def test_alpha_beta_rc():
assert Version('1.8.0rc1') == Version('1.8.0rc1')
for ver in ['1.8.0', '1.8.0rc2']:
assert Version('1.8.0rc1') < Version(ver)
for ver in ['1.8.0a2', '1.8.0b3', '1.7.2rc4']:
assert Version('1.8.0rc1') > Version(ver)
assert Version('1.8.0b1') > Version('1.8.0a2')
def test_main_versions():
assert Version('1.8.0') == Version('1.8.0')
for ver in ['1.9.0', '2.0.0', '1.8.1']:
assert Version('1.8.0') < Version(ver)
for ver in ['1.7.0', '1.7.1', '0.9.9']:
assert Version('1.8.0') > Version(ver)
def test_dev0_version():
dev0_version = '1.9.0.dev0+f16acvda'
assert Version('1.9.0.dev0+Unknown') < Version('1.9.0')
for ver in ['1.9.0', '1.9.0a1', '1.9.0b2', '1.9.0b2.dev0+ffffffff']:
assert Version(dev0_version) < Version(ver)
assert Version(dev0_version) == Version(dev0_version)
def test_dev_version():
assert Version('1.9.0.dev+Unknown') < Version('1.9.0')
for ver in [
'1.9.0', '1.9.0a1', '1.9.0b2', '1.9.0b2.dev+ffffffff', '1.9.0.dev1'
]:
assert Version('1.9.0.dev+f16acvda') < Version(ver)
assert Version('1.9.0.dev+f16acvda') == Version('1.9.0.dev+f16acvda')
class TestDifferentialEvolutionSolver(object):
def setup_method(self):
self.old_seterr = np.seterr(invalid='raise')
self.limits = np.array([[0., 0.],
[2., 2.]])
self.bounds = [(0., 2.), (0., 2.)]
self.dummy_solver = DifferentialEvolutionSolver(self.quadratic,
[(0, 100)])
# dummy_solver2 will be used to test mutation strategies
self.dummy_solver2 = DifferentialEvolutionSolver(self.quadratic,
[(0, 1)],
popsize=7,
mutation=0.5)
# create a population that's only 7 members long
# [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7]
population = np.atleast_2d(np.arange(0.1, 0.8, 0.1)).T
self.dummy_solver2.population = population
def teardown_method(self):
np.seterr(**self.old_seterr)
def quadratic(self, x):
return x[0]**2
def test__strategy_resolves(self):
# test that the correct mutation function is resolved by
# different requested strategy arguments
solver = DifferentialEvolutionSolver(rosen,
self.bounds,
strategy='best1exp')
assert_equal(solver.strategy, 'best1exp')
assert_equal(solver.mutation_func.__name__, '_best1')
solver = DifferentialEvolutionSolver(rosen,
self.bounds,
strategy='best1bin')
assert_equal(solver.strategy, 'best1bin')
assert_equal(solver.mutation_func.__name__, '_best1')
solver = DifferentialEvolutionSolver(rosen,
self.bounds,
strategy='rand1bin')
assert_equal(solver.strategy, 'rand1bin')
assert_equal(solver.mutation_func.__name__, '_rand1')
solver = DifferentialEvolutionSolver(rosen,
self.bounds,
strategy='rand1exp')
assert_equal(solver.strategy, 'rand1exp')
assert_equal(solver.mutation_func.__name__, '_rand1')
solver = DifferentialEvolutionSolver(rosen,
self.bounds,
strategy='rand2exp')
assert_equal(solver.strategy, 'rand2exp')
assert_equal(solver.mutation_func.__name__, '_rand2')
solver = DifferentialEvolutionSolver(rosen,
self.bounds,
strategy='best2bin')
assert_equal(solver.strategy, 'best2bin')
assert_equal(solver.mutation_func.__name__, '_best2')
solver = DifferentialEvolutionSolver(rosen,
self.bounds,
strategy='rand2bin')
assert_equal(solver.strategy, 'rand2bin')
assert_equal(solver.mutation_func.__name__, '_rand2')
solver = DifferentialEvolutionSolver(rosen,
self.bounds,
strategy='rand2exp')
assert_equal(solver.strategy, 'rand2exp')
assert_equal(solver.mutation_func.__name__, '_rand2')
solver = DifferentialEvolutionSolver(rosen,
self.bounds,
strategy='randtobest1bin')
assert_equal(solver.strategy, 'randtobest1bin')
assert_equal(solver.mutation_func.__name__, '_randtobest1')
solver = DifferentialEvolutionSolver(rosen,
self.bounds,
strategy='randtobest1exp')
assert_equal(solver.strategy, 'randtobest1exp')
assert_equal(solver.mutation_func.__name__, '_randtobest1')
solver = DifferentialEvolutionSolver(rosen,
self.bounds,
strategy='currenttobest1bin')
assert_equal(solver.strategy, 'currenttobest1bin')
assert_equal(solver.mutation_func.__name__, '_currenttobest1')
solver = DifferentialEvolutionSolver(rosen,
self.bounds,
strategy='currenttobest1exp')
assert_equal(solver.strategy, 'currenttobest1exp')
assert_equal(solver.mutation_func.__name__, '_currenttobest1')
def test__mutate1(self):
# strategies */1/*, i.e. rand/1/bin, best/1/exp, etc.
result = np.array([0.05])
trial = self.dummy_solver2._best1((2, 3, 4, 5, 6))
assert_allclose(trial, result)
result = np.array([0.25])
trial = self.dummy_solver2._rand1((2, 3, 4, 5, 6))
assert_allclose(trial, result)
def test__mutate2(self):
# strategies */2/*, i.e. rand/2/bin, best/2/exp, etc.
# [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7]
result = np.array([-0.1])
trial = self.dummy_solver2._best2((2, 3, 4, 5, 6))
assert_allclose(trial, result)
result = np.array([0.1])
trial = self.dummy_solver2._rand2((2, 3, 4, 5, 6))
assert_allclose(trial, result)
def test__randtobest1(self):
# strategies randtobest/1/*
result = np.array([0.15])
trial = self.dummy_solver2._randtobest1((2, 3, 4, 5, 6))
assert_allclose(trial, result)
def test__currenttobest1(self):
# strategies currenttobest/1/*
result = np.array([0.1])
trial = self.dummy_solver2._currenttobest1(1, (2, 3, 4, 5, 6))
assert_allclose(trial, result)
def test_can_init_with_dithering(self):
mutation = (0.5, 1)
solver = DifferentialEvolutionSolver(self.quadratic,
self.bounds,
mutation=mutation)
assert_equal(solver.dither, list(mutation))
def test_invalid_mutation_values_arent_accepted(self):
func = rosen
mutation = (0.5, 3)
assert_raises(ValueError,
DifferentialEvolutionSolver,
func,
self.bounds,
mutation=mutation)
mutation = (-1, 1)
assert_raises(ValueError,
DifferentialEvolutionSolver,
func,
self.bounds,
mutation=mutation)
mutation = (0.1, np.nan)
assert_raises(ValueError,
DifferentialEvolutionSolver,
func,
self.bounds,
mutation=mutation)
mutation = 0.5
solver = DifferentialEvolutionSolver(func,
self.bounds,
mutation=mutation)
assert_equal(0.5, solver.scale)
assert_equal(None, solver.dither)
def test__scale_parameters(self):
trial = np.array([0.3])
assert_equal(30, self.dummy_solver._scale_parameters(trial))
# it should also work with the limits reversed
self.dummy_solver.limits = np.array([[100], [0.]])
assert_equal(30, self.dummy_solver._scale_parameters(trial))
def test__unscale_parameters(self):
trial = np.array([30])
assert_equal(0.3, self.dummy_solver._unscale_parameters(trial))
# it should also work with the limits reversed
self.dummy_solver.limits = np.array([[100], [0.]])
assert_equal(0.3, self.dummy_solver._unscale_parameters(trial))
def test__ensure_constraint(self):
trial = np.array([1.1, -100, 0.9, 2., 300., -0.00001])
self.dummy_solver._ensure_constraint(trial)
assert_equal(trial[2], 0.9)
assert_(np.logical_and(trial >= 0, trial <= 1).all())
def test_differential_evolution(self):
# test that the Jmin of DifferentialEvolutionSolver
# is the same as the function evaluation
solver = DifferentialEvolutionSolver(self.quadratic, [(-2, 2)])
result = solver.solve()
assert_almost_equal(result.fun, self.quadratic(result.x))
def test_best_solution_retrieval(self):
# test that the getter property method for the best solution works.
solver = DifferentialEvolutionSolver(self.quadratic, [(-2, 2)])
result = solver.solve()
assert_almost_equal(result.x, solver.x)
def test_callback_terminates(self):
# test that if the callback returns true, then the minimization halts
bounds = [(0, 2), (0, 2)]
def callback(param, convergence=0.):
return True
result = differential_evolution(rosen, bounds, callback=callback)
assert_string_equal(result.message,
'callback function requested stop early '
'by returning True')
def test_args_tuple_is_passed(self):
# test that the args tuple is passed to the cost function properly.
bounds = [(-10, 10)]
args = (1., 2., 3.)
def quadratic(x, *args):
if type(args) != tuple:
raise ValueError('args should be a tuple')
return args[0] + args[1] * x + args[2] * x**2.
result = differential_evolution(quadratic,
bounds,
args=args,
polish=True)
assert_almost_equal(result.fun, 2 / 3.)
def test_init_with_invalid_strategy(self):
# test that passing an invalid strategy raises ValueError
func = rosen
bounds = [(-3, 3)]
assert_raises(ValueError,
differential_evolution,
func,
bounds,
strategy='abc')
def test_bounds_checking(self):
# test that the bounds checking works
func = rosen
bounds = [(-3)]
assert_raises(ValueError,
differential_evolution,
func,
bounds)
bounds = [(-3, 3), (3, 4, 5)]
assert_raises(ValueError,
differential_evolution,
func,
bounds)
# test that we can use a new-type Bounds object
result = differential_evolution(rosen, Bounds([0, 0], [2, 2]))
assert_almost_equal(result.x, (1., 1.))
def test_select_samples(self):
# select_samples should return 5 separate random numbers.
limits = np.arange(12., dtype='float64').reshape(2, 6)
bounds = list(zip(limits[0, :], limits[1, :]))
solver = DifferentialEvolutionSolver(None, bounds, popsize=1)
candidate = 0
r1, r2, r3, r4, r5 = solver._select_samples(candidate, 5)
assert_equal(
len(np.unique(np.array([candidate, r1, r2, r3, r4, r5]))), 6)
def test_maxiter_stops_solve(self):
# test that if the maximum number of iterations is exceeded
# the solver stops.
solver = DifferentialEvolutionSolver(rosen, self.bounds, maxiter=1)
result = solver.solve()
assert_equal(result.success, False)
assert_equal(result.message,
'Maximum number of iterations has been exceeded.')
def test_maxfun_stops_solve(self):
# test that if the maximum number of function evaluations is exceeded
# during initialisation the solver stops
solver = DifferentialEvolutionSolver(rosen, self.bounds, maxfun=1,
polish=False)
result = solver.solve()
assert_equal(result.nfev, 2)
assert_equal(result.success, False)
assert_equal(result.message,
'Maximum number of function evaluations has '
'been exceeded.')
# test that if the maximum number of function evaluations is exceeded
# during the actual minimisation, then the solver stops.
# Have to turn polishing off, as this will still occur even if maxfun
# is reached. For popsize=5 and len(bounds)=2, then there are only 10
# function evaluations during initialisation.
solver = DifferentialEvolutionSolver(rosen,
self.bounds,
popsize=5,
polish=False,
maxfun=40)
result = solver.solve()
assert_equal(result.nfev, 41)
assert_equal(result.success, False)
assert_equal(result.message,
'Maximum number of function evaluations has '
'been exceeded.')
# now repeat for updating='deferred version
solver = DifferentialEvolutionSolver(rosen,
self.bounds,
popsize=5,
polish=False,
maxfun=40,
updating='deferred')
result = solver.solve()
assert_equal(result.nfev, 40)
assert_equal(result.success, False)
assert_equal(result.message,
'Maximum number of function evaluations has '
'been reached.')
def test_quadratic(self):
# test the quadratic function from object
solver = DifferentialEvolutionSolver(self.quadratic,
[(-100, 100)],
tol=0.02)
solver.solve()
assert_equal(np.argmin(solver.population_energies), 0)
def test_quadratic_from_diff_ev(self):
# test the quadratic function from differential_evolution function
differential_evolution(self.quadratic,
[(-100, 100)],
tol=0.02)
def test_seed_gives_repeatability(self):
result = differential_evolution(self.quadratic,
[(-100, 100)],
polish=False,
seed=1,
tol=0.5)
result2 = differential_evolution(self.quadratic,
[(-100, 100)],
polish=False,
seed=1,
tol=0.5)
assert_equal(result.x, result2.x)
assert_equal(result.nfev, result2.nfev)
@pytest.mark.skipif(Version(np.__version__) < Version('1.17'),
reason='Generator not available for numpy, < 1.17')
def test_random_generator(self):
# check that np.random.Generator can be used (numpy >= 1.17)
# obtain a np.random.Generator object
rng = np.random.default_rng()
inits = ['random', 'latinhypercube']
for init in inits:
differential_evolution(self.quadratic,
[(-100, 100)],
polish=False,
seed=rng,
tol=0.5,
init=init)
def test_exp_runs(self):
# test whether exponential mutation loop runs
solver = DifferentialEvolutionSolver(rosen,
self.bounds,
strategy='best1exp',
maxiter=1)
solver.solve()
def test_gh_4511_regression(self):
# This modification of the differential evolution docstring example
# uses a custom popsize that had triggered an off-by-one error.
# Because we do not care about solving the optimization problem in
# this test, we use maxiter=1 to reduce the testing time.
bounds = [(-5, 5), (-5, 5)]
# result = differential_evolution(rosen, bounds, popsize=1815,
# maxiter=1)
# the original issue arose because of rounding error in arange, with
# linspace being a much better solution. 1815 is quite a large popsize
# to use and results in a long test time (~13s). I used the original
# issue to figure out the lowest number of samples that would cause
# this rounding error to occur, 49.
differential_evolution(rosen, bounds, popsize=49, maxiter=1)
def test_calculate_population_energies(self):
# if popsize is 3, then the overall generation has size (6,)
solver = DifferentialEvolutionSolver(rosen, self.bounds, popsize=3)
solver._calculate_population_energies(solver.population)
solver._promote_lowest_energy()
assert_equal(np.argmin(solver.population_energies), 0)
# initial calculation of the energies should require 6 nfev.
assert_equal(solver._nfev, 6)
def test_iteration(self):
# test that DifferentialEvolutionSolver is iterable
# if popsize is 3, then the overall generation has size (6,)
solver = DifferentialEvolutionSolver(rosen, self.bounds, popsize=3,
maxfun=12)
x, fun = next(solver)
assert_equal(np.size(x, 0), 2)
# 6 nfev are required for initial calculation of energies, 6 nfev are
# required for the evolution of the 6 population members.
assert_equal(solver._nfev, 12)
# the next generation should halt because it exceeds maxfun
assert_raises(StopIteration, next, solver)
# check a proper minimisation can be done by an iterable solver
solver = DifferentialEvolutionSolver(rosen, self.bounds)
_, fun_prev = next(solver)
for i, soln in enumerate(solver):
x_current, fun_current = soln
assert(fun_prev >= fun_current)
_, fun_prev = x_current, fun_current
# need to have this otherwise the solver would never stop.
if i == 50:
break
def test_convergence(self):
solver = DifferentialEvolutionSolver(rosen, self.bounds, tol=0.2,
polish=False)
solver.solve()
assert_(solver.convergence < 0.2)
def test_maxiter_none_GH5731(self):
# Pre 0.17 the previous default for maxiter and maxfun was None.
# the numerical defaults are now 1000 and np.inf. However, some scripts
# will still supply None for both of those, this will raise a TypeError
# in the solve method.
solver = DifferentialEvolutionSolver(rosen, self.bounds, maxiter=None,
maxfun=None)
solver.solve()
def test_population_initiation(self):
# test the different modes of population initiation
# init must be either 'latinhypercube' or 'random'
# raising ValueError is something else is passed in
assert_raises(ValueError,
DifferentialEvolutionSolver,
*(rosen, self.bounds),
**{'init': 'rubbish'})
solver = DifferentialEvolutionSolver(rosen, self.bounds)
# check that population initiation:
# 1) resets _nfev to 0
# 2) all population energies are np.inf
solver.init_population_random()
assert_equal(solver._nfev, 0)
assert_(np.all(np.isinf(solver.population_energies)))
solver.init_population_lhs()
assert_equal(solver._nfev, 0)
assert_(np.all(np.isinf(solver.population_energies)))
# we should be able to initialize with our own array
population = np.linspace(-1, 3, 10).reshape(5, 2)
solver = DifferentialEvolutionSolver(rosen, self.bounds,
init=population,
strategy='best2bin',
atol=0.01, seed=1, popsize=5)
assert_equal(solver._nfev, 0)
assert_(np.all(np.isinf(solver.population_energies)))
assert_(solver.num_population_members == 5)
assert_(solver.population_shape == (5, 2))
# check that the population was initialized correctly
unscaled_population = np.clip(solver._unscale_parameters(population),
0, 1)
assert_almost_equal(solver.population[:5], unscaled_population)
# population values need to be clipped to bounds
assert_almost_equal(np.min(solver.population[:5]), 0)
assert_almost_equal(np.max(solver.population[:5]), 1)
# shouldn't be able to initialize with an array if it's the wrong shape
# this would have too many parameters
population = np.linspace(-1, 3, 15).reshape(5, 3)
assert_raises(ValueError,
DifferentialEvolutionSolver,
*(rosen, self.bounds),
**{'init': population})
def test_infinite_objective_function(self):
# Test that there are no problems if the objective function
# returns inf on some runs
def sometimes_inf(x):
if x[0] < .5:
return np.inf
return x[1]
bounds = [(0, 1), (0, 1)]
differential_evolution(sometimes_inf, bounds=bounds, disp=False)
def test_deferred_updating(self):
# check setting of deferred updating, with default workers
bounds = [(0., 2.), (0., 2.)]
solver = DifferentialEvolutionSolver(rosen, bounds, updating='deferred')
assert_(solver._updating == 'deferred')
assert_(solver._mapwrapper._mapfunc is map)
solver.solve()
@knownfail_on_py38
def test_immediate_updating(self):
# check setting of immediate updating, with default workers
bounds = [(0., 2.), (0., 2.)]
solver = DifferentialEvolutionSolver(rosen, bounds)
assert_(solver._updating == 'immediate')
# should raise a UserWarning because the updating='immediate'
# is being overridden by the workers keyword
with warns(UserWarning):
solver = DifferentialEvolutionSolver(rosen, bounds, workers=2)
assert_(solver._updating == 'deferred')
del solver
gc.collect() # ensure MapWrapper cleans up properly
@knownfail_on_py38
def test_parallel(self):
# smoke test for parallelization with deferred updating
bounds = [(0., 2.), (0., 2.)]
with multiprocessing.Pool(2) as p, DifferentialEvolutionSolver(
rosen, bounds, updating='deferred', workers=p.map) as solver:
assert_(solver._mapwrapper.pool is not None)
assert_(solver._updating == 'deferred')
solver.solve()
with DifferentialEvolutionSolver(rosen, bounds, updating='deferred',
workers=2) as solver:
assert_(solver._mapwrapper.pool is not None)
assert_(solver._updating == 'deferred')
solver.solve()
del solver
gc.collect() # ensure MapWrapper cleans up properly
def test_converged(self):
solver = DifferentialEvolutionSolver(rosen, [(0, 2), (0, 2)])
solver.solve()
assert_(solver.converged())
def test_constraint_violation_fn(self):
def constr_f(x):
return [x[0] + x[1]]
def constr_f2(x):
return [x[0]**2 + x[1], x[0] - x[1]]
nlc = NonlinearConstraint(constr_f, -np.inf, 1.9)
solver = DifferentialEvolutionSolver(rosen, [(0, 2), (0, 2)],
constraints=(nlc))
cv = solver._constraint_violation_fn([1.0, 1.0])
assert_almost_equal(cv, 0.1)
nlc2 = NonlinearConstraint(constr_f2, -np.inf, 1.8)
solver = DifferentialEvolutionSolver(rosen, [(0, 2), (0, 2)],
constraints=(nlc, nlc2))
# for multiple constraints the constraint violations should
# be concatenated.
cv = solver._constraint_violation_fn([1.2, 1.])
assert_almost_equal(cv, [0.3, 0.64, 0])
cv = solver._constraint_violation_fn([2., 2.])
assert_almost_equal(cv, [2.1, 4.2, 0])
# should accept valid values
cv = solver._constraint_violation_fn([0.5, 0.5])
assert_almost_equal(cv, [0., 0., 0.])
def test_constraint_population_feasibilities(self):
def constr_f(x):
return [x[0] + x[1]]
def constr_f2(x):
return [x[0]**2 + x[1], x[0] - x[1]]
nlc = NonlinearConstraint(constr_f, -np.inf, 1.9)
solver = DifferentialEvolutionSolver(rosen, [(0, 2), (0, 2)],
constraints=(nlc))
# are population feasibilities correct
# [0.5, 0.5] corresponds to scaled values of [1., 1.]
feas, cv = solver._calculate_population_feasibilities(
np.array([[0.5, 0.5], [1., 1.]]))
assert_equal(feas, [False, False])
assert_almost_equal(cv, np.array([[0.1], [2.1]]))
assert cv.shape == (2, 1)
nlc2 = NonlinearConstraint(constr_f2, -np.inf, 1.8)
solver = DifferentialEvolutionSolver(rosen, [(0, 2), (0, 2)],
constraints=(nlc, nlc2))
feas, cv = solver._calculate_population_feasibilities(
np.array([[0.5, 0.5], [0.6, 0.5]]))
assert_equal(feas, [False, False])
assert_almost_equal(cv, np.array([[0.1, 0.2, 0], [0.3, 0.64, 0]]))
feas, cv = solver._calculate_population_feasibilities(
np.array([[0.5, 0.5], [1., 1.]]))
assert_equal(feas, [False, False])
assert_almost_equal(cv, np.array([[0.1, 0.2, 0], [2.1, 4.2, 0]]))
assert cv.shape == (2, 3)
feas, cv = solver._calculate_population_feasibilities(
np.array([[0.25, 0.25], [1., 1.]]))
assert_equal(feas, [True, False])
assert_almost_equal(cv, np.array([[0.0, 0.0, 0.], [2.1, 4.2, 0]]))
assert cv.shape == (2, 3)
def test_constraint_solve(self):
def constr_f(x):
return np.array([x[0] + x[1]])
nlc = NonlinearConstraint(constr_f, -np.inf, 1.9)
solver = DifferentialEvolutionSolver(rosen, [(0, 2), (0, 2)],
constraints=(nlc))
# trust-constr warns if the constraint function is linear
with warns(UserWarning):
res = solver.solve()
assert constr_f(res.x) <= 1.9
assert res.success
def test_impossible_constraint(self):
def constr_f(x):
return np.array([x[0] + x[1]])
nlc = NonlinearConstraint(constr_f, -np.inf, -1)
solver = DifferentialEvolutionSolver(rosen, [(0, 2), (0, 2)],
constraints=(nlc), popsize=3,
seed=1)
# a UserWarning is issued because the 'trust-constr' polishing is
# attempted on the least infeasible solution found.
with warns(UserWarning):
res = solver.solve()
assert res.maxcv > 0
assert not res.success
# test _promote_lowest_energy works when none of the population is
# feasible. In this case, the solution with the lowest constraint
# violation should be promoted.
solver = DifferentialEvolutionSolver(rosen, [(0, 2), (0, 2)],
constraints=(nlc), polish=False)
next(solver)
assert not solver.feasible.all()
assert not np.isfinite(solver.population_energies).all()
# now swap two of the entries in the population
l = 20
cv = solver.constraint_violation[0]
solver.population_energies[[0, l]] = solver.population_energies[[l, 0]]
solver.population[[0, l], :] = solver.population[[l, 0], :]
solver.constraint_violation[[0, l], :] = (
solver.constraint_violation[[l, 0], :])
solver._promote_lowest_energy()
assert_equal(solver.constraint_violation[0], cv)
def test_accept_trial(self):
# _accept_trial(self, energy_trial, feasible_trial, cv_trial,
# energy_orig, feasible_orig, cv_orig)
def constr_f(x):
return [x[0] + x[1]]
nlc = NonlinearConstraint(constr_f, -np.inf, 1.9)
solver = DifferentialEvolutionSolver(rosen, [(0, 2), (0, 2)],
constraints=(nlc))
fn = solver._accept_trial
# both solutions are feasible, select lower energy
assert fn(0.1, True, np.array([0.]), 1.0, True, np.array([0.]))
assert (fn(1.0, True, np.array([0.]), 0.1, True, np.array([0.]))
== False)
assert fn(0.1, True, np.array([0.]), 0.1, True, np.array([0.]))
# trial is feasible, original is not
assert fn(9.9, True, np.array([0.]), 1.0, False, np.array([1.]))
# trial and original are infeasible
# cv_trial have to be <= cv_original to be better
assert (fn(0.1, False, np.array([0.5, 0.5]),
1.0, False, np.array([1., 1.0])))
assert (fn(0.1, False, np.array([0.5, 0.5]),
1.0, False, np.array([1., 0.50])))
assert (fn(1.0, False, np.array([0.5, 0.5]),
1.0, False, np.array([1., 0.4])) == False)
def test_constraint_wrapper(self):
lb = np.array([0, 20, 30])
ub = np.array([0.5, np.inf, 70])
x0 = np.array([1, 2, 3])
pc = _ConstraintWrapper(Bounds(lb, ub), x0)
assert (pc.violation(x0) > 0).any()
assert (pc.violation([0.25, 21, 31]) == 0).all()
x0 = np.array([1, 2, 3, 4])
A = np.array([[1, 2, 3, 4], [5, 0, 0, 6], [7, 0, 8, 0]])
pc = _ConstraintWrapper(LinearConstraint(A, -np.inf, 0), x0)
assert (pc.violation(x0) > 0).any()
assert (pc.violation([-10, 2, -10, 4]) == 0).all()
def fun(x):
return A.dot(x)
nonlinear = NonlinearConstraint(fun, -np.inf, 0)
pc = _ConstraintWrapper(nonlinear, [-10, 2, -10, 4])
assert (pc.violation(x0) > 0).any()
assert (pc.violation([-10, 2, -10, 4]) == 0).all()
def test_constraint_wrapper_violation(self):
def cons_f(x):
return np.array([x[0] ** 2 + x[1], x[0] ** 2 - x[1]])
nlc = NonlinearConstraint(cons_f, [-1, -0.8500], [2, 2])
pc = _ConstraintWrapper(nlc, [0.5, 1])
assert np.size(pc.bounds[0]) == 2
assert_array_equal(pc.violation([0.5, 1]), [0., 0.])
assert_almost_equal(pc.violation([0.5, 1.2]), [0., 0.1])
assert_almost_equal(pc.violation([1.2, 1.2]), [0.64, 0])
assert_almost_equal(pc.violation([0.1, -1.2]), [0.19, 0])
assert_almost_equal(pc.violation([0.1, 2]), [0.01, 1.14])
def test_L1(self):
# Lampinen ([5]) test problem 1
def f(x):
x = np.hstack(([0], x)) # 1-indexed to match reference
fun = np.sum(5*x[1:5]) - 5*x[1:5]@x[1:5] - np.sum(x[5:])
return fun
A = np.zeros((10, 14)) # 1-indexed to match reference
A[1, [1, 2, 10, 11]] = 2, 2, 1, 1
A[2, [1, 10]] = -8, 1
A[3, [4, 5, 10]] = -2, -1, 1
A[4, [1, 3, 10, 11]] = 2, 2, 1, 1
A[5, [2, 11]] = -8, 1
A[6, [6, 7, 11]] = -2, -1, 1
A[7, [2, 3, 11, 12]] = 2, 2, 1, 1
A[8, [3, 12]] = -8, 1
A[9, [8, 9, 12]] = -2, -1, 1
A = A[1:, 1:]
b = np.array([10, 0, 0, 10, 0, 0, 10, 0, 0])
L = LinearConstraint(A, -np.inf, b)
bounds = [(0, 1)]*9 + [(0, 100)]*3 + [(0, 1)]
# using a lower popsize to speed the test up
res = differential_evolution(f, bounds, strategy='best1bin', seed=1234,
constraints=(L), popsize=2)
x_opt = (1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 1)
f_opt = -15
assert_allclose(f(x_opt), f_opt)
assert res.success
assert_allclose(res.x, x_opt, atol=5e-4)
assert_allclose(res.fun, f_opt, atol=5e-3)
assert_(np.all([email protected] <= b))
assert_(np.all(res.x >= np.array(bounds)[:, 0]))
assert_(np.all(res.x <= np.array(bounds)[:, 1]))
# now repeat the same solve, using the same overall constraints,
# but specify half the constraints in terms of LinearConstraint,
# and the other half by NonlinearConstraint
def c1(x):
x = np.hstack(([0], x))
return [2*x[2] + 2*x[3] + x[11] + x[12],
-8*x[3] + x[12]]
def c2(x):
x = np.hstack(([0], x))
return -2*x[8] - x[9] + x[12]
L = LinearConstraint(A[:5, :], -np.inf, b[:5])
L2 = LinearConstraint(A[5:6, :], -np.inf, b[5:6])
N = NonlinearConstraint(c1, -np.inf, b[6:8])
N2 = NonlinearConstraint(c2, -np.inf, b[8:9])
constraints = (L, N, L2, N2)
with suppress_warnings() as sup:
sup.filter(UserWarning)
res = differential_evolution(f, bounds, strategy='rand1bin',
seed=1234, constraints=constraints,
popsize=2)
assert_allclose(res.x, x_opt, atol=5e-4)
assert_allclose(res.fun, f_opt, atol=5e-3)
assert_(np.all([email protected] <= b))
assert_(np.all(res.x >= np.array(bounds)[:, 0]))
assert_(np.all(res.x <= np.array(bounds)[:, 1]))
def test_L2(self):
# Lampinen ([5]) test problem 2
def f(x):
x = np.hstack(([0], x)) # 1-indexed to match reference
fun = ((x[1]-10)**2 + 5*(x[2]-12)**2 + x[3]**4 + 3*(x[4]-11)**2 +
10*x[5]**6 + 7*x[6]**2 + x[7]**4 - 4*x[6]*x[7] - 10*x[6] -
8*x[7])
return fun
def c1(x):
x = np.hstack(([0], x)) # 1-indexed to match reference
return [127 - 2*x[1]**2 - 3*x[2]**4 - x[3] - 4*x[4]**2 - 5*x[5],
196 - 23*x[1] - x[2]**2 - 6*x[6]**2 + 8*x[7],
282 - 7*x[1] - 3*x[2] - 10*x[3]**2 - x[4] + x[5],
-4*x[1]**2 - x[2]**2 + 3*x[1]*x[2] - 2*x[3]**2 -
5*x[6] + 11*x[7]]
N = NonlinearConstraint(c1, 0, np.inf)
bounds = [(-10, 10)]*7
constraints = (N)
with suppress_warnings() as sup:
sup.filter(UserWarning)
res = differential_evolution(f, bounds, strategy='rand1bin',
seed=1234, constraints=constraints)
f_opt = 680.6300599487869
x_opt = (2.330499, 1.951372, -0.4775414, 4.365726,
-0.6244870, 1.038131, 1.594227)
assert_allclose(f(x_opt), f_opt)
assert_allclose(res.fun, f_opt)
assert_allclose(res.x, x_opt, atol=1e-5)
assert res.success
assert_(np.all(np.array(c1(res.x)) >= 0))
assert_(np.all(res.x >= np.array(bounds)[:, 0]))
assert_(np.all(res.x <= np.array(bounds)[:, 1]))
def test_L3(self):
# Lampinen ([5]) test problem 3
def f(x):
x = np.hstack(([0], x)) # 1-indexed to match reference
fun = (x[1]**2 + x[2]**2 + x[1]*x[2] - 14*x[1] - 16*x[2] +
(x[3]-10)**2 + 4*(x[4]-5)**2 + (x[5]-3)**2 + 2*(x[6]-1)**2 +
5*x[7]**2 + 7*(x[8]-11)**2 + 2*(x[9]-10)**2 +
(x[10] - 7)**2 + 45
)
return fun # maximize
A = np.zeros((4, 11))
A[1, [1, 2, 7, 8]] = -4, -5, 3, -9
A[2, [1, 2, 7, 8]] = -10, 8, 17, -2
A[3, [1, 2, 9, 10]] = 8, -2, -5, 2
A = A[1:, 1:]
b = np.array([-105, 0, -12])
def c1(x):
x = np.hstack(([0], x)) # 1-indexed to match reference
return [3*x[1] - 6*x[2] - 12*(x[9]-8)**2 + 7*x[10],
-3*(x[1]-2)**2 - 4*(x[2]-3)**2 - 2*x[3]**2 + 7*x[4] + 120,
-x[1]**2 - 2*(x[2]-2)**2 + 2*x[1]*x[2] - 14*x[5] + 6*x[6],
-5*x[1]**2 - 8*x[2] - (x[3]-6)**2 + 2*x[4] + 40,
-0.5*(x[1]-8)**2 - 2*(x[2]-4)**2 - 3*x[5]**2 + x[6] + 30]
L = LinearConstraint(A, b, np.inf)
N = NonlinearConstraint(c1, 0, np.inf)
bounds = [(-10, 10)]*10
constraints = (L, N)
with suppress_warnings() as sup:
sup.filter(UserWarning)
res = differential_evolution(f, bounds, seed=1234,
constraints=constraints, popsize=3)
x_opt = (2.171996, 2.363683, 8.773926, 5.095984, 0.9906548,
1.430574, 1.321644, 9.828726, 8.280092, 8.375927)
f_opt = 24.3062091
assert_allclose(f(x_opt), f_opt, atol=1e-5)
assert_allclose(res.x, x_opt, atol=1e-6)
assert_allclose(res.fun, f_opt, atol=1e-5)
assert res.success
assert_(np.all(A @ res.x >= b))
assert_(np.all(np.array(c1(res.x)) >= 0))
assert_(np.all(res.x >= np.array(bounds)[:, 0]))
assert_(np.all(res.x <= np.array(bounds)[:, 1]))
def test_L4(self):
# Lampinen ([5]) test problem 4
def f(x):
return np.sum(x[:3])
A = np.zeros((4, 9))
A[1, [4, 6]] = 0.0025, 0.0025
A[2, [5, 7, 4]] = 0.0025, 0.0025, -0.0025
A[3, [8, 5]] = 0.01, -0.01
A = A[1:, 1:]
b = np.array([1, 1, 1])
def c1(x):
x = np.hstack(([0], x)) # 1-indexed to match reference
return [x[1]*x[6] - 833.33252*x[4] - 100*x[1] + 83333.333,
x[2]*x[7] - 1250*x[5] - x[2]*x[4] + 1250*x[4],
x[3]*x[8] - 1250000 - x[3]*x[5] + 2500*x[5]]
L = LinearConstraint(A, -np.inf, 1)
N = NonlinearConstraint(c1, 0, np.inf)
bounds = [(100, 10000)] + [(1000, 10000)]*2 + [(10, 1000)]*5
constraints = (L, N)
with suppress_warnings() as sup:
sup.filter(UserWarning)
res = differential_evolution(f, bounds, strategy='rand1bin',
seed=1234, constraints=constraints,
popsize=3)
f_opt = 7049.248
x_opt = [579.306692, 1359.97063, 5109.9707, 182.0177, 295.601172,
217.9823, 286.416528, 395.601172]
assert_allclose(f(x_opt), f_opt, atol=0.001)
assert_allclose(res.fun, f_opt, atol=0.001)
assert_allclose(res.x, x_opt, atol=0.002)
assert res.success
assert_(np.all(A @ res.x <= b))
assert_(np.all(np.array(c1(res.x)) >= 0))
assert_(np.all(res.x >= np.array(bounds)[:, 0]))
assert_(np.all(res.x <= np.array(bounds)[:, 1]))
def test_L5(self):
# Lampinen ([5]) test problem 5
def f(x):
x = np.hstack(([0], x)) # 1-indexed to match reference
fun = (np.sin(2*np.pi*x[1])**3*np.sin(2*np.pi*x[2]) /
(x[1]**3*(x[1]+x[2])))
return -fun # maximize
def c1(x):
x = np.hstack(([0], x)) # 1-indexed to match reference
return [x[1]**2 - x[2] + 1,
1 - x[1] + (x[2]-4)**2]
N = NonlinearConstraint(c1, -np.inf, 0)
bounds = [(0, 10)]*2
constraints = (N)
res = differential_evolution(f, bounds, strategy='rand1bin', seed=1234,
constraints=constraints)
x_opt = (1.22797135, 4.24537337)
f_opt = -0.095825
print(res)
assert_allclose(f(x_opt), f_opt, atol=2e-5)
assert_allclose(res.fun, f_opt, atol=1e-4)
assert res.success
assert_(np.all(np.array(c1(res.x)) <= 0))
assert_(np.all(res.x >= np.array(bounds)[:, 0]))
assert_(np.all(res.x <= np.array(bounds)[:, 1]))
def test_L6(self):
# Lampinen ([5]) test problem 6
def f(x):
x = np.hstack(([0], x)) # 1-indexed to match reference
fun = (x[1]-10)**3 + (x[2] - 20)**3
return fun
def c1(x):
x = np.hstack(([0], x)) # 1-indexed to match reference
return [(x[1]-5)**2 + (x[2] - 5)**2 - 100,
-(x[1]-6)**2 - (x[2] - 5)**2 + 82.81]
N = NonlinearConstraint(c1, 0, np.inf)
bounds = [(13, 100), (0, 100)]
constraints = (N)
res = differential_evolution(f, bounds, strategy='rand1bin', seed=1234,
constraints=constraints, tol=1e-7)
x_opt = (14.095, 0.84296)
f_opt = -6961.814744
assert_allclose(f(x_opt), f_opt, atol=1e-6)
assert_allclose(res.fun, f_opt, atol=0.001)
assert_allclose(res.x, x_opt, atol=1e-4)
assert res.success
assert_(np.all(np.array(c1(res.x)) >= 0))
assert_(np.all(res.x >= np.array(bounds)[:, 0]))
assert_(np.all(res.x <= np.array(bounds)[:, 1]))
def test_L7(self):
# Lampinen ([5]) test problem 7
def f(x):
x = np.hstack(([0], x)) # 1-indexed to match reference
fun = (5.3578547*x[3]**2 + 0.8356891*x[1]*x[5] +
37.293239*x[1] - 40792.141)
return fun
def c1(x):
x = np.hstack(([0], x)) # 1-indexed to match reference
return [
85.334407 + 0.0056858*x[2]*x[5] + 0.0006262*x[1]*x[4] -
0.0022053*x[3]*x[5],
80.51249 + 0.0071317*x[2]*x[5] + 0.0029955*x[1]*x[2] +
0.0021813*x[3]**2,
9.300961 + 0.0047026*x[3]*x[5] + 0.0012547*x[1]*x[3] +
0.0019085*x[3]*x[4]
]
N = NonlinearConstraint(c1, [0, 90, 20], [92, 110, 25])
bounds = [(78, 102), (33, 45)] + [(27, 45)]*3
constraints = (N)
res = differential_evolution(f, bounds, strategy='rand1bin', seed=1234,
constraints=constraints)
# using our best solution, rather than Lampinen/Koziel. Koziel solution
# doesn't satisfy constraints, Lampinen f_opt just plain wrong.
x_opt = [78.00000686, 33.00000362, 29.99526064, 44.99999971,
36.77579979]
f_opt = -30665.537578
assert_allclose(f(x_opt), f_opt)
assert_allclose(res.x, x_opt, atol=1e-3)
assert_allclose(res.fun, f_opt, atol=1e-3)
assert res.success
assert_(np.all(np.array(c1(res.x)) >= np.array([0, 90, 20])))
assert_(np.all(np.array(c1(res.x)) <= np.array([92, 110, 25])))
assert_(np.all(res.x >= np.array(bounds)[:, 0]))
assert_(np.all(res.x <= np.array(bounds)[:, 1]))
@pytest.mark.slow
@pytest.mark.xfail(platform.machine() == 'ppc64le',
reason="fails on ppc64le")
def test_L8(self):
def f(x):
x = np.hstack(([0], x)) # 1-indexed to match reference
fun = 3*x[1] + 0.000001*x[1]**3 + 2*x[2] + 0.000002/3*x[2]**3
return fun
A = np.zeros((3, 5))
A[1, [4, 3]] = 1, -1
A[2, [3, 4]] = 1, -1
A = A[1:, 1:]
b = np.array([-.55, -.55])
def c1(x):
x = np.hstack(([0], x)) # 1-indexed to match reference
return [
1000*np.sin(-x[3]-0.25) + 1000*np.sin(-x[4]-0.25) +
894.8 - x[1],
1000*np.sin(x[3]-0.25) + 1000*np.sin(x[3]-x[4]-0.25) +
894.8 - x[2],
1000*np.sin(x[4]-0.25) + 1000*np.sin(x[4]-x[3]-0.25) +
1294.8
]
L = LinearConstraint(A, b, np.inf)
N = NonlinearConstraint(c1, np.full(3, -0.001), np.full(3, 0.001))
bounds = [(0, 1200)]*2+[(-.55, .55)]*2
constraints = (L, N)
with suppress_warnings() as sup:
sup.filter(UserWarning)
res = differential_evolution(f, bounds, strategy='rand1bin',
seed=1234, constraints=constraints,
maxiter=5000)
x_opt = (679.9453, 1026.067, 0.1188764, -0.3962336)
f_opt = 5126.4981
assert_allclose(f(x_opt), f_opt, atol=1e-3)
assert_allclose(res.x[:2], x_opt[:2], atol=2e-3)
assert_allclose(res.x[2:], x_opt[2:], atol=2e-3)
assert_allclose(res.fun, f_opt, atol=2e-2)
assert res.success
assert_(np.all([email protected] >= b))
assert_(np.all(np.array(c1(res.x)) >= -0.001))
assert_(np.all(np.array(c1(res.x)) <= 0.001))
assert_(np.all(res.x >= np.array(bounds)[:, 0]))
assert_(np.all(res.x <= np.array(bounds)[:, 1]))
def test_L9(self):
# Lampinen ([5]) test problem 9
def f(x):
x = np.hstack(([0], x)) # 1-indexed to match reference
return x[1]**2 + (x[2]-1)**2
def c1(x):
x = np.hstack(([0], x)) # 1-indexed to match reference
return [x[2] - x[1]**2]
N = NonlinearConstraint(c1, [-.001], [0.001])
bounds = [(-1, 1)]*2
constraints = (N)
res = differential_evolution(f, bounds, strategy='rand1bin', seed=1234,
constraints=constraints)
x_opt = [np.sqrt(2)/2, 0.5]
f_opt = 0.75
assert_allclose(f(x_opt), f_opt)
assert_allclose(np.abs(res.x), x_opt, atol=1e-3)
assert_allclose(res.fun, f_opt, atol=1e-3)
assert res.success
assert_(np.all(np.array(c1(res.x)) >= -0.001))
assert_(np.all(np.array(c1(res.x)) <= 0.001))
assert_(np.all(res.x >= np.array(bounds)[:, 0]))
assert_(np.all(res.x <= np.array(bounds)[:, 1]))
class TestDualAnnealing:
def setup_method(self):
# A function that returns always infinity for initialization tests
self.weirdfunc = lambda x: np.inf
# 2-D bounds for testing function
self.ld_bounds = [(-5.12, 5.12)] * 2
# 4-D bounds for testing function
self.hd_bounds = self.ld_bounds * 4
# Number of values to be generated for testing visit function
self.nbtestvalues = 5000
self.high_temperature = 5230
self.low_temperature = 0.1
self.qv = 2.62
self.seed = 1234
self.rs = check_random_state(self.seed)
self.nb_fun_call = 0
self.ngev = 0
def callback(self, x, f, context):
# For testing callback mechanism. Should stop for e <= 1 as
# the callback function returns True
if f <= 1.0:
return True
def func(self, x, args=()):
# Using Rastrigin function for performing tests
if args:
shift = args
else:
shift = 0
y = np.sum((x - shift)**2 -
10 * np.cos(2 * np.pi *
(x - shift))) + 10 * np.size(x) + shift
self.nb_fun_call += 1
return y
def rosen_der_wrapper(self, x, args=()):
self.ngev += 1
return rosen_der(x, *args)
# FIXME: there are some discontinuities in behaviour as a function of `qv`,
# this needs investigating - see gh-12384
@pytest.mark.parametrize('qv', [1.1, 1.41, 2, 2.62, 2.9])
def test_visiting_stepping(self, qv):
lu = list(zip(*self.ld_bounds))
lower = np.array(lu[0])
upper = np.array(lu[1])
dim = lower.size
vd = VisitingDistribution(lower, upper, qv, self.rs)
values = np.zeros(dim)
x_step_low = vd.visiting(values, 0, self.high_temperature)
# Make sure that only the first component is changed
assert_equal(np.not_equal(x_step_low, 0), True)
values = np.zeros(dim)
x_step_high = vd.visiting(values, dim, self.high_temperature)
# Make sure that component other than at dim has changed
assert_equal(np.not_equal(x_step_high[0], 0), True)
@pytest.mark.parametrize('qv', [2.25, 2.62, 2.9])
def test_visiting_dist_high_temperature(self, qv):
lu = list(zip(*self.ld_bounds))
lower = np.array(lu[0])
upper = np.array(lu[1])
vd = VisitingDistribution(lower, upper, qv, self.rs)
# values = np.zeros(self.nbtestvalues)
# for i in np.arange(self.nbtestvalues):
# values[i] = vd.visit_fn(self.high_temperature)
values = vd.visit_fn(self.high_temperature, self.nbtestvalues)
# Visiting distribution is a distorted version of Cauchy-Lorentz
# distribution, and as no 1st and higher moments (no mean defined,
# no variance defined).
# Check that big tails values are generated
assert_array_less(np.min(values), 1e-10)
assert_array_less(1e+10, np.max(values))
def test_reset(self):
owf = ObjectiveFunWrapper(self.weirdfunc)
lu = list(zip(*self.ld_bounds))
lower = np.array(lu[0])
upper = np.array(lu[1])
es = EnergyState(lower, upper)
assert_raises(ValueError, es.reset, owf, check_random_state(None))
def test_low_dim(self):
ret = dual_annealing(self.func, self.ld_bounds, seed=self.seed)
assert_allclose(ret.fun, 0., atol=1e-12)
assert ret.success
def test_high_dim(self):
ret = dual_annealing(self.func, self.hd_bounds, seed=self.seed)
assert_allclose(ret.fun, 0., atol=1e-12)
assert ret.success
def test_low_dim_no_ls(self):
ret = dual_annealing(self.func,
self.ld_bounds,
no_local_search=True,
seed=self.seed)
assert_allclose(ret.fun, 0., atol=1e-4)
def test_high_dim_no_ls(self):
ret = dual_annealing(self.func,
self.hd_bounds,
no_local_search=True,
seed=self.seed)
assert_allclose(ret.fun, 0., atol=1e-4)
def test_nb_fun_call(self):
ret = dual_annealing(self.func, self.ld_bounds, seed=self.seed)
assert_equal(self.nb_fun_call, ret.nfev)
def test_nb_fun_call_no_ls(self):
ret = dual_annealing(self.func,
self.ld_bounds,
no_local_search=True,
seed=self.seed)
assert_equal(self.nb_fun_call, ret.nfev)
def test_max_reinit(self):
assert_raises(ValueError, dual_annealing, self.weirdfunc,
self.ld_bounds)
def test_reproduce(self):
res1 = dual_annealing(self.func, self.ld_bounds, seed=self.seed)
res2 = dual_annealing(self.func, self.ld_bounds, seed=self.seed)
res3 = dual_annealing(self.func, self.ld_bounds, seed=self.seed)
# If we have reproducible results, x components found has to
# be exactly the same, which is not the case with no seeding
assert_equal(res1.x, res2.x)
assert_equal(res1.x, res3.x)
@pytest.mark.skipif(Version(np.__version__) < Version('1.17'),
reason='Generator not available for numpy, < 1.17')
def test_rand_gen(self):
# check that np.random.Generator can be used (numpy >= 1.17)
# obtain a np.random.Generator object
rng = np.random.default_rng(1)
res1 = dual_annealing(self.func, self.ld_bounds, seed=rng)
# seed again
rng = np.random.default_rng(1)
res2 = dual_annealing(self.func, self.ld_bounds, seed=rng)
# If we have reproducible results, x components found has to
# be exactly the same, which is not the case with no seeding
assert_equal(res1.x, res2.x)
def test_bounds_integrity(self):
wrong_bounds = [(-5.12, 5.12), (1, 0), (5.12, 5.12)]
assert_raises(ValueError, dual_annealing, self.func, wrong_bounds)
def test_bound_validity(self):
invalid_bounds = [(-5, 5), (-np.inf, 0), (-5, 5)]
assert_raises(ValueError, dual_annealing, self.func, invalid_bounds)
invalid_bounds = [(-5, 5), (0, np.inf), (-5, 5)]
assert_raises(ValueError, dual_annealing, self.func, invalid_bounds)
invalid_bounds = [(-5, 5), (0, np.nan), (-5, 5)]
assert_raises(ValueError, dual_annealing, self.func, invalid_bounds)
def test_local_search_option_bounds(self):
func = lambda x: np.sum((x - 5) * (x - 1))
bounds = list(zip([-6, -5], [6, 5]))
# Test bounds can be passed (see gh-10831)
with np.testing.suppress_warnings() as sup:
sup.record(RuntimeWarning, "Values in x were outside bounds ")
dual_annealing(func,
bounds=bounds,
local_search_options={
"method": "SLSQP",
"bounds": bounds
})
with np.testing.suppress_warnings() as sup:
sup.record(RuntimeWarning, "Method CG cannot handle ")
dual_annealing(func,
bounds=bounds,
local_search_options={
"method": "CG",
"bounds": bounds
})
# Verify warning happened for Method cannot handle bounds.
assert sup.log
def test_max_fun_ls(self):
ret = dual_annealing(self.func,
self.ld_bounds,
maxfun=100,
seed=self.seed)
ls_max_iter = min(
max(
len(self.ld_bounds) * LocalSearchWrapper.LS_MAXITER_RATIO,
LocalSearchWrapper.LS_MAXITER_MIN),
LocalSearchWrapper.LS_MAXITER_MAX)
assert ret.nfev <= 100 + ls_max_iter
assert not ret.success
def test_max_fun_no_ls(self):
ret = dual_annealing(self.func,
self.ld_bounds,
no_local_search=True,
maxfun=500,
seed=self.seed)
assert ret.nfev <= 500
assert not ret.success
def test_maxiter(self):
ret = dual_annealing(self.func,
self.ld_bounds,
maxiter=700,
seed=self.seed)
assert ret.nit <= 700
# Testing that args are passed correctly for dual_annealing
def test_fun_args_ls(self):
ret = dual_annealing(self.func,
self.ld_bounds,
args=((3.14159, )),
seed=self.seed)
assert_allclose(ret.fun, 3.14159, atol=1e-6)
# Testing that args are passed correctly for pure simulated annealing
def test_fun_args_no_ls(self):
ret = dual_annealing(self.func,
self.ld_bounds,
args=((3.14159, )),
no_local_search=True,
seed=self.seed)
assert_allclose(ret.fun, 3.14159, atol=1e-4)
def test_callback_stop(self):
# Testing that callback make the algorithm stop for
# fun value <= 1.0 (see callback method)
ret = dual_annealing(self.func,
self.ld_bounds,
callback=self.callback,
seed=self.seed)
assert ret.fun <= 1.0
assert 'stop early' in ret.message[0]
assert not ret.success
@pytest.mark.parametrize('method, atol', [
('Nelder-Mead', 2e-5),
('COBYLA', 1e-5),
('Powell', 1e-8),
('CG', 1e-8),
('BFGS', 1e-8),
('TNC', 1e-8),
('SLSQP', 2e-7),
])
def test_multi_ls_minimizer(self, method, atol):
ret = dual_annealing(self.func,
self.ld_bounds,
local_search_options=dict(method=method),
seed=self.seed)
assert_allclose(ret.fun, 0., atol=atol)
def test_wrong_restart_temp(self):
assert_raises(ValueError,
dual_annealing,
self.func,
self.ld_bounds,
restart_temp_ratio=1)
assert_raises(ValueError,
dual_annealing,
self.func,
self.ld_bounds,
restart_temp_ratio=0)
def test_gradient_gnev(self):
minimizer_opts = {
'jac': self.rosen_der_wrapper,
}
ret = dual_annealing(rosen,
self.ld_bounds,
local_search_options=minimizer_opts,
seed=self.seed)
assert ret.njev == self.ngev
def test_from_docstring(self):
func = lambda x: np.sum(x * x - 10 * np.cos(2 * np.pi * x)
) + 10 * np.size(x)
lw = [-5.12] * 10
up = [5.12] * 10
ret = dual_annealing(func, bounds=list(zip(lw, up)), seed=1234)
assert_allclose(ret.x, [
-4.26437714e-09, -3.91699361e-09, -1.86149218e-09, -3.97165720e-09,
-6.29151648e-09, -6.53145322e-09, -3.93616815e-09, -6.55623025e-09,
-6.05775280e-09, -5.00668935e-09
],
atol=4e-8)
assert_allclose(ret.fun, 0.000000, atol=5e-13)
@pytest.mark.parametrize('new_e, temp_step, accepted, accept_rate', [
(0, 100, 1000, 1.0097587941791923),
(0, 2, 1000, 1.2599210498948732),
(10, 100, 878, 0.8786035869128718),
(10, 60, 695, 0.6812920690579612),
(2, 100, 990, 0.9897404249173424),
])
def test_accept_reject_probabilistic(self, new_e, temp_step, accepted,
accept_rate):
# Test accepts unconditionally with e < current_energy and
# probabilistically with e > current_energy
rs = check_random_state(123)
count_accepted = 0
iterations = 1000
accept_param = -5
current_energy = 1
for _ in range(iterations):
energy_state = EnergyState(lower=None, upper=None)
# Set energy state with current_energy, any location.
energy_state.update_current(current_energy, [0])
chain = StrategyChain(accept_param, None, None, None, rs,
energy_state)
# Normally this is set in run()
chain.temperature_step = temp_step
# Check if update is accepted.
chain.accept_reject(j=1, e=new_e, x_visit=[2])
if energy_state.current_energy == new_e:
count_accepted += 1
assert count_accepted == accepted
# Check accept rate
pqv = 1 - (1 - accept_param) * (new_e - current_energy) / temp_step
rate = 0 if pqv <= 0 else np.exp(np.log(pqv) / (1 - accept_param))
assert_allclose(rate, accept_rate)
"""`uarray` provides functions for generating multimethods that dispatch to
multiple different backends
This should be imported, rather than `_uarray` so that an installed version could
be used instead, if available. This means that users can call
`uarray.set_backend` directly instead of going through SciPy.
"""
# Prefer an installed version of uarray, if available
try:
import uarray as _uarray
except ImportError:
_has_uarray = False
else:
from scipy._lib._pep440 import Version
_has_uarray = Version(_uarray.__version__) >= Version("0.5")
del _uarray
if _has_uarray:
from uarray import *
from uarray import _Function
else:
from ._uarray import *
from ._uarray import _Function
del _has_uarray
class TestBasinHopping:
def setup_method(self):
""" Tests setup.
Run tests based on the 1-D and 2-D functions described above.
"""
self.x0 = (1.0, [1.0, 1.0])
self.sol = (-0.195, np.array([-0.195, -0.1]))
self.tol = 3 # number of decimal places
self.niter = 100
self.disp = False
# fix random seed
np.random.seed(1234)
self.kwargs = {"method": "L-BFGS-B", "jac": True}
self.kwargs_nograd = {"method": "L-BFGS-B"}
def test_TypeError(self):
# test the TypeErrors are raised on bad input
i = 1
# if take_step is passed, it must be callable
assert_raises(TypeError, basinhopping, func2d, self.x0[i], take_step=1)
# if accept_test is passed, it must be callable
assert_raises(TypeError,
basinhopping,
func2d,
self.x0[i],
accept_test=1)
def test_input_validation(self):
msg = 'target_accept_rate has to be in range \\(0, 1\\)'
with assert_raises(ValueError, match=msg):
basinhopping(func1d, self.x0[0], target_accept_rate=0.)
with assert_raises(ValueError, match=msg):
basinhopping(func1d, self.x0[0], target_accept_rate=1.)
msg = 'stepwise_factor has to be in range \\(0, 1\\)'
with assert_raises(ValueError, match=msg):
basinhopping(func1d, self.x0[0], stepwise_factor=0.)
with assert_raises(ValueError, match=msg):
basinhopping(func1d, self.x0[0], stepwise_factor=1.)
def test_1d_grad(self):
# test 1-D minimizations with gradient
i = 0
res = basinhopping(func1d,
self.x0[i],
minimizer_kwargs=self.kwargs,
niter=self.niter,
disp=self.disp)
assert_almost_equal(res.x, self.sol[i], self.tol)
def test_2d(self):
# test 2d minimizations with gradient
i = 1
res = basinhopping(func2d,
self.x0[i],
minimizer_kwargs=self.kwargs,
niter=self.niter,
disp=self.disp)
assert_almost_equal(res.x, self.sol[i], self.tol)
assert_(res.nfev > 0)
def test_njev(self):
# test njev is returned correctly
i = 1
minimizer_kwargs = self.kwargs.copy()
# L-BFGS-B doesn't use njev, but BFGS does
minimizer_kwargs["method"] = "BFGS"
res = basinhopping(func2d,
self.x0[i],
minimizer_kwargs=minimizer_kwargs,
niter=self.niter,
disp=self.disp)
assert_(res.nfev > 0)
assert_equal(res.nfev, res.njev)
def test_jac(self):
# test Jacobian returned
minimizer_kwargs = self.kwargs.copy()
# BFGS returns a Jacobian
minimizer_kwargs["method"] = "BFGS"
res = basinhopping(func2d_easyderiv, [0.0, 0.0],
minimizer_kwargs=minimizer_kwargs,
niter=self.niter,
disp=self.disp)
assert_(hasattr(res.lowest_optimization_result, "jac"))
# in this case, the Jacobian is just [df/dx, df/dy]
_, jacobian = func2d_easyderiv(res.x)
assert_almost_equal(res.lowest_optimization_result.jac, jacobian,
self.tol)
def test_2d_nograd(self):
# test 2-D minimizations without gradient
i = 1
res = basinhopping(func2d_nograd,
self.x0[i],
minimizer_kwargs=self.kwargs_nograd,
niter=self.niter,
disp=self.disp)
assert_almost_equal(res.x, self.sol[i], self.tol)
def test_all_minimizers(self):
# Test 2-D minimizations with gradient. Nelder-Mead, Powell, and COBYLA
# don't accept jac=True, so aren't included here.
i = 1
methods = ['CG', 'BFGS', 'Newton-CG', 'L-BFGS-B', 'TNC', 'SLSQP']
minimizer_kwargs = copy.copy(self.kwargs)
for method in methods:
minimizer_kwargs["method"] = method
res = basinhopping(func2d,
self.x0[i],
minimizer_kwargs=minimizer_kwargs,
niter=self.niter,
disp=self.disp)
assert_almost_equal(res.x, self.sol[i], self.tol)
def test_all_nograd_minimizers(self):
# Test 2-D minimizations without gradient. Newton-CG requires jac=True,
# so not included here.
i = 1
methods = [
'CG', 'BFGS', 'L-BFGS-B', 'TNC', 'SLSQP', 'Nelder-Mead', 'Powell',
'COBYLA'
]
minimizer_kwargs = copy.copy(self.kwargs_nograd)
for method in methods:
minimizer_kwargs["method"] = method
res = basinhopping(func2d_nograd,
self.x0[i],
minimizer_kwargs=minimizer_kwargs,
niter=self.niter,
disp=self.disp)
tol = self.tol
if method == 'COBYLA':
tol = 2
assert_almost_equal(res.x, self.sol[i], decimal=tol)
def test_pass_takestep(self):
# test that passing a custom takestep works
# also test that the stepsize is being adjusted
takestep = MyTakeStep1()
initial_step_size = takestep.stepsize
i = 1
res = basinhopping(func2d,
self.x0[i],
minimizer_kwargs=self.kwargs,
niter=self.niter,
disp=self.disp,
take_step=takestep)
assert_almost_equal(res.x, self.sol[i], self.tol)
assert_(takestep.been_called)
# make sure that the build in adaptive step size has been used
assert_(initial_step_size != takestep.stepsize)
def test_pass_simple_takestep(self):
# test that passing a custom takestep without attribute stepsize
takestep = myTakeStep2
i = 1
res = basinhopping(func2d_nograd,
self.x0[i],
minimizer_kwargs=self.kwargs_nograd,
niter=self.niter,
disp=self.disp,
take_step=takestep)
assert_almost_equal(res.x, self.sol[i], self.tol)
def test_pass_accept_test(self):
# test passing a custom accept test
# makes sure it's being used and ensures all the possible return values
# are accepted.
accept_test = MyAcceptTest()
i = 1
# there's no point in running it more than a few steps.
basinhopping(func2d,
self.x0[i],
minimizer_kwargs=self.kwargs,
niter=10,
disp=self.disp,
accept_test=accept_test)
assert_(accept_test.been_called)
def test_pass_callback(self):
# test passing a custom callback function
# This makes sure it's being used. It also returns True after 10 steps
# to ensure that it's stopping early.
callback = MyCallBack()
i = 1
# there's no point in running it more than a few steps.
res = basinhopping(func2d,
self.x0[i],
minimizer_kwargs=self.kwargs,
niter=30,
disp=self.disp,
callback=callback)
assert_(callback.been_called)
assert_("callback" in res.message[0])
# One of the calls of MyCallBack is during BasinHoppingRunner
# construction, so there are only 9 remaining before MyCallBack stops
# the minimization.
assert_equal(res.nit, 9)
def test_minimizer_fail(self):
# test if a minimizer fails
i = 1
self.kwargs["options"] = dict(maxiter=0)
self.niter = 10
res = basinhopping(func2d,
self.x0[i],
minimizer_kwargs=self.kwargs,
niter=self.niter,
disp=self.disp)
# the number of failed minimizations should be the number of
# iterations + 1
assert_equal(res.nit + 1, res.minimization_failures)
def test_niter_zero(self):
# gh5915, what happens if you call basinhopping with niter=0
i = 0
basinhopping(func1d,
self.x0[i],
minimizer_kwargs=self.kwargs,
niter=0,
disp=self.disp)
def test_seed_reproducibility(self):
# seed should ensure reproducibility between runs
minimizer_kwargs = {"method": "L-BFGS-B", "jac": True}
f_1 = []
def callback(x, f, accepted):
f_1.append(f)
basinhopping(func2d, [1.0, 1.0],
minimizer_kwargs=minimizer_kwargs,
niter=10,
callback=callback,
seed=10)
f_2 = []
def callback2(x, f, accepted):
f_2.append(f)
basinhopping(func2d, [1.0, 1.0],
minimizer_kwargs=minimizer_kwargs,
niter=10,
callback=callback2,
seed=10)
assert_equal(np.array(f_1), np.array(f_2))
@pytest.mark.skipif(Version(np.__version__) < Version('1.17'),
reason='Generator not available for numpy, < 1.17')
def test_random_gen(self):
# check that np.random.Generator can be used (numpy >= 1.17)
rng = np.random.default_rng(1)
minimizer_kwargs = {"method": "L-BFGS-B", "jac": True}
res1 = basinhopping(func2d, [1.0, 1.0],
minimizer_kwargs=minimizer_kwargs,
niter=10,
seed=rng)
rng = np.random.default_rng(1)
res2 = basinhopping(func2d, [1.0, 1.0],
minimizer_kwargs=minimizer_kwargs,
niter=10,
seed=rng)
assert_equal(res1.x, res2.x)
def test_monotonic_basin_hopping(self):
# test 1-D minimizations with gradient and T=0
i = 0
res = basinhopping(func1d,
self.x0[i],
minimizer_kwargs=self.kwargs,
niter=self.niter,
disp=self.disp,
T=0)
assert_almost_equal(res.x, self.sol[i], self.tol)
def test_legacy_version():
# Non-PEP-440 version identifiers always compare less. For NumPy this only
# occurs on dev builds prior to 1.10.0 which are unsupported anyway.
assert parse('invalid') < Version('0.0.0')
assert parse('1.9.0-f16acvda') < Version('1.0.0')
def test_dev0_a_b_rc_mixed():
assert Version('1.9.0a2.dev0+f16acvda') == Version('1.9.0a2.dev0+f16acvda')
assert Version('1.9.0a2.dev0+6acvda54') < Version('1.9.0a2')
def test_version_1_point_10():
# regression test for gh-2998.
assert Version('1.9.0') < Version('1.10.0')
assert Version('1.11.0') < Version('1.11.1')
assert Version('1.11.0') == Version('1.11.0')
assert Version('1.99.11') < Version('1.99.12')
class TestUtils:
def test_scale(self):
# 1d scalar
space = [[0], [1], [0.5]]
out = [[-2], [6], [2]]
scaled_space = qmc.scale(space, l_bounds=-2, u_bounds=6)
assert_allclose(scaled_space, out)
# 2d space
space = [[0, 0], [1, 1], [0.5, 0.5]]
bounds = np.array([[-2, 0], [6, 5]])
out = [[-2, 0], [6, 5], [2, 2.5]]
scaled_space = qmc.scale(space, l_bounds=bounds[0], u_bounds=bounds[1])
assert_allclose(scaled_space, out)
scaled_back_space = qmc.scale(scaled_space, l_bounds=bounds[0],
u_bounds=bounds[1], reverse=True)
assert_allclose(scaled_back_space, space)
# broadcast
space = [[0, 0, 0], [1, 1, 1], [0.5, 0.5, 0.5]]
l_bounds, u_bounds = 0, [6, 5, 3]
out = [[0, 0, 0], [6, 5, 3], [3, 2.5, 1.5]]
scaled_space = qmc.scale(space, l_bounds=l_bounds, u_bounds=u_bounds)
assert_allclose(scaled_space, out)
def test_scale_random(self):
np.random.seed(0)
sample = np.random.rand(30, 10)
a = -np.random.rand(10) * 10
b = np.random.rand(10) * 10
scaled = qmc.scale(sample, a, b, reverse=False)
unscaled = qmc.scale(scaled, a, b, reverse=True)
assert_allclose(unscaled, sample)
def test_scale_errors(self):
with pytest.raises(ValueError, match=r"Sample is not a 2D array"):
space = [0, 1, 0.5]
qmc.scale(space, l_bounds=-2, u_bounds=6)
with pytest.raises(ValueError, match=r"Bounds are not consistent"
r" a < b"):
space = [[0, 0], [1, 1], [0.5, 0.5]]
bounds = np.array([[-2, 6], [6, 5]])
qmc.scale(space, l_bounds=bounds[0], u_bounds=bounds[1])
with pytest.raises(ValueError, match=r"shape mismatch: objects cannot "
r"be broadcast to a "
r"single shape"):
space = [[0, 0], [1, 1], [0.5, 0.5]]
l_bounds, u_bounds = [-2, 0, 2], [6, 5]
qmc.scale(space, l_bounds=l_bounds, u_bounds=u_bounds)
with pytest.raises(ValueError, match=r"Sample dimension is different "
r"than bounds dimension"):
space = [[0, 0], [1, 1], [0.5, 0.5]]
bounds = np.array([[-2, 0, 2], [6, 5, 5]])
qmc.scale(space, l_bounds=bounds[0], u_bounds=bounds[1])
with pytest.raises(ValueError, match=r"Sample is not in unit "
r"hypercube"):
space = [[0, 0], [1, 1.5], [0.5, 0.5]]
bounds = np.array([[-2, 0], [6, 5]])
qmc.scale(space, l_bounds=bounds[0], u_bounds=bounds[1])
with pytest.raises(ValueError, match=r"Sample is out of bounds"):
out = [[-2, 0], [6, 5], [8, 2.5]]
bounds = np.array([[-2, 0], [6, 5]])
qmc.scale(out, l_bounds=bounds[0], u_bounds=bounds[1],
reverse=True)
def test_discrepancy(self):
space_1 = np.array([[1, 3], [2, 6], [3, 2], [4, 5], [5, 1], [6, 4]])
space_1 = (2.0 * space_1 - 1.0) / (2.0 * 6.0)
space_2 = np.array([[1, 5], [2, 4], [3, 3], [4, 2], [5, 1], [6, 6]])
space_2 = (2.0 * space_2 - 1.0) / (2.0 * 6.0)
# From Fang et al. Design and modeling for computer experiments, 2006
assert_allclose(qmc.discrepancy(space_1), 0.0081, atol=1e-4)
assert_allclose(qmc.discrepancy(space_2), 0.0105, atol=1e-4)
# From Zhou Y.-D. et al. Mixture discrepancy for quasi-random point
# sets. Journal of Complexity, 29 (3-4), pp. 283-301, 2013.
# Example 4 on Page 298
sample = np.array([[2, 1, 1, 2, 2, 2],
[1, 2, 2, 2, 2, 2],
[2, 1, 1, 1, 1, 1],
[1, 1, 1, 1, 2, 2],
[1, 2, 2, 2, 1, 1],
[2, 2, 2, 2, 1, 1],
[2, 2, 2, 1, 2, 2]])
sample = (2.0 * sample - 1.0) / (2.0 * 2.0)
assert_allclose(qmc.discrepancy(sample, method='MD'), 2.5000,
atol=1e-4)
assert_allclose(qmc.discrepancy(sample, method='WD'), 1.3680,
atol=1e-4)
assert_allclose(qmc.discrepancy(sample, method='CD'), 0.3172,
atol=1e-4)
# From Tim P. et al. Minimizing the L2 and Linf star discrepancies
# of a single point in the unit hypercube. JCAM, 2005
# Table 1 on Page 283
for dim in [2, 4, 8, 16, 32, 64]:
ref = np.sqrt(3**(-dim))
assert_allclose(qmc.discrepancy(np.array([[1]*dim]),
method='L2-star'), ref)
def test_discrepancy_errors(self):
sample = np.array([[1, 3], [2, 6], [3, 2], [4, 5], [5, 1], [6, 4]])
with pytest.raises(
ValueError, match=r"Sample is not in unit hypercube"
):
qmc.discrepancy(sample)
with pytest.raises(ValueError, match=r"Sample is not a 2D array"):
qmc.discrepancy([1, 3])
sample = [[0, 0], [1, 1], [0.5, 0.5]]
with pytest.raises(ValueError, match=r"'toto' is not a valid ..."):
qmc.discrepancy(sample, method="toto")
def test_discrepancy_parallel(self, monkeypatch):
sample = np.array([[2, 1, 1, 2, 2, 2],
[1, 2, 2, 2, 2, 2],
[2, 1, 1, 1, 1, 1],
[1, 1, 1, 1, 2, 2],
[1, 2, 2, 2, 1, 1],
[2, 2, 2, 2, 1, 1],
[2, 2, 2, 1, 2, 2]])
sample = (2.0 * sample - 1.0) / (2.0 * 2.0)
assert_allclose(qmc.discrepancy(sample, method='MD', workers=8),
2.5000,
atol=1e-4)
assert_allclose(qmc.discrepancy(sample, method='WD', workers=8),
1.3680,
atol=1e-4)
assert_allclose(qmc.discrepancy(sample, method='CD', workers=8),
0.3172,
atol=1e-4)
# From Tim P. et al. Minimizing the L2 and Linf star discrepancies
# of a single point in the unit hypercube. JCAM, 2005
# Table 1 on Page 283
for dim in [2, 4, 8, 16, 32, 64]:
ref = np.sqrt(3 ** (-dim))
assert_allclose(qmc.discrepancy(np.array([[1] * dim]),
method='L2-star', workers=-1), ref)
monkeypatch.setattr(os, 'cpu_count', lambda: None)
with pytest.raises(NotImplementedError, match="Cannot determine the"):
qmc.discrepancy(sample, workers=-1)
with pytest.raises(ValueError, match="Invalid number of workers..."):
qmc.discrepancy(sample, workers=-2)
@pytest.mark.skipif(Version(np.__version__) < Version('1.17'),
reason='default_rng not available for numpy, < 1.17')
def test_update_discrepancy(self):
# From Fang et al. Design and modeling for computer experiments, 2006
space_1 = np.array([[1, 3], [2, 6], [3, 2], [4, 5], [5, 1], [6, 4]])
space_1 = (2.0 * space_1 - 1.0) / (2.0 * 6.0)
disc_init = qmc.discrepancy(space_1[:-1], iterative=True)
disc_iter = update_discrepancy(space_1[-1], space_1[:-1], disc_init)
assert_allclose(disc_iter, 0.0081, atol=1e-4)
# n<d
rng = np.random.default_rng(241557431858162136881731220526394276199)
space_1 = rng.random((4, 10))
disc_ref = qmc.discrepancy(space_1)
disc_init = qmc.discrepancy(space_1[:-1], iterative=True)
disc_iter = update_discrepancy(space_1[-1], space_1[:-1], disc_init)
assert_allclose(disc_iter, disc_ref, atol=1e-4)
# errors
with pytest.raises(ValueError, match=r"Sample is not in unit "
r"hypercube"):
update_discrepancy(space_1[-1], space_1[:-1] + 1, disc_init)
with pytest.raises(ValueError, match=r"Sample is not a 2D array"):
update_discrepancy(space_1[-1], space_1[0], disc_init)
x_new = [1, 3]
with pytest.raises(ValueError, match=r"x_new is not in unit "
r"hypercube"):
update_discrepancy(x_new, space_1[:-1], disc_init)
x_new = [[0.5, 0.5]]
with pytest.raises(ValueError, match=r"x_new is not a 1D array"):
update_discrepancy(x_new, space_1[:-1], disc_init)
x_new = [0.3, 0.1, 0]
with pytest.raises(ValueError, match=r"x_new and sample must be "
r"broadcastable"):
update_discrepancy(x_new, space_1[:-1], disc_init)
def test_discrepancy_alternative_implementation(self):
"""Alternative definitions from Matt Haberland."""
def disc_c2(x):
n, s = x.shape
xij = x
disc1 = np.sum(np.prod((1
+ 1/2*np.abs(xij-0.5)
- 1/2*np.abs(xij-0.5)**2), axis=1))
xij = x[None, :, :]
xkj = x[:, None, :]
disc2 = np.sum(np.sum(np.prod(1
+ 1/2*np.abs(xij - 0.5)
+ 1/2*np.abs(xkj - 0.5)
- 1/2*np.abs(xij - xkj), axis=2),
axis=0))
return (13/12)**s - 2/n * disc1 + 1/n**2*disc2
def disc_wd(x):
n, s = x.shape
xij = x[None, :, :]
xkj = x[:, None, :]
disc = np.sum(np.sum(np.prod(3/2
- np.abs(xij - xkj)
+ np.abs(xij - xkj)**2, axis=2),
axis=0))
return -(4/3)**s + 1/n**2 * disc
def disc_md(x):
n, s = x.shape
xij = x
disc1 = np.sum(np.prod((5/3
- 1/4*np.abs(xij-0.5)
- 1/4*np.abs(xij-0.5)**2), axis=1))
xij = x[None, :, :]
xkj = x[:, None, :]
disc2 = np.sum(np.sum(np.prod(15/8
- 1/4*np.abs(xij - 0.5)
- 1/4*np.abs(xkj - 0.5)
- 3/4*np.abs(xij - xkj)
+ 1/2*np.abs(xij - xkj)**2,
axis=2), axis=0))
return (19/12)**s - 2/n * disc1 + 1/n**2*disc2
def disc_star_l2(x):
n, s = x.shape
return np.sqrt(
3 ** (-s) - 2 ** (1 - s) / n
* np.sum(np.prod(1 - x ** 2, axis=1))
+ np.sum([
np.prod(1 - np.maximum(x[k, :], x[j, :]))
for k in range(n) for j in range(n)
]) / n ** 2
)
np.random.seed(0)
sample = np.random.rand(30, 10)
disc_curr = qmc.discrepancy(sample, method='CD')
disc_alt = disc_c2(sample)
assert_allclose(disc_curr, disc_alt)
disc_curr = qmc.discrepancy(sample, method='WD')
disc_alt = disc_wd(sample)
assert_allclose(disc_curr, disc_alt)
disc_curr = qmc.discrepancy(sample, method='MD')
disc_alt = disc_md(sample)
assert_allclose(disc_curr, disc_alt)
disc_curr = qmc.discrepancy(sample, method='L2-star')
disc_alt = disc_star_l2(sample)
assert_allclose(disc_curr, disc_alt)
def test_n_primes(self):
primes = n_primes(10)
assert primes[-1] == 29
primes = n_primes(168)
assert primes[-1] == 997
primes = n_primes(350)
assert primes[-1] == 2357
def test_primes(self):
primes = primes_from_2_to(50)
out = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]
assert_allclose(primes, out)