image-match/python/py/Lib/site-packages/scipy/optimize/tests/test_constraint_conversion.py

"""
Unit test for constraint conversion
"""
import warnings

import numpy as np
from numpy.testing import (assert_array_almost_equal,
                           assert_allclose)
import pytest
from scipy.optimize import (NonlinearConstraint, LinearConstraint,
                            OptimizeWarning, minimize, BFGS)
from .test_minimize_constrained import (Maratos, HyperbolicIneq, Rosenbrock,
                                        IneqRosenbrock, EqIneqRosenbrock,
                                        BoundedRosenbrock, Elec)


class TestOldToNew:
    x0 = (2, 0)
    bnds = ((0, None), (0, None))
    method = "trust-constr"

    def test_constraint_dictionary_1(self):
        def fun(x):
            return (x[0] - 1) ** 2 + (x[1] - 2.5) ** 2
        cons = ({'type': 'ineq', 'fun': lambda x: x[0] - 2 * x[1] + 2},
                {'type': 'ineq', 'fun': lambda x: -x[0] - 2 * x[1] + 6},
                {'type': 'ineq', 'fun': lambda x: -x[0] + 2 * x[1] + 2})

        with warnings.catch_warnings():
            warnings.filterwarnings("ignore", "delta_grad == 0.0", UserWarning)
            res = minimize(fun, self.x0, method=self.method,
                           bounds=self.bnds, constraints=cons)
        assert_allclose(res.x, [1.4, 1.7], rtol=1e-4)
        assert_allclose(res.fun, 0.8, rtol=1e-4)

    def test_constraint_dictionary_2(self):
        def fun(x):
            return (x[0] - 1) ** 2 + (x[1] - 2.5) ** 2
        cons = {'type': 'eq',
                'fun': lambda x, p1, p2: p1*x[0] - p2*x[1],
                'args': (1, 1.1),
                'jac': lambda x, p1, p2: np.array([[p1, -p2]])}
        with warnings.catch_warnings():
            warnings.filterwarnings("ignore", "delta_grad == 0.0", UserWarning)
            res = minimize(fun, self.x0, method=self.method,
                           bounds=self.bnds, constraints=cons)
        assert_allclose(res.x, [1.7918552, 1.62895927])
        assert_allclose(res.fun, 1.3857466063348418)

    def test_constraint_dictionary_3(self):
        def fun(x):
            return (x[0] - 1) ** 2 + (x[1] - 2.5) ** 2
        cons = [{'type': 'ineq', 'fun': lambda x: x[0] - 2 * x[1] + 2},
                NonlinearConstraint(lambda x: x[0] - x[1], 0, 0)]

        with warnings.catch_warnings():
            warnings.filterwarnings("ignore", "delta_grad == 0.0", UserWarning)
            res = minimize(fun, self.x0, method=self.method,
                           bounds=self.bnds, constraints=cons)
        assert_allclose(res.x, [1.75, 1.75], rtol=1e-4)
        assert_allclose(res.fun, 1.125, rtol=1e-4)


class TestNewToOld:
    @pytest.mark.fail_slow(2)
    def test_multiple_constraint_objects(self):
        def fun(x):
            return (x[0] - 1) ** 2 + (x[1] - 2.5) ** 2 + (x[2] - 0.75) ** 2
        x0 = [2, 0, 1]
        coni = []  # only inequality constraints (can use cobyla)
        methods = ["slsqp", "cobyla", "cobyqa", "trust-constr"]

        # mixed old and new
        coni.append([{'type': 'ineq', 'fun': lambda x: x[0] - 2 * x[1] + 2},
                     NonlinearConstraint(lambda x: x[0] - x[1], -1, 1)])

        coni.append([LinearConstraint([1, -2, 0], -2, np.inf),
                     NonlinearConstraint(lambda x: x[0] - x[1], -1, 1)])

        coni.append([NonlinearConstraint(lambda x: x[0] - 2 * x[1] + 2, 0, np.inf),
                     NonlinearConstraint(lambda x: x[0] - x[1], -1, 1)])

        for con in coni:
            funs = {}
            for method in methods:
                with warnings.catch_warnings():
                    warnings.simplefilter("ignore", UserWarning)
                    result = minimize(fun, x0, method=method, constraints=con)
                    funs[method] = result.fun
            assert_allclose(funs['slsqp'], funs['trust-constr'], rtol=1e-4)
            assert_allclose(funs['cobyla'], funs['trust-constr'], rtol=1e-4)
            assert_allclose(funs['cobyqa'], funs['trust-constr'],
                            rtol=1e-4)

    @pytest.mark.fail_slow(20)
    def test_individual_constraint_objects(self):
        def fun(x):
            return (x[0] - 1) ** 2 + (x[1] - 2.5) ** 2 + (x[2] - 0.75) ** 2
        x0 = [2, 0, 1]

        cone = []  # with equality constraints (can't use cobyla)
        coni = []  # only inequality constraints (can use cobyla)
        methods = ["slsqp", "cobyla", "cobyqa", "trust-constr"]

        # nonstandard data types for constraint equality bounds
        cone.append(NonlinearConstraint(lambda x: x[0] - x[1], 1, 1))
        cone.append(NonlinearConstraint(lambda x: x[0] - x[1], [1.21], [1.21]))
        cone.append(NonlinearConstraint(lambda x: x[0] - x[1],
                                        1.21, np.array([1.21])))

        # multiple equalities
        cone.append(NonlinearConstraint(
                    lambda x: [x[0] - x[1], x[1] - x[2]],
                    1.21, 1.21))  # two same equalities
        cone.append(NonlinearConstraint(
                    lambda x: [x[0] - x[1], x[1] - x[2]],
                    [1.21, 1.4], [1.21, 1.4]))  # two different equalities
        cone.append(NonlinearConstraint(
                    lambda x: [x[0] - x[1], x[1] - x[2]],
                    [1.21, 1.21], 1.21))  # equality specified two ways
        cone.append(NonlinearConstraint(
                    lambda x: [x[0] - x[1], x[1] - x[2]],
                    [1.21, -np.inf], [1.21, np.inf]))  # equality + unbounded

        # nonstandard data types for constraint inequality bounds
        coni.append(NonlinearConstraint(lambda x: x[0] - x[1], 1.21, np.inf))
        coni.append(NonlinearConstraint(lambda x: x[0] - x[1], [1.21], np.inf))
        coni.append(NonlinearConstraint(lambda x: x[0] - x[1],
                                        1.21, np.array([np.inf])))
        coni.append(NonlinearConstraint(lambda x: x[0] - x[1], -np.inf, -3))
        coni.append(NonlinearConstraint(lambda x: x[0] - x[1],
                                        np.array(-np.inf), -3))

        # multiple inequalities/equalities
        coni.append(NonlinearConstraint(
                    lambda x: [x[0] - x[1], x[1] - x[2]],
                    1.21, np.inf))  # two same inequalities
        cone.append(NonlinearConstraint(
                    lambda x: [x[0] - x[1], x[1] - x[2]],
                    [1.21, -np.inf], [1.21, 1.4]))  # mixed equality/inequality
        coni.append(NonlinearConstraint(
                    lambda x: [x[0] - x[1], x[1] - x[2]],
                    [1.1, .8], [1.2, 1.4]))  # bounded above and below
        coni.append(NonlinearConstraint(
                    lambda x: [x[0] - x[1], x[1] - x[2]],
                    [-1.2, -1.4], [-1.1, -.8]))  # - bounded above and below

        # quick check of LinearConstraint class (very little new code to test)
        cone.append(LinearConstraint([1, -1, 0], 1.21, 1.21))
        cone.append(LinearConstraint([[1, -1, 0], [0, 1, -1]], 1.21, 1.21))
        cone.append(LinearConstraint([[1, -1, 0], [0, 1, -1]],
                                     [1.21, -np.inf], [1.21, 1.4]))

        for con in coni:
            funs = {}
            for method in methods:
                with warnings.catch_warnings():
                    warnings.simplefilter("ignore", UserWarning)
                    result = minimize(fun, x0, method=method, constraints=con)
                    funs[method] = result.fun
            assert_allclose(funs['slsqp'], funs['trust-constr'], rtol=1e-3)
            assert_allclose(funs['cobyla'], funs['trust-constr'], rtol=1e-3)
            assert_allclose(funs['cobyqa'], funs['trust-constr'],
                            rtol=1e-3)

        for con in cone:
            funs = {}
            for method in [method for method in methods if method != 'cobyla']:
                with warnings.catch_warnings():
                    warnings.simplefilter("ignore", UserWarning)
                    result = minimize(fun, x0, method=method, constraints=con)
                    funs[method] = result.fun
            assert_allclose(funs['slsqp'], funs['trust-constr'], rtol=1e-3)
            assert_allclose(funs['cobyqa'], funs['trust-constr'],
                            rtol=1e-3)


class TestNewToOldSLSQP:
    method = 'slsqp'
    elec = Elec(n_electrons=2)
    elec.x_opt = np.array([-0.58438468, 0.58438466, 0.73597047,
                           -0.73597044, 0.34180668, -0.34180667])
    brock = BoundedRosenbrock()
    brock.x_opt = [0, 0]
    list_of_problems = [Maratos(),
                        HyperbolicIneq(),
                        Rosenbrock(),
                        IneqRosenbrock(),
                        EqIneqRosenbrock(),
                        elec,
                        brock
                        ]

    def test_list_of_problems(self):

        for prob in self.list_of_problems:

            with warnings.catch_warnings():
                warnings.simplefilter("ignore", UserWarning)
                result = minimize(prob.fun, prob.x0,
                                  method=self.method,
                                  bounds=prob.bounds,
                                  constraints=prob.constr)

            assert_array_almost_equal(result.x, prob.x_opt, decimal=3)

    def test_warn_mixed_constraints(self):
        # warns about inefficiency of mixed equality/inequality constraints
        def fun(x):
            return (x[0] - 1) ** 2 + (x[1] - 2.5) ** 2 + (x[2] - 0.75) ** 2
        cons = NonlinearConstraint(lambda x: [x[0]**2 - x[1], x[1] - x[2]],
                                   [1.1, .8], [1.1, 1.4])
        bnds = ((0, None), (0, None), (0, None))
        with warnings.catch_warnings():
            warnings.filterwarnings("ignore", "delta_grad == 0.0", UserWarning)
            with pytest.warns(OptimizeWarning):
                 minimize(fun, (2, 0, 1),
                          method=self.method, bounds=bnds, constraints=cons)

    def test_warn_ignored_options(self):
        # warns about constraint options being ignored
        def fun(x):
            return (x[0] - 1) ** 2 + (x[1] - 2.5) ** 2 + (x[2] - 0.75) ** 2
        x0 = (2, 0, 1)

        if self.method == "slsqp":
            bnds = ((0, None), (0, None), (0, None))
        else:
            bnds = None

        cons = NonlinearConstraint(lambda x: x[0], 2, np.inf)
        res = minimize(fun, x0, method=self.method,
                       bounds=bnds, constraints=cons)
        # no warnings without constraint options
        assert_allclose(res.fun, 1)

        cons = LinearConstraint([1, 0, 0], 2, np.inf)
        res = minimize(fun, x0, method=self.method,
                       bounds=bnds, constraints=cons)
        # no warnings without constraint options
        assert_allclose(res.fun, 1)

        cons = []
        cons.append(NonlinearConstraint(lambda x: x[0]**2, 2, np.inf,
                                        keep_feasible=True))
        cons.append(NonlinearConstraint(lambda x: x[0]**2, 2, np.inf,
                                        hess=BFGS()))
        cons.append(NonlinearConstraint(lambda x: x[0]**2, 2, np.inf,
                                        finite_diff_jac_sparsity=42))
        cons.append(NonlinearConstraint(lambda x: x[0]**2, 2, np.inf,
                                        finite_diff_rel_step=42))
        cons.append(LinearConstraint([1, 0, 0], 2, np.inf,
                                     keep_feasible=True))
        for con in cons:
            with pytest.warns(OptimizeWarning):
                minimize(fun, x0,
                         method=self.method, bounds=bnds, constraints=cons)


class TestNewToOldCobyla:
    method = 'cobyla'

    list_of_problems = [
                        Elec(n_electrons=2),
                        Elec(n_electrons=4),
                        ]

    @pytest.mark.slow
    def test_list_of_problems(self):

        for prob in self.list_of_problems:

            with warnings.catch_warnings():
                warnings.simplefilter("ignore", UserWarning)
                truth = minimize(prob.fun, prob.x0,
                                 method='trust-constr',
                                 bounds=prob.bounds,
                                 constraints=prob.constr)
                result = minimize(prob.fun, prob.x0,
                                  method=self.method,
                                  bounds=prob.bounds,
                                  constraints=prob.constr)

            assert_allclose(result.fun, truth.fun, rtol=1e-3)