Python scipy.optimize.rosen() Examples

def test_l_bfgs_b_maxiter(self):
        # gh7854
        # Ensure that not more than maxiters are ever run.
        class Callback(object):
            def __init__(self):
                self.nit = 0
                self.fun = None
                self.x = None

            def __call__(self, x):
                self.x = x
                self.fun = optimize.rosen(x)
                self.nit += 1

        c = Callback()
        res = optimize.minimize(optimize.rosen, [0., 0.], method='l-bfgs-b',
                                callback=c, options={'maxiter': 5})

        assert_equal(res.nit, 5)
        assert_almost_equal(res.x, c.x)
        assert_almost_equal(res.fun, c.fun)
        assert_equal(res.status, 1)
        assert_(res.success is False)
        assert_equal(res.message.decode(), 'STOP: TOTAL NO. of ITERATIONS REACHED LIMIT') 

def test_minimize_l_bfgs_b_maxfun_interruption(self):
        # gh-6162
        f = optimize.rosen
        g = optimize.rosen_der
        values = []
        x0 = np.ones(7) * 1000

        def objfun(x):
            value = f(x)
            values.append(value)
            return value

        # Look for an interesting test case.
        # Request a maxfun that stops at a particularly bad function
        # evaluation somewhere between 100 and 300 evaluations.
        low, medium, high = 30, 100, 300
        optimize.fmin_l_bfgs_b(objfun, x0, fprime=g, maxfun=high)
        v, k = max((y, i) for i, y in enumerate(values[medium:]))
        maxfun = medium + k
        # If the minimization strategy is reasonable,
        # the minimize() result should not be worse than the best
        # of the first 30 function evaluations.
        target = min(values[:low])
        xmin, fmin, d = optimize.fmin_l_bfgs_b(f, x0, fprime=g, maxfun=maxfun)
        assert_array_less(fmin, target) 

def rosenbrock_problem():
    """Problem based on rosenbrock objective.

    Features
    --------
    * 3-dim
    * has fixed parameters
    """
    objective = pypesto.Objective(fun=so.rosen)

    dim_full = 2
    lb = -5 * np.ones((dim_full, 1))
    ub = 5 * np.ones((dim_full, 1))

    problem = pypesto.Problem(
            objective=objective, lb=lb, ub=ub,
            x_fixed_indices=[1], x_fixed_vals=[2])
    return problem 

def test_bounds_checking(self):
        # test that the bounds checking works
        func = rosen
        bounds = [(-3, None)]
        assert_raises(ValueError,
                          differential_evolution,
                          func,
                          bounds)
        bounds = [(-3)]
        assert_raises(ValueError,
                          differential_evolution,
                          func,
                          bounds)
        bounds = [(-3, 3), (3, 4, 5)]
        assert_raises(ValueError,
                          differential_evolution,
                          func,
                          bounds) 

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)
        for i, soln in enumerate(solver):
            x_current, fun_current = soln
            # need to have this otherwise the solver would never stop.
            if i == 1000:
                break

        assert_almost_equal(fun_current, 0) 

def f(u, *args):
        return rosen(u.ravel()) 

def fun(self, x, *args):
        self.nfev += 1

        return rosen(x) 

def f(u, *args):
        return rosen(u.ravel()) 

def create_problem():
    # define a pypesto objective
    objective = pypesto.Objective(fun=so.rosen,
                                  grad=so.rosen_der,
                                  hess=so.rosen_hess)

    # define a pypesto problem
    (lb, ub) = create_bounds()
    problem = pypesto.Problem(objective=objective, lb=lb, ub=ub)

    return problem 

def rosen_for_sensi(max_sensi_order, integrated=False, x=None):
    """
    Rosenbrock function from scipy.optimize.
    """
    if x is None:
        x = [0, 1]

    return obj_for_sensi(so.rosen,
                         so.rosen_der,
                         so.rosen_hess,
                         max_sensi_order, integrated, x) 

def compute_r(self):
        
        result = np.array((rosen(self.x.r) ))
        
        return result 

def test_unconstrained(self):
        """Test against the Rosenbrock function."""

        x0 = np.random.uniform(0, 2, (1000, 5))
        sol = np.array([1., 1., 1., 1., 1.])
        res = minimize(rosen, x0)
        converged = res.success
        assert converged, res.message
        np.testing.assert_array_almost_equal(sol, res.x, 3) 

def _optimize(self, optimizer):
        x_0 = [1.3, 0.7, 0.8, 1.9, 1.2]
        bounds = [(-6, 6)] * len(x_0)
        res = optimizer.optimize(len(x_0), rosen, initial_point=x_0, variable_bounds=bounds)
        np.testing.assert_array_almost_equal(res[0], [1.0] * len(x_0), decimal=2)
        return res

    # ESCH and ISRES do not do well with rosen 

def test_gsls(self):
        """ gsls test """
        optimizer = GSLS(sample_size_factor=40, sampling_radius=1.0e-12, maxiter=10000,
                         max_eval=10000, min_step_size=1.0e-12)
        x_0 = [1.3, 0.7, 0.8, 1.9, 1.2]
        _, x_value, n_evals = optimizer.optimize(len(x_0), rosen, initial_point=x_0)

        # Ensure value is near-optimal
        self.assertLessEqual(x_value, 0.01)
        self.assertLessEqual(n_evals, 10000) 

def _optimize(self, optimizer):
        x_0 = [1.3, 0.7, 0.8, 1.9, 1.2]
        res = optimizer.optimize(len(x_0), rosen, initial_point=x_0)
        np.testing.assert_array_almost_equal(res[0], [1.0] * len(x_0), decimal=2)
        return res 

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_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()

        assert_equal(np.argmin(solver.population_energies), 0)

        # initial calculation of the energies should require 6 nfev.
        assert_equal(solver._nfev, 6) 

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) 

def test_exp_runs(self):
        # test whether exponential mutation loop runs
        solver = DifferentialEvolutionSolver(rosen,
                                             self.bounds,
                                             strategy='best1exp',
                                             maxiter=1)

        solver.solve() 

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.') 

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_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_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 setup_method(self):
        self.x0 = [5, 5]
        self.func = optimize.rosen
        self.jac = optimize.rosen_der
        self.hess = optimize.rosen_hess
        self.hessp = optimize.rosen_hess_prod
        self.bounds = [(0., 10.), (0., 10.)] 

def test_custom(self):
        # This function comes from the documentation example.
        def custmin(fun, x0, args=(), maxfev=None, stepsize=0.1,
                maxiter=100, callback=None, **options):
            bestx = x0
            besty = fun(x0)
            funcalls = 1
            niter = 0
            improved = True
            stop = False

            while improved and not stop and niter < maxiter:
                improved = False
                niter += 1
                for dim in range(np.size(x0)):
                    for s in [bestx[dim] - stepsize, bestx[dim] + stepsize]:
                        testx = np.copy(bestx)
                        testx[dim] = s
                        testy = fun(testx, *args)
                        funcalls += 1
                        if testy < besty:
                            besty = testy
                            bestx = testx
                            improved = True
                    if callback is not None:
                        callback(bestx)
                    if maxfev is not None and funcalls >= maxfev:
                        stop = True
                        break

            return optimize.OptimizeResult(fun=besty, x=bestx, nit=niter,
                                           nfev=funcalls, success=(niter > 1))

        x0 = [1.35, 0.9, 0.8, 1.1, 1.2]
        res = optimize.minimize(optimize.rosen, x0, method=custmin,
                                options=dict(stepsize=0.05))
        assert_allclose(res.x, 1.0, rtol=1e-4, atol=1e-4) 

def test_minimize_l_bfgs_maxls(self):
        # check that the maxls is passed down to the Fortran routine
        sol = optimize.minimize(optimize.rosen, np.array([-1.2,1.0]),
                                method='L-BFGS-B', jac=optimize.rosen_der,
                                options={'disp': False, 'maxls': 1})
        assert_(not sol.success) 

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 initialise 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 initialised 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 initialise 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_minimize_callback_copies_array(self, method):
        # Check that arrays passed to callbacks are not modified
        # inplace by the optimizer afterward

        if method in ('fmin_tnc', 'fmin_l_bfgs_b'):
            func = lambda x: (optimize.rosen(x), optimize.rosen_der(x))
        else:
            func = optimize.rosen
            jac = optimize.rosen_der
            hess = optimize.rosen_hess

        x0 = np.zeros(10)

        # Set options
        kwargs = {}
        if method.startswith('fmin'):
            routine = getattr(optimize, method)
            if method == 'fmin_slsqp':
                kwargs['iter'] = 5
            elif method == 'fmin_tnc':
                kwargs['maxfun'] = 100
            else:
                kwargs['maxiter'] = 5
        else:
            def routine(*a, **kw):
                kw['method'] = method
                return optimize.minimize(*a, **kw)

            if method == 'TNC':
                kwargs['options'] = dict(maxiter=100)
            else:
                kwargs['options'] = dict(maxiter=5)

        if method in ('fmin_ncg',):
            kwargs['fprime'] = jac
        elif method in ('Newton-CG',):
            kwargs['jac'] = jac
        elif method in ('trust-krylov', 'trust-exact', 'trust-ncg', 'dogleg',
                        'trust-constr'):
            kwargs['jac'] = jac
            kwargs['hess'] = hess

        # Run with callback
        results = []

        def callback(x, *args, **kwargs):
            results.append((x, np.copy(x)))

        sol = routine(func, x0, callback=callback, **kwargs)

        # Check returned arrays coincide with their copies and have no memory overlap
        assert_(len(results) > 2)
        assert_(all(np.all(x == y) for x, y in results))
        assert_(not any(np.may_share_memory(x[0], y[0]) for x, y in itertools.combinations(results, 2)))