, test3_1.expected_fun, atol=1e-5)

    def test_7_1_minkwargs(self):
        """Test the minimizer_kwargs arguments for solvers with constraints"""
        # Test solvers
        for solver in ['COBYLA', 'SLSQP']:
            # Note that passing global constraints to SLSQP is tested in other
            # unittests which run test4_1 normally
            minimizer_kwargs = {'method': solver,
                                'constraints': test3_1.cons}
            print("Solver = {}".format(solver))
            print("=" * 100)
            run_test(test3_1, n=128, test_atol=1e-3,
                     minimizer_kwargs=minimizer_kwargs, sampling_method='sobol')

    def test_7_2_minkwargs(self):
        """Test the minimizer_kwargs default inits"""
        minimizer_kwargs = {'ftol': 1e-5}
        options = {'disp': True}  # For coverage purposes
        SHGO(test3_1.f, test3_1.bounds, constraints=test3_1.cons[0],
             minimizer_kwargs=minimizer_kwargs, options=options)

    def test_7_3_minkwargs(self):
        """Test minimizer_kwargs arguments for solvers without constraints"""
        for solver in ['Nelder-Mead', 'Powell', 'CG', 'BFGS', 'Newton-CG',
                       'L-BFGS-B', 'TNC', 'dogleg', 'trust-ncg', 'trust-exact',
                       'trust-krylov']:
            def jac(x):
                return numpy.array([2 * x[0], 2 * x[1]]).T

            def hess(x):
                return numpy.array([[2, 0], [0, 2]])

            minimizer_kwargs = {'method': solver,
                                'jac': jac,
                                'hess': hess}
            logging.info("Solver = {}".format(solver))
            logging.info("=" * 100)
            run_test(test1_1, n=128, test_atol=1e-3,
                     minimizer_kwargs=minimizer_kwargs, sampling_method='sobol')

    def test_8_homology_group_diff(self):
        options = {'minhgrd': 1,
                   'minimize_every_iter': True}

        run_test(test1_1, n=None, iters=None, options=options,
                 sampling_method='simplicial')

    def test_9_cons_g(self):
        """Test single function constraint passing"""
        SHGO(test3_1.f, test3_1.bounds, constraints=test3_1.cons[0])

    def test_10_finite_time(self):
        """Test single function constraint passing"""
        options = {'maxtime': 1e-15}
        shgo(test1_1.f, test1_1.bounds, n=1, iters=None,
             options=options, sampling_method='sobol')

    def test_11_f_min_time(self):
        """Test to cover the case where f_lowest == 0"""
        options = {'maxtime': 1e-15,
                   'f_min': 0.0}
        shgo(test1_2.f, test1_2.bounds, n=1, iters=None,
             options=options, sampling_method='sobol')

    def test_12_sobol_inf_cons(self):
        """Test to cover the case where f_lowest == 0"""
        options = {'maxtime': 1e-15,
                   'f_min': 0.0}
        shgo(test1_2.f, test1_2.bounds, n=1, iters=None,
             options=options, sampling_method='sobol')

    def test_14_local_iter(self):
        """Test limited local iterations for a pseudo-global mode"""
        options = {'local_iter': 4}
        run_test(test5_1, n=64, options=options)

    def test_15_min_every_iter(self):
        """Test minimize every iter options and cover function cache"""
        options = {'minimize_every_iter': True}
        run_test(test1_1, n=1, iters=7, options=options,
                 sampling_method='sobol')

    def test_16_disp_bounds_minimizer(self):
        """Test disp=True with minimizers that do not support bounds """
        options = {'disp': True}
        minimizer_kwargs = {'method': 'nelder-mead'}
        run_test(test1_2, sampling_method='simplicial',
                 options=options, minimizer_kwargs=minimizer_kwargs)

    def test_17_custom_sampling(self):
        """Test the functionality to add custom sampling methods to shgo"""
        def sample(n, d):
            return numpy.random.uniform(size=(n,d))

        run_test(test1_1, n=30, sampling_method=sample)

    def test_18_bounds_class(self):
        # test that new and old bounds yield same result
        def f(x):
            return numpy.square(x).sum()

        lb = [-6., 1., -5.]
        ub = [-1., 3., 5.]
        bounds_old = list(zip(lb, ub))
        bounds_new = Bounds(lb, ub)

        res_old_bounds = shgo(f, bounds_old)
        res_new_bounds = shgo(f, bounds_new)

        assert res_new_bounds.nfev == res_old_bounds.nfev
        assert res_new_bounds.message == res_old_bounds.message
        assert res_new_bounds.success == res_old_bounds.success
        x_opt = numpy.array([-1., 1., 0.])
        numpy.testing.assert_allclose(res_new_bounds.x, x_opt)
        numpy.testing.assert_allclose(res_new_bounds.x,
                                      res_old_bounds.x)


# Failure test functions
class TestShgoFailures:
    def test_1_maxiter(self):
        """Test failure on insufficient iterations"""
        options = {'maxiter': 2}
        res = shgo(test4_1.f, test4_1.bounds, n=4, iters=None,
                   options=options, sampling_method='sobol')

        numpy.testing.assert_equal(False, res.success)
        numpy.testing.assert_equal(4, res.nfev)

    def test_2_sampling(self):
        """Rejection of unknown sampling method"""
        assert_raises(ValueError, shgo, test1_1.f, test1_1.bounds,
                      sampling_method='not_Sobol')

    def test_3_1_no_min_pool_sobol(self):
        """Check that the routine stops when no minimiser is found
           after maximum specified function evaluations"""
        options = {'maxfev': 10,
                   'disp': True}
        res = shgo(test_table.f, test_table.bounds, n=4, options=options,
                   sampling_method='sobol')
        numpy.testing.assert_equal(False, res.success)

        numpy.testing.assert_equal(16, res.nfev)

    def test_3_2_no_min_pool_simplicial(self):
        """Check that the routine stops when no minimiser is found
           after maximum specified sampling evaluations"""
        options = {'maxev': 10,
                   'disp': True}
        res = shgo(test_table.f, test_table.bounds, n=3, options=options,
                   sampling_method='simplicial')
        numpy.testing.assert_equal(False, res.success)

    def test_4_1_bound_err(self):
        """Specified bounds ub > lb"""
        bounds = [(6, 3), (3, 5)]
        assert_raises(ValueError, shgo, test1_1.f, bounds)

    def test_4_2_bound_err(self):
        """Specified bounds are of the form (lb, ub)"""
        bounds = [(3, 5, 5), (3, 5)]
        assert_raises(ValueError, shgo, test1_1.f, bounds)

    def test_5_1_1_infeasible_sobol(self):
        """Ensures the algorithm terminates on infeasible problems
           after maxev is exceeded. Use infty constraints option"""
        options = {'maxev': 64,
                   'disp': True}

        res = shgo(test_infeasible.f, test_infeasible.bounds,
                   constraints=test_infeasible.cons, n=64, options=options,
                   sampling_method='sobol')

        numpy.testing.assert_equal(False, res.success)

    def test_5_1_2_infeasible_sobol(self):
        """Ensures the algorithm terminates on infeasible problems
           after maxev is exceeded. Do not use infty constraints option"""
        options = {'maxev': 64,
                   'disp': True,
                   'infty_constraints': False}

        res = shgo(test_infeasible.f, test_infeasible.bounds,
                   constraints=test_infeasible.cons, n=64, options=options,
                   sampling_method='sobol')

        numpy.testing.assert_equal(False, res.success)

    def test_5_2_infeasible_simplicial(self):
        """Ensures the algorithm terminates on infeasible problems
           after maxev is exceeded."""
        options = {'maxev': 1000,
                   'disp': False}

        res = shgo(test_infeasible.f, test_infeasible.bounds,
                   constraints=test_infeasible.cons, n=100, options=options,
                   sampling_method='simplicial')

        numpy.testing.assert_equal(False, res.success)

    def test_6_1_lower_known_f_min(self):
        """Test Global mode limiting local evalutions with f* too high"""
        options = {  # Specify known function value
            'f_min': test2_1.expected_fun + 2.0,
            'f_tol': 1e-6,
            # Specify number of local iterations to perform+
            'minimize_every_iter': True,
            'local_iter': 1,
            'infty_constraints': False}
        args = (test2_1.f, test2_1.bounds)
        kwargs = {'constraints': test2_1.cons,
                  'n': None,
                  'iters': None,
                  'options': options,
                  'sampling_method': 'sobol'
                  }
        warns(UserWarning, shgo, *args, **kwargs)

    @pytest.mark.parametrize('derivative', ['jac', 'hess', 'hessp'])
    def test_21_2_derivative_options(self, derivative):
        """shgo used to raise an error when passing `options` with 'jac'
        # see gh-12829. check that this is resolved
        """
        def objective(x):
            return 3 * x[0] * x[0] + 2 * x[0] + 5

        def gradient(x):
            return 6 * x[0] + 2

        def hess(x):
            return 6

        def hessp(x, p):
            return 6 * p

        derivative_funcs = {'jac': gradient, 'hess': hess, 'hessp': hessp}
        options = {derivative: derivative_funcs[derivative]}
        minimizer_kwargs = {'method': 'trust-constr'}

        bounds = [(-100, 100)]
        res = shgo(objective, bounds, minimizer_kwargs=minimizer_kwargs,
                   options=options)
        ref = minimize(objective, x0=[0], bounds=bounds, **minimizer_kwargs,
                       **options)

        assert res.success
        numpy.testing.assert_allclose(res.fun, ref.fun)
        numpy.testing.assert_allclose(res.x, ref.x)