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ckpts/universal/global_step40/zero/12.input_layernorm.weight/exp_avg.pt

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ckpts/universal/global_step40/zero/12.input_layernorm.weight/exp_avg_sq.pt

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ckpts/universal/global_step40/zero/7.attention.query_key_value.weight/exp_avg.pt

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ckpts/universal/global_step40/zero/7.attention.query_key_value.weight/exp_avg_sq.pt

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ckpts/universal/global_step40/zero/7.attention.query_key_value.weight/fp32.pt

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venv/lib/python3.10/site-packages/scipy/optimize/tests/test__basinhopping.py

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+"""
+Unit tests for the basin hopping global minimization algorithm.
+"""
+import copy
+
+from numpy.testing import (assert_almost_equal, assert_equal, assert_,
+                           assert_allclose)
+import pytest
+from pytest import raises as assert_raises
+import numpy as np
+from numpy import cos, sin
+
+from scipy.optimize import basinhopping, OptimizeResult
+from scipy.optimize._basinhopping import (
+    Storage, RandomDisplacement, Metropolis, AdaptiveStepsize)
+
+
+def func1d(x):
+    f = cos(14.5 * x - 0.3) + (x + 0.2) * x
+    df = np.array(-14.5 * sin(14.5 * x - 0.3) + 2. * x + 0.2)
+    return f, df
+
+
+def func2d_nograd(x):
+    f = cos(14.5 * x[0] - 0.3) + (x[1] + 0.2) * x[1] + (x[0] + 0.2) * x[0]
+    return f
+
+
+def func2d(x):
+    f = cos(14.5 * x[0] - 0.3) + (x[1] + 0.2) * x[1] + (x[0] + 0.2) * x[0]
+    df = np.zeros(2)
+    df[0] = -14.5 * sin(14.5 * x[0] - 0.3) + 2. * x[0] + 0.2
+    df[1] = 2. * x[1] + 0.2
+    return f, df
+
+
+def func2d_easyderiv(x):
+    f = 2.0*x[0]**2 + 2.0*x[0]*x[1] + 2.0*x[1]**2 - 6.0*x[0]
+    df = np.zeros(2)
+    df[0] = 4.0*x[0] + 2.0*x[1] - 6.0
+    df[1] = 2.0*x[0] + 4.0*x[1]
+
+    return f, df
+
+
+class MyTakeStep1(RandomDisplacement):
+    """use a copy of displace, but have it set a special parameter to
+    make sure it's actually being used."""
+    def __init__(self):
+        self.been_called = False
+        super().__init__()
+
+    def __call__(self, x):
+        self.been_called = True
+        return super().__call__(x)
+
+
+def myTakeStep2(x):
+    """redo RandomDisplacement in function form without the attribute stepsize
+    to make sure everything still works ok
+    """
+    s = 0.5
+    x += np.random.uniform(-s, s, np.shape(x))
+    return x
+
+
+class MyAcceptTest:
+    """pass a custom accept test
+
+    This does nothing but make sure it's being used and ensure all the
+    possible return values are accepted
+    """
+    def __init__(self):
+        self.been_called = False
+        self.ncalls = 0
+        self.testres = [False, 'force accept', True, np.bool_(True),
+                        np.bool_(False), [], {}, 0, 1]
+
+    def __call__(self, **kwargs):
+        self.been_called = True
+        self.ncalls += 1
+        if self.ncalls - 1 < len(self.testres):
+            return self.testres[self.ncalls - 1]
+        else:
+            return True
+
+
+class MyCallBack:
+    """pass 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.
+
+    """
+    def __init__(self):
+        self.been_called = False
+        self.ncalls = 0
+
+    def __call__(self, x, f, accepted):
+        self.been_called = True
+        self.ncalls += 1
+        if self.ncalls == 10:
+            return True
+
+
+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))
+
+    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)
+
+
+class Test_Storage:
+    def setup_method(self):
+        self.x0 = np.array(1)
+        self.f0 = 0
+
+        minres = OptimizeResult(success=True)
+        minres.x = self.x0
+        minres.fun = self.f0
+
+        self.storage = Storage(minres)
+
+    def test_higher_f_rejected(self):
+        new_minres = OptimizeResult(success=True)
+        new_minres.x = self.x0 + 1
+        new_minres.fun = self.f0 + 1
+
+        ret = self.storage.update(new_minres)
+        minres = self.storage.get_lowest()
+        assert_equal(self.x0, minres.x)
+        assert_equal(self.f0, minres.fun)
+        assert_(not ret)
+
+    @pytest.mark.parametrize('success', [True, False])
+    def test_lower_f_accepted(self, success):
+        new_minres = OptimizeResult(success=success)
+        new_minres.x = self.x0 + 1
+        new_minres.fun = self.f0 - 1
+
+        ret = self.storage.update(new_minres)
+        minres = self.storage.get_lowest()
+        assert (self.x0 != minres.x) == success  # can't use `is`
+        assert (self.f0 != minres.fun) == success  # left side is NumPy bool
+        assert ret is success
+
+
+class Test_RandomDisplacement:
+    def setup_method(self):
+        self.stepsize = 1.0
+        self.displace = RandomDisplacement(stepsize=self.stepsize)
+        self.N = 300000
+        self.x0 = np.zeros([self.N])
+
+    def test_random(self):
+        # the mean should be 0
+        # the variance should be (2*stepsize)**2 / 12
+        # note these tests are random, they will fail from time to time
+        x = self.displace(self.x0)
+        v = (2. * self.stepsize) ** 2 / 12
+        assert_almost_equal(np.mean(x), 0., 1)
+        assert_almost_equal(np.var(x), v, 1)
+
+
+class Test_Metropolis:
+    def setup_method(self):
+        self.T = 2.
+        self.met = Metropolis(self.T)
+        self.res_new = OptimizeResult(success=True, fun=0.)
+        self.res_old = OptimizeResult(success=True, fun=1.)
+
+    def test_boolean_return(self):
+        # the return must be a bool, else an error will be raised in
+        # basinhopping
+        ret = self.met(res_new=self.res_new, res_old=self.res_old)
+        assert isinstance(ret, bool)
+
+    def test_lower_f_accepted(self):
+        assert_(self.met(res_new=self.res_new, res_old=self.res_old))
+
+    def test_accept(self):
+        # test that steps are randomly accepted for f_new > f_old
+        one_accept = False
+        one_reject = False
+        for i in range(1000):
+            if one_accept and one_reject:
+                break
+            res_new = OptimizeResult(success=True, fun=1.)
+            res_old = OptimizeResult(success=True, fun=0.5)
+            ret = self.met(res_new=res_new, res_old=res_old)
+            if ret:
+                one_accept = True
+            else:
+                one_reject = True
+        assert_(one_accept)
+        assert_(one_reject)
+
+    def test_GH7495(self):
+        # an overflow in exp was producing a RuntimeWarning
+        # create own object here in case someone changes self.T
+        met = Metropolis(2)
+        res_new = OptimizeResult(success=True, fun=0.)
+        res_old = OptimizeResult(success=True, fun=2000)
+        with np.errstate(over='raise'):
+            met.accept_reject(res_new=res_new, res_old=res_old)
+
+    def test_gh7799(self):
+        # gh-7799 reported a problem in which local search was successful but
+        # basinhopping returned an invalid solution. Show that this is fixed.
+        def func(x):
+            return (x**2-8)**2+(x+2)**2
+
+        x0 = -4
+        limit = 50  # Constrain to func value >= 50
+        con = {'type': 'ineq', 'fun': lambda x: func(x) - limit},
+        res = basinhopping(func, x0, 30, minimizer_kwargs={'constraints': con})
+        assert res.success
+        assert_allclose(res.fun, limit, rtol=1e-6)
+
+    def test_accept_gh7799(self):
+        # Metropolis should not accept the result of an unsuccessful new local
+        # search if the old local search was successful
+
+        met = Metropolis(0)  # monotonic basin hopping
+        res_new = OptimizeResult(success=True, fun=0.)
+        res_old = OptimizeResult(success=True, fun=1.)
+
+        # if new local search was successful and energy is lower, accept
+        assert met(res_new=res_new, res_old=res_old)
+        # if new res is unsuccessful, don't accept - even if energy is lower
+        res_new.success = False
+        assert not met(res_new=res_new, res_old=res_old)
+        # ...unless the old res was unsuccessful, too. In that case, why not?
+        res_old.success = False
+        assert met(res_new=res_new, res_old=res_old)
+
+    def test_reject_all_gh7799(self):
+        # Test the behavior when there is no feasible solution
+        def fun(x):
+            return x@x
+
+        def constraint(x):
+            return x + 1
+
+        kwargs = {'constraints': {'type': 'eq', 'fun': constraint},
+                  'bounds': [(0, 1), (0, 1)], 'method': 'slsqp'}
+        res = basinhopping(fun, x0=[2, 3], niter=10, minimizer_kwargs=kwargs)
+        assert not res.success
+
+
+class Test_AdaptiveStepsize:
+    def setup_method(self):
+        self.stepsize = 1.
+        self.ts = RandomDisplacement(stepsize=self.stepsize)
+        self.target_accept_rate = 0.5
+        self.takestep = AdaptiveStepsize(takestep=self.ts, verbose=False,
+                                         accept_rate=self.target_accept_rate)
+
+    def test_adaptive_increase(self):
+        # if few steps are rejected, the stepsize should increase
+        x = 0.
+        self.takestep(x)
+        self.takestep.report(False)
+        for i in range(self.takestep.interval):
+            self.takestep(x)
+            self.takestep.report(True)
+        assert_(self.ts.stepsize > self.stepsize)
+
+    def test_adaptive_decrease(self):
+        # if few steps are rejected, the stepsize should increase
+        x = 0.
+        self.takestep(x)
+        self.takestep.report(True)
+        for i in range(self.takestep.interval):
+            self.takestep(x)
+            self.takestep.report(False)
+        assert_(self.ts.stepsize < self.stepsize)
+
+    def test_all_accepted(self):
+        # test that everything works OK if all steps were accepted
+        x = 0.
+        for i in range(self.takestep.interval + 1):
+            self.takestep(x)
+            self.takestep.report(True)
+        assert_(self.ts.stepsize > self.stepsize)
+
+    def test_all_rejected(self):
+        # test that everything works OK if all steps were rejected
+        x = 0.
+        for i in range(self.takestep.interval + 1):
+            self.takestep(x)
+            self.takestep.report(False)
+        assert_(self.ts.stepsize < self.stepsize)

venv/lib/python3.10/site-packages/scipy/optimize/tests/test__differential_evolution.py

@@ -0,0 +1,1677 @@
+"""
+Unit tests for the differential global minimization algorithm.
+"""
+import multiprocessing
+import platform
+
+from scipy.optimize._differentialevolution import (DifferentialEvolutionSolver,
+                                                   _ConstraintWrapper)
+from scipy.optimize import differential_evolution, OptimizeResult
+from scipy.optimize._constraints import (Bounds, NonlinearConstraint,
+                                         LinearConstraint)
+from scipy.optimize import rosen, minimize
+from scipy.sparse import csr_matrix
+from scipy import stats
+
+import numpy as np
+from numpy.testing import (assert_equal, assert_allclose, assert_almost_equal,
+                           assert_string_equal, assert_, suppress_warnings)
+from pytest import raises as assert_raises, warns
+import pytest
+
+
+class TestDifferentialEvolutionSolver:
+
+    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_invalid_functional(self):
+        def func(x):
+            return np.array([np.sum(x ** 2), np.sum(x)])
+
+        with assert_raises(
+                RuntimeError,
+                match=r"func\(x, \*args\) must return a scalar value"):
+            differential_evolution(func, [(-2, 2), (-2, 2)])
+
+    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_equal_bounds(self):
+        with np.errstate(invalid='raise'):
+            solver = DifferentialEvolutionSolver(
+                self.quadratic,
+                bounds=[(2.0, 2.0), (1.0, 3.0)]
+            )
+            v = solver._unscale_parameters([2.0, 2.0])
+            assert_allclose(v, 0.5)
+
+        res = differential_evolution(self.quadratic, [(2.0, 2.0), (3.0, 3.0)])
+        assert_equal(res.x, [2.0, 3.0])
+
+    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)], maxiter=1, polish=False
+        )
+        result = solver.solve()
+        assert_equal(result.fun, self.quadratic(result.x))
+
+        solver = DifferentialEvolutionSolver(
+            self.quadratic, [(-2, 2)], maxiter=1, polish=True
+        )
+        result = solver.solve()
+        assert_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_equal(result.x, solver.x)
+
+    def test_intermediate_result(self):
+        # Check that intermediate result object passed into the callback
+        # function contains the expected information and that raising
+        # `StopIteration` causes the expected behavior.
+        maxiter = 10
+
+        def func(x):
+            val = rosen(x)
+            if val < func.val:
+                func.x = x
+                func.val = val
+            return val
+        func.x = None
+        func.val = np.inf
+
+        def callback(intermediate_result):
+            callback.nit += 1
+            callback.intermediate_result = intermediate_result
+            assert intermediate_result.population.ndim == 2
+            assert intermediate_result.population.shape[1] == 2
+            assert intermediate_result.nit == callback.nit
+
+            # Check that `x` and `fun` attributes are the best found so far
+            assert_equal(intermediate_result.x, callback.func.x)
+            assert_equal(intermediate_result.fun, callback.func.val)
+
+            # Check for consistency between `fun`, `population_energies`,
+            # `x`, and `population`
+            assert_equal(intermediate_result.fun, rosen(intermediate_result.x))
+            for i in range(len(intermediate_result.population_energies)):
+                res = intermediate_result.population_energies[i]
+                ref = rosen(intermediate_result.population[i])
+                assert_equal(res, ref)
+            assert_equal(intermediate_result.x,
+                         intermediate_result.population[0])
+            assert_equal(intermediate_result.fun,
+                         intermediate_result.population_energies[0])
+
+            assert intermediate_result.message == 'in progress'
+            assert intermediate_result.success is True
+            assert isinstance(intermediate_result, OptimizeResult)
+            if callback.nit == maxiter:
+                raise StopIteration
+        callback.nit = 0
+        callback.intermediate_result = None
+        callback.func = func
+
+        bounds = [(0, 2), (0, 2)]
+        kwargs = dict(func=func, bounds=bounds, seed=838245, polish=False)
+        res = differential_evolution(**kwargs, callback=callback)
+        ref = differential_evolution(**kwargs, maxiter=maxiter)
+
+        # Check that final `intermediate_result` is equivalent to returned
+        # result object and that terminating with callback `StopIteration`
+        # after `maxiter` iterations is equivalent to terminating with
+        # `maxiter` parameter.
+        assert res.success is ref.success is False
+        assert callback.nit == res.nit == maxiter
+        assert res.message == 'callback function requested stop early'
+        assert ref.message == 'Maximum number of iterations has been exceeded.'
+        for field, val in ref.items():
+            if field in {'message', 'success'}:  # checked separately
+                continue
+            assert_equal(callback.intermediate_result[field], val)
+            assert_equal(res[field], val)
+
+        # Check that polish occurs after `StopIteration` as advertised
+        callback.nit = 0
+        func.val = np.inf
+        kwargs['polish'] = True
+        res = differential_evolution(**kwargs, callback=callback)
+        assert res.fun < ref.fun
+
+    def test_callback_terminates(self):
+        # test that if the callback returns true, then the minimization halts
+        bounds = [(0, 2), (0, 2)]
+        expected_msg = 'callback function requested stop early'
+        def callback_python_true(param, convergence=0.):
+            return True
+
+        result = differential_evolution(
+            rosen, bounds, callback=callback_python_true
+        )
+        assert_string_equal(result.message, expected_msg)
+
+        # if callback raises StopIteration then solve should be interrupted
+        def callback_stop(intermediate_result):
+            raise StopIteration
+
+        result = differential_evolution(rosen, bounds, callback=callback_stop)
+        assert not result.success
+
+        def callback_evaluates_true(param, convergence=0.):
+            # DE should stop if bool(self.callback) is True
+            return [10]
+
+        result = differential_evolution(rosen, bounds, callback=callback_evaluates_true)
+        assert_string_equal(result.message, expected_msg)
+        assert not result.success
+
+        def callback_evaluates_false(param, convergence=0.):
+            return []
+
+        result = differential_evolution(rosen, bounds,
+                                        callback=callback_evaluates_false)
+        assert result.success
+
+    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
+        # 47 function evaluations is not a multiple of the population size,
+        # so maxfun is reached partway through a population evaluation.
+        solver = DifferentialEvolutionSolver(rosen,
+                                             self.bounds,
+                                             popsize=5,
+                                             polish=False,
+                                             maxfun=47,
+                                             updating='deferred')
+        result = solver.solve()
+
+        assert_equal(result.nfev, 47)
+        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)
+
+    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', 'sobol', 'halton']
+        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)))
+
+        solver.init_population_qmc(qmc_engine='halton')
+        assert_equal(solver._nfev, 0)
+        assert_(np.all(np.isinf(solver.population_energies)))
+
+        solver = DifferentialEvolutionSolver(rosen, self.bounds, init='sobol')
+        solver.init_population_qmc(qmc_engine='sobol')
+        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})
+
+        # provide an initial solution
+        # bounds are [(0, 2), (0, 2)]
+        x0 = np.random.uniform(low=0.0, high=2.0, size=2)
+        solver = DifferentialEvolutionSolver(
+            rosen, self.bounds, x0=x0
+        )
+        # parameters are scaled to unit interval
+        assert_allclose(solver.population[0], x0 / 2.0)
+
+    def test_x0(self):
+        # smoke test that checks that x0 is usable.
+        res = differential_evolution(rosen, self.bounds, x0=[0.2, 0.8])
+        assert res.success
+
+        # check what happens if some of the x0 lay outside the bounds
+        with assert_raises(ValueError):
+            differential_evolution(rosen, self.bounds, x0=[0.2, 2.1])
+
+    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()
+
+    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')
+
+        # Safely forking from a multithreaded process is
+        # problematic, and deprecated in Python 3.12, so
+        # we use a slower but portable alternative
+        # see gh-19848
+        ctx = multiprocessing.get_context("spawn")
+        with ctx.Pool(2) as p:
+            # should raise a UserWarning because the updating='immediate'
+            # is being overridden by the workers keyword
+            with warns(UserWarning):
+                with DifferentialEvolutionSolver(rosen, bounds, workers=p.map) as s:
+                    pass
+            assert s._updating == 'deferred'
+
+    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()
+
+    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 np.array([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(np.array([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.
+        xs = [(1.2, 1), (2.0, 2.0), (0.5, 0.5)]
+        vs = [(0.3, 0.64, 0.0), (2.1, 4.2, 0.0), (0, 0, 0)]
+
+        for x, v in zip(xs, vs):
+            cv = solver._constraint_violation_fn(np.array(x))
+            assert_allclose(cv, np.atleast_2d(v))
+
+        # vectorized calculation of a series of solutions
+        assert_allclose(
+            solver._constraint_violation_fn(np.array(xs)), np.array(vs)
+        )
+
+        # the following line is used in _calculate_population_feasibilities.
+        # _constraint_violation_fn returns an (1, M) array when
+        # x.shape == (N,), i.e. a single solution. Therefore this list
+        # comprehension should generate (S, 1, M) array.
+        constraint_violation = np.array([solver._constraint_violation_fn(x)
+                                         for x in np.array(xs)])
+        assert constraint_violation.shape == (3, 1, 3)
+
+        # we need reasonable error messages if the constraint function doesn't
+        # return the right thing
+        def constr_f3(x):
+            # returns (S, M), rather than (M, S)
+            return constr_f2(x).T
+
+        nlc2 = NonlinearConstraint(constr_f3, -np.inf, 1.8)
+        solver = DifferentialEvolutionSolver(rosen, [(0, 2), (0, 2)],
+                                             constraints=(nlc, nlc2),
+                                             vectorized=False)
+        solver.vectorized = True
+        with pytest.raises(
+                RuntimeError, match="An array returned from a Constraint"
+        ):
+            solver._constraint_violation_fn(np.array(xs))
+
+    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)
+
+        for vectorize in [False, True]:
+            solver = DifferentialEvolutionSolver(rosen, [(0, 2), (0, 2)],
+                                                 constraints=(nlc, nlc2),
+                                                 vectorized=vectorize,
+                                                 updating='deferred')
+
+            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]), 0.1, True, np.array([0.0])) is 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 not (fn(1.0, False, np.array([0.5, 0.5]),
+                       1.0, False, np.array([1.0, 0.4])))
+
+    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()
+
+        # check vectorized Bounds constraint
+        xs = np.arange(1, 16).reshape(5, 3)
+        violations = []
+        for x in xs:
+            violations.append(pc.violation(x))
+        np.testing.assert_allclose(pc.violation(xs.T), np.array(violations).T)
+
+        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()
+
+        # check vectorized LinearConstraint, for 7 lots of parameter vectors
+        # with each parameter vector being 4 long, with 3 constraints
+        # xs is the same shape as stored in the differential evolution
+        # population, but it's sent to the violation function as (len(x), M)
+        xs = np.arange(1, 29).reshape(7, 4)
+        violations = []
+        for x in xs:
+            violations.append(pc.violation(x))
+        np.testing.assert_allclose(pc.violation(xs.T), np.array(violations).T)
+
+        pc = _ConstraintWrapper(LinearConstraint(csr_matrix(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):
+            # written in vectorised form to accept an array of (N, S)
+            # returning (M, S)
+            # where N is the number of parameters,
+            # S is the number of solution vectors to be examined,
+            # and M is the number of constraint components
+            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
+
+        xs = [(0.5, 1), (0.5, 1.2), (1.2, 1.2), (0.1, -1.2), (0.1, 2.0)]
+        vs = [(0, 0), (0, 0.1), (0.64, 0), (0.19, 0), (0.01, 1.14)]
+
+        for x, v in zip(xs, vs):
+            assert_allclose(pc.violation(x), v)
+
+        # now check that we can vectorize the constraint wrapper
+        assert_allclose(pc.violation(np.array(xs).T),
+                        np.array(vs).T)
+        assert pc.fun(np.array(xs).T).shape == (2, len(xs))
+        assert pc.violation(np.array(xs).T).shape == (2, len(xs))
+        assert pc.num_constr == 2
+        assert pc.parameter_count == 2
+
+    def test_matrix_linear_constraint(self):
+        # gh20041 supplying an np.matrix to construct a LinearConstraint caused
+        # _ConstraintWrapper to start returning constraint violations of the
+        # wrong shape.
+        with suppress_warnings() as sup:
+            sup.filter(PendingDeprecationWarning)
+            matrix = np.matrix([[1, 1, 1, 1.],
+                                [2, 2, 2, 2.]])
+        lc = LinearConstraint(matrix, 0, 1)
+        x0 = np.ones(4)
+        cw = _ConstraintWrapper(lc, x0)
+        # the shape of the constraint violation should be the same as the number
+        # of constraints applied.
+        assert cw.violation(x0).shape == (2,)
+
+        # let's try a vectorised violation call.
+        xtrial = np.arange(4 * 5).reshape(4, 5)
+        assert cw.violation(xtrial).shape == (2, 5)
+
+
+    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, atol=6e-4)
+        assert res.success
+        assert_allclose(res.x, x_opt, atol=6e-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 using a sparse matrix for the LinearConstraint instead of an
+        # array
+
+        L = LinearConstraint(csr_matrix(A), -np.inf, b)
+
+        # using a lower popsize to speed the test up
+        res = differential_evolution(f, bounds, strategy='best1bin', seed=1234,
+                                     constraints=(L), popsize=2)
+
+        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=6e-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)
+
+        # use higher tol here for 32-bit Windows, see gh-11693
+        if (platform.system() == 'Windows' and np.dtype(np.intp).itemsize < 8):
+            assert_allclose(res.x, x_opt, rtol=2.4e-6, atol=0.0035)
+        else:
+            # tolerance determined from macOS + MKL failure, see gh-12701
+            assert_allclose(res.x, x_opt, rtol=5e-6, atol=0.0024)
+
+        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
+        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)
+            # original Lampinen test was with rand1bin, but that takes a
+            # huge amount of CPU time. Changing strategy to best1bin speeds
+            # things up a lot
+            res = differential_evolution(f, bounds, strategy='best1bin',
+                                         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]))
+
+    def test_integrality(self):
+        # test fitting discrete distribution to data
+        rng = np.random.default_rng(6519843218105)
+        dist = stats.nbinom
+        shapes = (5, 0.5)
+        x = dist.rvs(*shapes, size=10000, random_state=rng)
+
+        def func(p, *args):
+            dist, x = args
+            # negative log-likelihood function
+            ll = -np.log(dist.pmf(x, *p)).sum(axis=-1)
+            if np.isnan(ll):  # occurs when x is outside of support
+                ll = np.inf  # we don't want that
+            return ll
+
+        integrality = [True, False]
+        bounds = [(1, 18), (0, 0.95)]
+
+        res = differential_evolution(func, bounds, args=(dist, x),
+                                     integrality=integrality, polish=False,
+                                     seed=rng)
+        # tolerance has to be fairly relaxed for the second parameter
+        # because we're fitting a distribution to random variates.
+        assert res.x[0] == 5
+        assert_allclose(res.x, shapes, rtol=0.025)
+
+        # check that we can still use integrality constraints with polishing
+        res2 = differential_evolution(func, bounds, args=(dist, x),
+                                      integrality=integrality, polish=True,
+                                      seed=rng)
+
+        def func2(p, *args):
+            n, dist, x = args
+            return func(np.array([n, p[0]]), dist, x)
+
+        # compare the DE derived solution to an LBFGSB solution (that doesn't
+        # have to find the integral values). Note we're setting x0 to be the
+        # output from the first DE result, thereby making the polishing step
+        # and this minimisation pretty much equivalent.
+        LBFGSB = minimize(func2, res2.x[1], args=(5, dist, x),
+                          bounds=[(0, 0.95)])
+        assert_allclose(res2.x[1], LBFGSB.x)
+        assert res2.fun <= res.fun
+
+    def test_integrality_limits(self):
+        def f(x):
+            return x
+
+        integrality = [True, False, True]
+        bounds = [(0.2, 1.1), (0.9, 2.2), (3.3, 4.9)]
+
+        # no integrality constraints
+        solver = DifferentialEvolutionSolver(f, bounds=bounds, polish=False,
+                                             integrality=False)
+        assert_allclose(solver.limits[0], [0.2, 0.9, 3.3])
+        assert_allclose(solver.limits[1], [1.1, 2.2, 4.9])
+
+        # with integrality constraints
+        solver = DifferentialEvolutionSolver(f, bounds=bounds, polish=False,
+                                             integrality=integrality)
+        assert_allclose(solver.limits[0], [0.5, 0.9, 3.5])
+        assert_allclose(solver.limits[1], [1.5, 2.2, 4.5])
+        assert_equal(solver.integrality, [True, False, True])
+        assert solver.polish is False
+
+        bounds = [(-1.2, -0.9), (0.9, 2.2), (-10.3, 4.1)]
+        solver = DifferentialEvolutionSolver(f, bounds=bounds, polish=False,
+                                             integrality=integrality)
+        assert_allclose(solver.limits[0], [-1.5, 0.9, -10.5])
+        assert_allclose(solver.limits[1], [-0.5, 2.2, 4.5])
+
+        # A lower bound of -1.2 is converted to
+        # np.nextafter(np.ceil(-1.2) - 0.5, np.inf)
+        # with a similar process to the upper bound. Check that the
+        # conversions work
+        assert_allclose(np.round(solver.limits[0]), [-1.0, 1.0, -10.0])
+        assert_allclose(np.round(solver.limits[1]), [-1.0, 2.0, 4.0])
+
+        bounds = [(-10.2, -8.1), (0.9, 2.2), (-10.9, -9.9999)]
+        solver = DifferentialEvolutionSolver(f, bounds=bounds, polish=False,
+                                             integrality=integrality)
+        assert_allclose(solver.limits[0], [-10.5, 0.9, -10.5])
+        assert_allclose(solver.limits[1], [-8.5, 2.2, -9.5])
+
+        bounds = [(-10.2, -10.1), (0.9, 2.2), (-10.9, -9.9999)]
+        with pytest.raises(ValueError, match='One of the integrality'):
+            DifferentialEvolutionSolver(f, bounds=bounds, polish=False,
+                                        integrality=integrality)
+
+    def test_vectorized(self):
+        def quadratic(x):
+            return np.sum(x**2)
+
+        def quadratic_vec(x):
+            return np.sum(x**2, axis=0)
+
+        # A vectorized function needs to accept (len(x), S) and return (S,)
+        with pytest.raises(RuntimeError, match='The vectorized function'):
+            differential_evolution(quadratic, self.bounds,
+                                   vectorized=True, updating='deferred')
+
+        # vectorized overrides the updating keyword, check for warning
+        with warns(UserWarning, match="differential_evolution: the 'vector"):
+            differential_evolution(quadratic_vec, self.bounds,
+                                   vectorized=True)
+
+        # vectorized defers to the workers keyword, check for warning
+        with warns(UserWarning, match="differential_evolution: the 'workers"):
+            differential_evolution(quadratic_vec, self.bounds,
+                                   vectorized=True, workers=map,
+                                   updating='deferred')
+
+        ncalls = [0]
+
+        def rosen_vec(x):
+            ncalls[0] += 1
+            return rosen(x)
+
+        bounds = [(0, 10), (0, 10)]
+        res1 = differential_evolution(rosen, bounds, updating='deferred',
+                                      seed=1)
+        res2 = differential_evolution(rosen_vec, bounds, vectorized=True,
+                                      updating='deferred', seed=1)
+
+        # the two minimisation runs should be functionally equivalent
+        assert_allclose(res1.x, res2.x)
+        assert ncalls[0] == res2.nfev
+        assert res1.nit == res2.nit
+
+    def test_vectorized_constraints(self):
+        def constr_f(x):
+            return np.array([x[0] + x[1]])
+
+        def constr_f2(x):
+            return np.array([x[0]**2 + x[1], x[0] - x[1]])
+
+        nlc1 = NonlinearConstraint(constr_f, -np.inf, 1.9)
+        nlc2 = NonlinearConstraint(constr_f2, (0.9, 0.5), (2.0, 2.0))
+
+        def rosen_vec(x):
+            # accept an (len(x0), S) array, returning a (S,) array
+            v = 100 * (x[1:] - x[:-1]**2.0)**2.0
+            v += (1 - x[:-1])**2.0
+            return np.squeeze(v)
+
+        bounds = [(0, 10), (0, 10)]
+
+        res1 = differential_evolution(rosen, bounds, updating='deferred',
+                                      seed=1, constraints=[nlc1, nlc2],
+                                      polish=False)
+        res2 = differential_evolution(rosen_vec, bounds, vectorized=True,
+                                      updating='deferred', seed=1,
+                                      constraints=[nlc1, nlc2],
+                                      polish=False)
+        # the two minimisation runs should be functionally equivalent
+        assert_allclose(res1.x, res2.x)
+
+    def test_constraint_violation_error_message(self):
+
+        def func(x):
+            return np.cos(x[0]) + np.sin(x[1])
+
+        # Intentionally infeasible constraints.
+        c0 = NonlinearConstraint(lambda x: x[1] - (x[0]-1)**2, 0, np.inf)
+        c1 = NonlinearConstraint(lambda x: x[1] + x[0]**2, -np.inf, 0)
+
+        result = differential_evolution(func,
+                                        bounds=[(-1, 2), (-1, 1)],
+                                        constraints=[c0, c1],
+                                        maxiter=10,
+                                        polish=False,
+                                        seed=864197532)
+        assert result.success is False
+        # The numerical value in the error message might be sensitive to
+        # changes in the implementation.  It can be updated if the code is
+        # changed.  The essential part of the test is that there is a number
+        # after the '=', so if necessary, the text could be reduced to, say,
+        # "MAXCV = 0.".
+        assert "MAXCV = 0.414" in result.message
+
+    def test_strategy_fn(self):
+        # examines ability to customize strategy by mimicking one of the
+        # in-built strategies and comparing to the actual in-built strategy.
+        parameter_count = 4
+        popsize = 10
+        bounds = [(0, 10.)] * parameter_count
+        total_popsize = parameter_count * popsize
+        mutation = 0.8
+        recombination = 0.7
+
+        def custom_strategy_fn(candidate, population, rng=None):
+            trial = np.copy(population[candidate])
+            fill_point = rng.choice(parameter_count)
+
+            pool = np.arange(total_popsize)
+            rng.shuffle(pool)
+
+            idxs = []
+            while len(idxs) < 2 and len(pool) > 0:
+                idx = pool[0]
+                pool = pool[1:]
+                if idx != candidate:
+                    idxs.append(idx)
+
+            r0, r1 = idxs[:2]
+
+            bprime = (population[0] + mutation *
+                    (population[r0] - population[r1]))
+
+            crossovers = rng.uniform(size=parameter_count)
+            crossovers = crossovers < recombination
+            crossovers[fill_point] = True
+            trial = np.where(crossovers, bprime, trial)
+            return trial
+
+        solver = DifferentialEvolutionSolver(
+            rosen,
+            bounds,
+            popsize=popsize,
+            recombination=recombination,
+            mutation=mutation,
+            maxiter=2,
+            strategy=custom_strategy_fn,
+            seed=10,
+            polish=False
+        )
+        assert solver.strategy is custom_strategy_fn
+        res = solver.solve()
+
+        res2 = differential_evolution(
+            rosen,
+            bounds,
+            mutation=mutation,
+            popsize=popsize,
+            recombination=recombination,
+            maxiter=2,
+            strategy='best1bin',
+            polish=False,
+            seed=10
+        )
+        assert_allclose(res.population, res2.population)
+        assert_allclose(res.x, res2.x)
+
+        def custom_strategy_fn(candidate, population, rng=None):
+            return np.array([1.0, 2.0])
+
+        with pytest.raises(RuntimeError, match="strategy*"):
+            differential_evolution(
+                rosen,
+                bounds,
+                strategy=custom_strategy_fn
+            )

venv/lib/python3.10/site-packages/scipy/optimize/tests/test__root.py

@@ -0,0 +1,123 @@
+"""
+Unit tests for optimization routines from _root.py.
+"""
+from numpy.testing import assert_, assert_equal
+import pytest
+from pytest import raises as assert_raises, warns as assert_warns
+import numpy as np
+
+from scipy.optimize import root
+
+
+class TestRoot:
+    def test_tol_parameter(self):
+        # Check that the minimize() tol= argument does something
+        def func(z):
+            x, y = z
+            return np.array([x**3 - 1, y**3 - 1])
+
+        def dfunc(z):
+            x, y = z
+            return np.array([[3*x**2, 0], [0, 3*y**2]])
+
+        for method in ['hybr', 'lm', 'broyden1', 'broyden2', 'anderson',
+                       'diagbroyden', 'krylov']:
+            if method in ('linearmixing', 'excitingmixing'):
+                # doesn't converge
+                continue
+
+            if method in ('hybr', 'lm'):
+                jac = dfunc
+            else:
+                jac = None
+
+            sol1 = root(func, [1.1,1.1], jac=jac, tol=1e-4, method=method)
+            sol2 = root(func, [1.1,1.1], jac=jac, tol=0.5, method=method)
+            msg = f"{method}: {func(sol1.x)} vs. {func(sol2.x)}"
+            assert_(sol1.success, msg)
+            assert_(sol2.success, msg)
+            assert_(abs(func(sol1.x)).max() < abs(func(sol2.x)).max(),
+                    msg)
+
+    def test_tol_norm(self):
+
+        def norm(x):
+            return abs(x[0])
+
+        for method in ['excitingmixing',
+                       'diagbroyden',
+                       'linearmixing',
+                       'anderson',
+                       'broyden1',
+                       'broyden2',
+                       'krylov']:
+
+            root(np.zeros_like, np.zeros(2), method=method,
+                options={"tol_norm": norm})
+
+    def test_minimize_scalar_coerce_args_param(self):
+        # github issue #3503
+        def func(z, f=1):
+            x, y = z
+            return np.array([x**3 - 1, y**3 - f])
+        root(func, [1.1, 1.1], args=1.5)
+
+    def test_f_size(self):
+        # gh8320
+        # check that decreasing the size of the returned array raises an error
+        # and doesn't segfault
+        class fun:
+            def __init__(self):
+                self.count = 0
+
+            def __call__(self, x):
+                self.count += 1
+
+                if not (self.count % 5):
+                    ret = x[0] + 0.5 * (x[0] - x[1]) ** 3 - 1.0
+                else:
+                    ret = ([x[0] + 0.5 * (x[0] - x[1]) ** 3 - 1.0,
+                           0.5 * (x[1] - x[0]) ** 3 + x[1]])
+
+                return ret
+
+        F = fun()
+        with assert_raises(ValueError):
+            root(F, [0.1, 0.0], method='lm')
+
+    def test_gh_10370(self):
+        # gh-10370 reported that passing both `args` and `jac` to `root` with
+        # `method='krylov'` caused a failure. Ensure that this is fixed whether
+        # the gradient is passed via `jac` or as a second output of `fun`.
+        def fun(x, ignored):
+            return [3*x[0] - 0.25*x[1]**2 + 10, 0.1*x[0]**2 + 5*x[1] - 2]
+
+        def grad(x, ignored):
+            return [[3, 0.5 * x[1]], [0.2 * x[0], 5]]
+
+        def fun_grad(x, ignored):
+            return fun(x, ignored), grad(x, ignored)
+
+        x0 = np.zeros(2)
+
+        ref = root(fun, x0, args=(1,), method='krylov')
+        message = 'Method krylov does not use the jacobian'
+        with assert_warns(RuntimeWarning, match=message):
+            res1 = root(fun, x0, args=(1,), method='krylov', jac=grad)
+        with assert_warns(RuntimeWarning, match=message):
+            res2 = root(fun_grad, x0, args=(1,), method='krylov', jac=True)
+
+        assert_equal(res1.x, ref.x)
+        assert_equal(res2.x, ref.x)
+        assert res1.success is res2.success is ref.success is True
+    
+    @pytest.mark.parametrize("method", ["hybr", "lm", "broyden1", "broyden2",
+                                        "anderson", "linearmixing",
+                                        "diagbroyden", "excitingmixing",
+                                        "krylov", "df-sane"])
+    def test_method_in_result(self, method):
+        def func(x):
+            return x - 1
+        
+        res = root(func, x0=[1], method=method)
+        assert res.method == method

venv/lib/python3.10/site-packages/scipy/optimize/tests/test_isotonic_regression.py

@@ -0,0 +1,165 @@
+import numpy as np
+from numpy.testing import assert_allclose, assert_equal
+import pytest
+
+from scipy.optimize._pava_pybind import pava
+from scipy.optimize import isotonic_regression
+
+
+class TestIsotonicRegression:
+    @pytest.mark.parametrize(
+        ("y", "w", "msg"),
+        [
+            ([[0, 1]], None,
+             "array has incorrect number of dimensions: 2; expected 1"),
+            ([0, 1], [[1, 2]],
+             "Input arrays y and w must have one dimension of equal length"),
+            ([0, 1], [1],
+             "Input arrays y and w must have one dimension of equal length"),
+            (1, 2,
+             "Input arrays y and w must have one dimension of equal length"),
+            ([0, 1], [0, 1],
+             "Weights w must be strictly positive"),
+        ]
+    )
+    def test_raise_error(self, y, w, msg):
+        with pytest.raises(ValueError, match=msg):
+            isotonic_regression(y=y, weights=w)
+
+    def test_simple_pava(self):
+        # Test case of Busing 2020
+        # https://doi.org/10.18637/jss.v102.c01
+        y = np.array([8, 4, 8, 2, 2, 0, 8], dtype=np.float64)
+        w = np.ones_like(y)
+        r = np.full(shape=y.shape[0] + 1, fill_value=-1, dtype=np.intp)
+        pava(y, w, r)
+        assert_allclose(y, [4, 4, 4, 4, 4, 4, 8])
+        # Only first 2 elements of w are changed.
+        assert_allclose(w, [6, 1, 1, 1, 1, 1, 1])
+        # Only first 3 elements of r are changed.
+        assert_allclose(r, [0, 6, 7, -1, -1, -1, -1, -1])
+
+    @pytest.mark.parametrize("y_dtype", [np.float64, np.float32, np.int64, np.int32])
+    @pytest.mark.parametrize("w_dtype", [np.float64, np.float32, np.int64, np.int32])
+    @pytest.mark.parametrize("w", [None, "ones"])
+    def test_simple_isotonic_regression(self, w, w_dtype, y_dtype):
+        # Test case of Busing 2020
+        # https://doi.org/10.18637/jss.v102.c01
+        y = np.array([8, 4, 8, 2, 2, 0, 8], dtype=y_dtype)
+        if w is not None:
+            w = np.ones_like(y, dtype=w_dtype)
+        res = isotonic_regression(y, weights=w)
+        assert res.x.dtype == np.float64
+        assert res.weights.dtype == np.float64
+        assert_allclose(res.x, [4, 4, 4, 4, 4, 4, 8])
+        assert_allclose(res.weights, [6, 1])
+        assert_allclose(res.blocks, [0, 6, 7])
+        # Assert that y was not overwritten
+        assert_equal(y, np.array([8, 4, 8, 2, 2, 0, 8], dtype=np.float64))
+
+    @pytest.mark.parametrize("increasing", [True, False])
+    def test_linspace(self, increasing):
+        n = 10
+        y = np.linspace(0, 1, n) if increasing else np.linspace(1, 0, n)
+        res = isotonic_regression(y, increasing=increasing)
+        assert_allclose(res.x, y)
+        assert_allclose(res.blocks, np.arange(n + 1))
+
+    def test_weights(self):
+        w = np.array([1, 2, 5, 0.5, 0.5, 0.5, 1, 3])
+        y = np.array([3, 2, 1, 10, 9, 8, 20, 10])
+        res = isotonic_regression(y, weights=w)
+        assert_allclose(res.x, [12/8, 12/8, 12/8, 9, 9, 9, 50/4, 50/4])
+        assert_allclose(res.weights, [8, 1.5, 4])
+        assert_allclose(res.blocks, [0, 3, 6, 8])
+
+        # weights are like repeated observations, we repeat the 3rd element 5
+        # times.
+        w2 = np.array([1, 2, 1, 1, 1, 1, 1, 0.5, 0.5, 0.5, 1, 3])
+        y2 = np.array([3, 2, 1, 1, 1, 1, 1, 10, 9, 8, 20, 10])
+        res2 = isotonic_regression(y2, weights=w2)
+        assert_allclose(np.diff(res2.x[0:7]), 0)
+        assert_allclose(res2.x[4:], res.x)
+        assert_allclose(res2.weights, res.weights)
+        assert_allclose(res2.blocks[1:] - 4, res.blocks[1:])
+
+    def test_against_R_monotone(self):
+        y = [0, 6, 8, 3, 5, 2, 1, 7, 9, 4]
+        res = isotonic_regression(y)
+        # R code
+        # library(monotone)
+        # options(digits=8)
+        # monotone(c(0, 6, 8, 3, 5, 2, 1, 7, 9, 4))
+        x_R = [
+            0, 4.1666667, 4.1666667, 4.1666667, 4.1666667, 4.1666667,
+            4.1666667, 6.6666667, 6.6666667, 6.6666667,
+        ]
+        assert_allclose(res.x, x_R)
+        assert_equal(res.blocks, [0, 1, 7, 10])
+
+        n = 100
+        y = np.linspace(0, 1, num=n, endpoint=False)
+        y = 5 * y + np.sin(10 * y)
+        res = isotonic_regression(y)
+        # R code
+        # library(monotone)
+        # n <- 100
+        # y <- 5 * ((1:n)-1)/n + sin(10 * ((1:n)-1)/n)
+        # options(digits=8)
+        # monotone(y)
+        x_R = [
+            0.00000000, 0.14983342, 0.29866933, 0.44552021, 0.58941834, 0.72942554,
+            0.86464247, 0.99421769, 1.11735609, 1.23332691, 1.34147098, 1.44120736,
+            1.53203909, 1.57081100, 1.57081100, 1.57081100, 1.57081100, 1.57081100,
+            1.57081100, 1.57081100, 1.57081100, 1.57081100, 1.57081100, 1.57081100,
+            1.57081100, 1.57081100, 1.57081100, 1.57081100, 1.57081100, 1.57081100,
+            1.57081100, 1.57081100, 1.57081100, 1.57081100, 1.57081100, 1.57081100,
+            1.57081100, 1.57081100, 1.57081100, 1.57081100, 1.57081100, 1.57081100,
+            1.57081100, 1.57081100, 1.57081100, 1.57081100, 1.57081100, 1.57081100,
+            1.57081100, 1.57081100, 1.57081100, 1.62418532, 1.71654534, 1.81773256,
+            1.92723551, 2.04445967, 2.16873336, 2.29931446, 2.43539782, 2.57612334,
+            2.72058450, 2.86783750, 3.01691060, 3.16681390, 3.31654920, 3.46511999,
+            3.61154136, 3.75484992, 3.89411335, 4.02843976, 4.15698660, 4.27896904,
+            4.39366786, 4.50043662, 4.59870810, 4.68799998, 4.76791967, 4.83816823,
+            4.86564130, 4.86564130, 4.86564130, 4.86564130, 4.86564130, 4.86564130,
+            4.86564130, 4.86564130, 4.86564130, 4.86564130, 4.86564130, 4.86564130,
+            4.86564130, 4.86564130, 4.86564130, 4.86564130, 4.86564130, 4.86564130,
+            4.86564130, 4.86564130, 4.86564130, 4.86564130,
+        ]
+        assert_allclose(res.x, x_R)
+
+        # Test increasing
+        assert np.all(np.diff(res.x) >= 0)
+
+        # Test balance property: sum(y) == sum(x)
+        assert_allclose(np.sum(res.x), np.sum(y))
+
+        # Reverse order
+        res_inv = isotonic_regression(-y, increasing=False)
+        assert_allclose(-res_inv.x, res.x)
+        assert_equal(res_inv.blocks, res.blocks)
+
+    def test_readonly(self):
+        x = np.arange(3, dtype=float)
+        w = np.ones(3, dtype=float)
+
+        x.flags.writeable = False
+        w.flags.writeable = False
+
+        res = isotonic_regression(x, weights=w)
+        assert np.all(np.isfinite(res.x))
+        assert np.all(np.isfinite(res.weights))
+        assert np.all(np.isfinite(res.blocks))
+
+    def test_non_contiguous_arrays(self):
+        x = np.arange(10, dtype=float)[::3]
+        w = np.ones(10, dtype=float)[::3]
+        assert not x.flags.c_contiguous
+        assert not x.flags.f_contiguous
+        assert not w.flags.c_contiguous
+        assert not w.flags.f_contiguous
+
+        res = isotonic_regression(x, weights=w)
+        assert np.all(np.isfinite(res.x))
+        assert np.all(np.isfinite(res.weights))
+        assert np.all(np.isfinite(res.blocks))

venv/lib/python3.10/site-packages/scipy/optimize/tests/test_linesearch.py

@@ -0,0 +1,314 @@
+"""
+Tests for line search routines
+"""
+from numpy.testing import (assert_equal, assert_array_almost_equal,
+                           assert_array_almost_equal_nulp, assert_warns,
+                           suppress_warnings)
+import scipy.optimize._linesearch as ls
+from scipy.optimize._linesearch import LineSearchWarning
+import numpy as np
+
+
+def assert_wolfe(s, phi, derphi, c1=1e-4, c2=0.9, err_msg=""):
+    """
+    Check that strong Wolfe conditions apply
+    """
+    phi1 = phi(s)
+    phi0 = phi(0)
+    derphi0 = derphi(0)
+    derphi1 = derphi(s)
+    msg = (f"s = {s}; phi(0) = {phi0}; phi(s) = {phi1}; phi'(0) = {derphi0};"
+           f" phi'(s) = {derphi1}; {err_msg}")
+
+    assert phi1 <= phi0 + c1*s*derphi0, "Wolfe 1 failed: " + msg
+    assert abs(derphi1) <= abs(c2*derphi0), "Wolfe 2 failed: " + msg
+
+
+def assert_armijo(s, phi, c1=1e-4, err_msg=""):
+    """
+    Check that Armijo condition applies
+    """
+    phi1 = phi(s)
+    phi0 = phi(0)
+    msg = f"s = {s}; phi(0) = {phi0}; phi(s) = {phi1}; {err_msg}"
+    assert phi1 <= (1 - c1*s)*phi0, msg
+
+
+def assert_line_wolfe(x, p, s, f, fprime, **kw):
+    assert_wolfe(s, phi=lambda sp: f(x + p*sp),
+                 derphi=lambda sp: np.dot(fprime(x + p*sp), p), **kw)
+
+
+def assert_line_armijo(x, p, s, f, **kw):
+    assert_armijo(s, phi=lambda sp: f(x + p*sp), **kw)
+
+
+def assert_fp_equal(x, y, err_msg="", nulp=50):
+    """Assert two arrays are equal, up to some floating-point rounding error"""
+    try:
+        assert_array_almost_equal_nulp(x, y, nulp)
+    except AssertionError as e:
+        raise AssertionError(f"{e}\n{err_msg}") from e
+
+
+class TestLineSearch:
+    # -- scalar functions; must have dphi(0.) < 0
+    def _scalar_func_1(self, s):  # skip name check
+        self.fcount += 1
+        p = -s - s**3 + s**4
+        dp = -1 - 3*s**2 + 4*s**3
+        return p, dp
+
+    def _scalar_func_2(self, s):  # skip name check
+        self.fcount += 1
+        p = np.exp(-4*s) + s**2
+        dp = -4*np.exp(-4*s) + 2*s
+        return p, dp
+
+    def _scalar_func_3(self, s):  # skip name check
+        self.fcount += 1
+        p = -np.sin(10*s)
+        dp = -10*np.cos(10*s)
+        return p, dp
+
+    # -- n-d functions
+
+    def _line_func_1(self, x):  # skip name check
+        self.fcount += 1
+        f = np.dot(x, x)
+        df = 2*x
+        return f, df
+
+    def _line_func_2(self, x):  # skip name check
+        self.fcount += 1
+        f = np.dot(x, np.dot(self.A, x)) + 1
+        df = np.dot(self.A + self.A.T, x)
+        return f, df
+
+    # --
+
+    def setup_method(self):
+        self.scalar_funcs = []
+        self.line_funcs = []
+        self.N = 20
+        self.fcount = 0
+
+        def bind_index(func, idx):
+            # Remember Python's closure semantics!
+            return lambda *a, **kw: func(*a, **kw)[idx]
+
+        for name in sorted(dir(self)):
+            if name.startswith('_scalar_func_'):
+                value = getattr(self, name)
+                self.scalar_funcs.append(
+                    (name, bind_index(value, 0), bind_index(value, 1)))
+            elif name.startswith('_line_func_'):
+                value = getattr(self, name)
+                self.line_funcs.append(
+                    (name, bind_index(value, 0), bind_index(value, 1)))
+
+        np.random.seed(1234)
+        self.A = np.random.randn(self.N, self.N)
+
+    def scalar_iter(self):
+        for name, phi, derphi in self.scalar_funcs:
+            for old_phi0 in np.random.randn(3):
+                yield name, phi, derphi, old_phi0
+
+    def line_iter(self):
+        for name, f, fprime in self.line_funcs:
+            k = 0
+            while k < 9:
+                x = np.random.randn(self.N)
+                p = np.random.randn(self.N)
+                if np.dot(p, fprime(x)) >= 0:
+                    # always pick a descent direction
+                    continue
+                k += 1
+                old_fv = float(np.random.randn())
+                yield name, f, fprime, x, p, old_fv
+
+    # -- Generic scalar searches
+
+    def test_scalar_search_wolfe1(self):
+        c = 0
+        for name, phi, derphi, old_phi0 in self.scalar_iter():
+            c += 1
+            s, phi1, phi0 = ls.scalar_search_wolfe1(phi, derphi, phi(0),
+                                                    old_phi0, derphi(0))
+            assert_fp_equal(phi0, phi(0), name)
+            assert_fp_equal(phi1, phi(s), name)
+            assert_wolfe(s, phi, derphi, err_msg=name)
+
+        assert c > 3  # check that the iterator really works...
+
+    def test_scalar_search_wolfe2(self):
+        for name, phi, derphi, old_phi0 in self.scalar_iter():
+            s, phi1, phi0, derphi1 = ls.scalar_search_wolfe2(
+                phi, derphi, phi(0), old_phi0, derphi(0))
+            assert_fp_equal(phi0, phi(0), name)
+            assert_fp_equal(phi1, phi(s), name)
+            if derphi1 is not None:
+                assert_fp_equal(derphi1, derphi(s), name)
+            assert_wolfe(s, phi, derphi, err_msg=f"{name} {old_phi0:g}")
+
+    def test_scalar_search_wolfe2_with_low_amax(self):
+        def phi(alpha):
+            return (alpha - 5) ** 2
+
+        def derphi(alpha):
+            return 2 * (alpha - 5)
+
+        alpha_star, _, _, derphi_star = ls.scalar_search_wolfe2(phi, derphi, amax=0.001)
+        assert alpha_star is None  # Not converged
+        assert derphi_star is None  # Not converged
+
+    def test_scalar_search_wolfe2_regression(self):
+        # Regression test for gh-12157
+        # This phi has its minimum at alpha=4/3 ~ 1.333.
+        def phi(alpha):
+            if alpha < 1:
+                return - 3*np.pi/2 * (alpha - 1)
+            else:
+                return np.cos(3*np.pi/2 * alpha - np.pi)
+
+        def derphi(alpha):
+            if alpha < 1:
+                return - 3*np.pi/2
+            else:
+                return - 3*np.pi/2 * np.sin(3*np.pi/2 * alpha - np.pi)
+
+        s, _, _, _ = ls.scalar_search_wolfe2(phi, derphi)
+        # Without the fix in gh-13073, the scalar_search_wolfe2
+        # returned s=2.0 instead.
+        assert s < 1.5
+
+    def test_scalar_search_armijo(self):
+        for name, phi, derphi, old_phi0 in self.scalar_iter():
+            s, phi1 = ls.scalar_search_armijo(phi, phi(0), derphi(0))
+            assert_fp_equal(phi1, phi(s), name)
+            assert_armijo(s, phi, err_msg=f"{name} {old_phi0:g}")
+
+    # -- Generic line searches
+
+    def test_line_search_wolfe1(self):
+        c = 0
+        smax = 100
+        for name, f, fprime, x, p, old_f in self.line_iter():
+            f0 = f(x)
+            g0 = fprime(x)
+            self.fcount = 0
+            s, fc, gc, fv, ofv, gv = ls.line_search_wolfe1(f, fprime, x, p,
+                                                           g0, f0, old_f,
+                                                           amax=smax)
+            assert_equal(self.fcount, fc+gc)
+            assert_fp_equal(ofv, f(x))
+            if s is None:
+                continue
+            assert_fp_equal(fv, f(x + s*p))
+            assert_array_almost_equal(gv, fprime(x + s*p), decimal=14)
+            if s < smax:
+                c += 1
+                assert_line_wolfe(x, p, s, f, fprime, err_msg=name)
+
+        assert c > 3  # check that the iterator really works...
+
+    def test_line_search_wolfe2(self):
+        c = 0
+        smax = 512
+        for name, f, fprime, x, p, old_f in self.line_iter():
+            f0 = f(x)
+            g0 = fprime(x)
+            self.fcount = 0
+            with suppress_warnings() as sup:
+                sup.filter(LineSearchWarning,
+                           "The line search algorithm could not find a solution")
+                sup.filter(LineSearchWarning,
+                           "The line search algorithm did not converge")
+                s, fc, gc, fv, ofv, gv = ls.line_search_wolfe2(f, fprime, x, p,
+                                                               g0, f0, old_f,
+                                                               amax=smax)
+            assert_equal(self.fcount, fc+gc)
+            assert_fp_equal(ofv, f(x))
+            assert_fp_equal(fv, f(x + s*p))
+            if gv is not None:
+                assert_array_almost_equal(gv, fprime(x + s*p), decimal=14)
+            if s < smax:
+                c += 1
+                assert_line_wolfe(x, p, s, f, fprime, err_msg=name)
+        assert c > 3  # check that the iterator really works...
+
+    def test_line_search_wolfe2_bounds(self):
+        # See gh-7475
+
+        # For this f and p, starting at a point on axis 0, the strong Wolfe
+        # condition 2 is met if and only if the step length s satisfies
+        # |x + s| <= c2 * |x|
+        def f(x):
+            return np.dot(x, x)
+        def fp(x):
+            return 2 * x
+        p = np.array([1, 0])
+
+        # Smallest s satisfying strong Wolfe conditions for these arguments is 30
+        x = -60 * p
+        c2 = 0.5
+
+        s, _, _, _, _, _ = ls.line_search_wolfe2(f, fp, x, p, amax=30, c2=c2)
+        assert_line_wolfe(x, p, s, f, fp)
+
+        s, _, _, _, _, _ = assert_warns(LineSearchWarning,
+                                        ls.line_search_wolfe2, f, fp, x, p,
+                                        amax=29, c2=c2)
+        assert s is None
+
+        # s=30 will only be tried on the 6th iteration, so this won't converge
+        assert_warns(LineSearchWarning, ls.line_search_wolfe2, f, fp, x, p,
+                     c2=c2, maxiter=5)
+
+    def test_line_search_armijo(self):
+        c = 0
+        for name, f, fprime, x, p, old_f in self.line_iter():
+            f0 = f(x)
+            g0 = fprime(x)
+            self.fcount = 0
+            s, fc, fv = ls.line_search_armijo(f, x, p, g0, f0)
+            c += 1
+            assert_equal(self.fcount, fc)
+            assert_fp_equal(fv, f(x + s*p))
+            assert_line_armijo(x, p, s, f, err_msg=name)
+        assert c >= 9
+
+    # -- More specific tests
+
+    def test_armijo_terminate_1(self):
+        # Armijo should evaluate the function only once if the trial step
+        # is already suitable
+        count = [0]
+
+        def phi(s):
+            count[0] += 1
+            return -s + 0.01*s**2
+        s, phi1 = ls.scalar_search_armijo(phi, phi(0), -1, alpha0=1)
+        assert_equal(s, 1)
+        assert_equal(count[0], 2)
+        assert_armijo(s, phi)
+
+    def test_wolfe_terminate(self):
+        # wolfe1 and wolfe2 should also evaluate the function only a few
+        # times if the trial step is already suitable
+
+        def phi(s):
+            count[0] += 1
+            return -s + 0.05*s**2
+
+        def derphi(s):
+            count[0] += 1
+            return -1 + 0.05*2*s
+
+        for func in [ls.scalar_search_wolfe1, ls.scalar_search_wolfe2]:
+            count = [0]
+            r = func(phi, derphi, phi(0), None, derphi(0))
+            assert r[0] is not None, (r, func)
+            assert count[0] <= 2 + 2, (count, func)
+            assert_wolfe(r[0], phi, derphi, err_msg=str(func))

venv/lib/python3.10/site-packages/scipy/optimize/tests/test_nnls.py

@@ -0,0 +1,318 @@
+import numpy as np
+from numpy.testing import assert_allclose
+from pytest import raises as assert_raises
+from scipy.optimize import nnls
+
+
+class TestNNLS:
+    def setup_method(self):
+        self.rng = np.random.default_rng(1685225766635251)
+
+    def test_nnls(self):
+        a = np.arange(25.0).reshape(-1, 5)
+        x = np.arange(5.0)
+        y = a @ x
+        x, res = nnls(a, y)
+        assert res < 1e-7
+        assert np.linalg.norm((a @ x) - y) < 1e-7
+
+    def test_nnls_tall(self):
+        a = self.rng.uniform(low=-10, high=10, size=[50, 10])
+        x = np.abs(self.rng.uniform(low=-2, high=2, size=[10]))
+        x[::2] = 0
+        b = a @ x
+        xact, rnorm = nnls(a, b, atol=500*np.linalg.norm(a, 1)*np.spacing(1.))
+        assert_allclose(xact, x, rtol=0., atol=1e-10)
+        assert rnorm < 1e-12
+
+    def test_nnls_wide(self):
+        # If too wide then problem becomes too ill-conditioned ans starts
+        # emitting warnings, hence small m, n difference.
+        a = self.rng.uniform(low=-10, high=10, size=[100, 120])
+        x = np.abs(self.rng.uniform(low=-2, high=2, size=[120]))
+        x[::2] = 0
+        b = a @ x
+        xact, rnorm = nnls(a, b, atol=500*np.linalg.norm(a, 1)*np.spacing(1.))
+        assert_allclose(xact, x, rtol=0., atol=1e-10)
+        assert rnorm < 1e-12
+
+    def test_maxiter(self):
+        # test that maxiter argument does stop iterations
+        a = self.rng.uniform(size=(5, 10))
+        b = self.rng.uniform(size=5)
+        with assert_raises(RuntimeError):
+            nnls(a, b, maxiter=1)
+
+    def test_nnls_inner_loop_case1(self):
+        # See gh-20168
+        n = np.array(
+            [3, 2, 0, 1, 1, 1, 3, 8, 14, 16, 29, 23, 41, 47, 53, 57, 67, 76,
+             103, 89, 97, 94, 85, 95, 78, 78, 78, 77, 73, 50, 50, 56, 68, 98,
+             95, 112, 134, 145, 158, 172, 213, 234, 222, 215, 216, 216, 206,
+             183, 135, 156, 110, 92, 63, 60, 52, 29, 20, 16, 12, 5, 5, 5, 1, 2,
+             3, 0, 2])
+        k = np.array(
+            [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
+             0., 0., 0., 0.7205812007860187, 0., 1.4411624015720375,
+             0.7205812007860187, 2.882324803144075, 5.76464960628815,
+             5.76464960628815, 12.249880413362318, 15.132205216506394,
+             20.176273622008523, 27.382085629868712, 48.27894045266326,
+             47.558359251877235, 68.45521407467177, 97.99904330689854,
+             108.0871801179028, 135.46926574777152, 140.51333415327366,
+             184.4687874012208, 171.49832578707245, 205.36564222401535,
+             244.27702706646033, 214.01261663344755, 228.42424064916793,
+             232.02714665309804, 205.36564222401535, 172.9394881886445,
+             191.67459940908097, 162.1307701768542, 153.48379576742198,
+             110.96950492104689, 103.04311171240067, 86.46974409432225,
+             60.528820866025576, 43.234872047161126, 23.779179625938617,
+             24.499760826724636, 17.29394881886445, 11.5292992125763,
+             5.76464960628815, 5.044068405502131, 3.6029060039300935, 0.,
+             2.882324803144075, 0., 0., 0.])
+        d = np.array(
+            [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
+             0., 0., 0., 0.003889242101538, 0., 0.007606268390096, 0.,
+             0.025457371599973, 0.036952882091577, 0., 0.08518359183449,
+             0.048201126400243, 0.196234990022205, 0.144116240157247,
+             0.171145134062442, 0., 0., 0.269555036538714, 0., 0., 0.,
+             0.010893241091872, 0., 0., 0., 0., 0., 0., 0., 0.,
+             0.048167058272886, 0.011238724891049, 0., 0., 0.055162603456078,
+             0., 0., 0., 0., 0.027753339088588, 0., 0., 0., 0., 0., 0., 0., 0.,
+             0., 0.])
+        # The following code sets up a system of equations such that
+        # $k_i-p_i*n_i$ is minimized for $p_i$ with weights $n_i$ and
+        # monotonicity constraints on $p_i$. This translates to a system of
+        # equations of the form $k_i - (d_1 + ... + d_i) * n_i$ and
+        # non-negativity constraints on the $d_i$. If $n_i$ is zero the
+        # system is modified such that $d_i - d_{i+1}$ is then minimized.
+        N = len(n)
+        A = np.diag(n) @ np.tril(np.ones((N, N)))
+        w = n ** 0.5
+
+        nz = (n == 0).nonzero()[0]
+        A[nz, nz] = 1
+        A[nz, np.minimum(nz + 1, N - 1)] = -1
+        w[nz] = 1
+        k[nz] = 0
+        W = np.diag(w)
+
+        # Small perturbations can already make the infinite loop go away (just
+        # uncomment the next line)
+        # k = k + 1e-10 * np.random.normal(size=N)
+        dact, _ = nnls(W @ A, W @ k)
+        assert_allclose(dact, d, rtol=0., atol=1e-10)
+
+    def test_nnls_inner_loop_case2(self):
+        # See gh-20168
+        n = np.array(
+            [1, 0, 1, 2, 2, 2, 3, 3, 5, 4, 14, 14, 19, 26, 36, 42, 36, 64, 64,
+             64, 81, 85, 85, 95, 95, 95, 75, 76, 69, 81, 62, 59, 68, 64, 71, 67,
+             74, 78, 118, 135, 153, 159, 210, 195, 218, 243, 236, 215, 196, 175,
+             185, 149, 144, 103, 104, 75, 56, 40, 32, 26, 17, 9, 12, 8, 2, 1, 1,
+             1])
+        k = np.array(
+            [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
+             0., 0., 0., 0., 0., 0.7064355064917867, 0., 0., 2.11930651947536,
+             0.7064355064917867, 0., 3.5321775324589333, 7.064355064917867,
+             11.302968103868587, 16.95445215580288, 20.486629688261814,
+             20.486629688261814, 37.44108184406469, 55.808405012851146,
+             78.41434122058831, 103.13958394780086, 105.965325973768,
+             125.74552015553803, 149.057891869767, 176.60887662294667,
+             197.09550631120848, 211.930651947536, 204.86629688261814,
+             233.8301526487814, 221.1143135319292, 195.6826352982249,
+             197.80194181770025, 191.4440222592742, 187.91184472681525,
+             144.11284332432447, 131.39700420747232, 116.5618585711448,
+             93.24948685691584, 89.01087381796512, 53.68909849337579,
+             45.211872415474346, 31.083162285638615, 24.72524272721253,
+             16.95445215580288, 9.890097090885014, 9.890097090885014,
+             2.8257420259671466, 2.8257420259671466, 1.4128710129835733,
+             0.7064355064917867, 1.4128710129835733])
+        d = np.array(
+            [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
+             0., 0., 0., 0., 0., 0.0021916146355674473, 0., 0.,
+             0.011252740799789484, 0., 0., 0.037746623295934395,
+             0.03602328132946222, 0.09509167709829734, 0.10505765870204821,
+             0.01391037014274718, 0.0188296228752321, 0.20723559202324254,
+             0.3056220879462608, 0.13304643490426477, 0., 0., 0., 0., 0., 0.,
+             0., 0., 0., 0., 0., 0.043185876949706214, 0.0037266261379722554,
+             0., 0., 0., 0., 0., 0.094797899357143, 0., 0., 0., 0., 0., 0., 0.,
+             0., 0.23450935613672663, 0., 0., 0.07064355064917871])
+        # The following code sets up a system of equations such that
+        # $k_i-p_i*n_i$ is minimized for $p_i$ with weights $n_i$ and
+        # monotonicity constraints on $p_i$. This translates to a system of
+        # equations of the form $k_i - (d_1 + ... + d_i) * n_i$ and
+        # non-negativity constraints on the $d_i$. If $n_i$ is zero the
+        # system is modified such that $d_i - d_{i+1}$ is then minimized.
+        N = len(n)
+        A = np.diag(n) @ np.tril(np.ones((N, N)))
+        w = n ** 0.5
+
+        nz = (n == 0).nonzero()[0]
+        A[nz, nz] = 1
+        A[nz, np.minimum(nz + 1, N - 1)] = -1
+        w[nz] = 1
+        k[nz] = 0
+        W = np.diag(w)
+
+        dact, _ = nnls(W @ A, W @ k, atol=1e-7)
+
+        p = np.cumsum(dact)
+        assert np.all(dact >= 0)
+        assert np.linalg.norm(k - n * p, ord=np.inf) < 28
+        assert_allclose(dact, d, rtol=0., atol=1e-10)
+
+    def test_nnls_gh20302(self):
+        # See gh-20302
+        A = np.array(
+            [0.33408569134321575, 0.11136189711440525, 0.049140798007949286,
+             0.03712063237146841, 0.055680948557202625, 0.16642814595936478,
+             0.11095209730624318, 0.09791993030943345, 0.14793612974165757,
+             0.44380838922497273, 0.11099502671044059, 0.11099502671044059,
+             0.14693672599330593, 0.3329850801313218, 1.498432860590948,
+             0.0832374225132955, 0.11098323001772734, 0.19589481249472837,
+             0.5919105600945457, 3.5514633605672747, 0.06658716751427037,
+             0.11097861252378394, 0.24485832778293645, 0.9248217710315328,
+             6.936163282736496, 0.05547609388181014, 0.11095218776362029,
+             0.29376003042571264, 1.3314262531634435, 11.982836278470993,
+             0.047506113282944136, 0.11084759766020298, 0.3423969672933396,
+             1.8105107617833156, 19.010362998724812, 0.041507335004505576,
+             0.11068622667868154, 0.39074115283013344, 2.361306169145206,
+             28.335674029742474, 0.03682846280947718, 0.11048538842843154,
+             0.4387861797121048, 2.9831054875676517, 40.2719240821633,
+             0.03311278164362387, 0.11037593881207958, 0.4870572300443105,
+             3.6791979604026523, 55.187969406039784, 0.030079304092299915,
+             0.11029078167176636, 0.5353496017200152, 4.448394860761242,
+             73.3985152025605, 0.02545939709595835, 0.11032405408248619,
+             0.6328767609778363, 6.214921713313388, 121.19097340961108,
+             0.022080881724881523, 0.11040440862440762, 0.7307742886903428,
+             8.28033064683057, 186.30743955368786, 0.020715838214945492,
+             0.1104844704797093, 0.7800578384588346, 9.42800814760186,
+             226.27219554244465, 0.01843179728340054, 0.11059078370040323,
+             0.8784095015912599, 11.94380463964355, 322.48272527037585,
+             0.015812787653789077, 0.11068951357652354, 1.0257259848595766,
+             16.27135849574896, 512.5477926160922, 0.014438550529330062,
+             0.11069555405819713, 1.1234754801775881, 19.519316032262093,
+             673.4164031130423, 0.012760770585072577, 0.110593345070629,
+             1.2688431112524712, 24.920367089248398, 971.8943164806875,
+             0.011427556646114315, 0.11046638091243838, 1.413623342459821,
+             30.967408782453557, 1347.0822820367298, 0.010033330264470307,
+             0.11036663290917338, 1.6071533470570285, 40.063087746029936,
+             1983.122843428482, 0.008950061496507258, 0.11038409179025618,
+             1.802244865119193, 50.37194055362024, 2795.642700725923,
+             0.008071078821135658, 0.11030474388885401, 1.9956465761433504,
+             61.80742482572119, 3801.1566267818534, 0.007191031207777556,
+             0.11026247851925586, 2.238160187262168, 77.7718015155818,
+             5366.2543045751445, 0.00636834224248, 0.11038459886965334,
+             2.5328963107984297, 99.49331844784753, 7760.4788389321075,
+             0.005624259098118485, 0.11061042892966355, 2.879742607664547,
+             128.34496770138628, 11358.529641572684, 0.0050354270614989555,
+             0.11077939535297703, 3.2263279459292575, 160.85168205252265,
+             15924.316523199741, 0.0044997853165982555, 0.1109947044760903,
+             3.6244287189055613, 202.60233390369015, 22488.859063309606,
+             0.004023601950058174, 0.1113196539516095, 4.07713905729421,
+             255.6270320242126, 31825.565487014468, 0.0036024117873727094,
+             0.111674765408554, 4.582933773135057, 321.9583486728612,
+             44913.18963986413, 0.003201503089582304, 0.11205260813538065,
+             5.191786833370116, 411.79333489752383, 64857.45024636,
+             0.0028633044552448853, 0.11262330857296549, 5.864295861648949,
+             522.7223161899905, 92521.84996562831, 0.0025691897303891965,
+             0.11304434813712465, 6.584584405106342, 656.5615739804199,
+             129999.19164812315, 0.0022992911894424675, 0.11343169867916175,
+             7.4080129906658305, 828.2026426227864, 183860.98666225857,
+             0.0020449922071108764, 0.11383789952917212, 8.388975556433872,
+             1058.2750599896935, 265097.9025274183, 0.001831274615120854,
+             0.11414945100919989, 9.419351803810935, 1330.564050780237,
+             373223.2162438565, 0.0016363333454631633, 0.11454333418242145,
+             10.6143816579462, 1683.787012481595, 530392.9089317025,
+             0.0014598610433380044, 0.11484240207592301, 11.959688127956882,
+             2132.0874753402027, 754758.9662704318, 0.0012985240015312626,
+             0.11513579480243862, 13.514425358573531, 2715.5160990137824,
+             1083490.9235064993, 0.0011614735761289934, 0.11537304189548002,
+             15.171418602667567, 3415.195870828736, 1526592.554260445,
+             0.0010347472698811352, 0.11554677847006009, 17.080800985009617,
+             4322.412404600832, 2172012.2333119176, 0.0009232988811258664,
+             0.1157201264344419, 19.20004861829407, 5453.349531598553,
+             3075689.135821584, 0.0008228871862975205, 0.11602709326795038,
+             21.65735242414206, 6920.203923780365, 4390869.389638642,
+             0.00073528900066722, 0.11642075843897651, 24.40223571298994,
+             8755.811207598026, 6238515.485413593, 0.0006602764384729194,
+             0.11752920604817965, 27.694443541914293, 11171.386093291572,
+             8948280.260726549, 0.0005935538977939806, 0.11851292825953147,
+             31.325508920763063, 14174.185724149384, 12735505.873148222,
+             0.0005310755355633124, 0.11913794514470308, 35.381052949627765,
+             17987.010118815077, 18157886.71494382, 0.00047239949671590953,
+             0.1190446731724092, 39.71342528048061, 22679.438775422022,
+             25718483.571328573, 0.00041829129789387623, 0.11851586773659825,
+             44.45299332965028, 28542.57147989741, 36391778.63686921,
+             0.00037321512015419886, 0.11880681324908665, 50.0668539579632,
+             36118.26128449941, 51739409.29004541, 0.0003315539616702064,
+             0.1184752823034871, 56.04387059062639, 45383.29960621684,
+             72976345.76679668, 0.00029456064937920213, 0.11831519416731286,
+             62.91195073220101, 57265.53993693082, 103507463.43600245,
+             0.00026301867496859703, 0.11862142241083726, 70.8217262087034,
+             72383.14781936012, 146901598.49939138, 0.00023618734450420032,
+             0.11966825454879482, 80.26535457124461, 92160.51176984518,
+             210125966.835247, 0.00021165918071578316, 0.12043407382728061,
+             90.7169587544247, 116975.56852918258, 299515943.218972,
+             0.00018757727511329545, 0.11992440455576689, 101.49899864101785,
+             147056.26174166967, 423080865.0307836, 0.00016654469159895833,
+             0.11957908856805206, 113.65970431102812, 184937.67016486943,
+             597533612.3026931, 0.00014717439179415048, 0.11872067604728138,
+             126.77899683346702, 231758.58906776624, 841283678.3159915,
+             0.00012868496382376066, 0.1166314722122684, 139.93635237349534,
+             287417.30847929465, 1172231492.6328032, 0.00011225559452625302,
+             0.11427619522772557, 154.0034283704458, 355281.4912295324,
+             1627544511.322488, 9.879511142981067e-05, 0.11295574406808354,
+             170.96532050841535, 442971.0111288653, 2279085852.2580123,
+             8.71257780313587e-05, 0.11192758284428547, 190.35067416684697,
+             554165.2523674504, 3203629323.93623, 7.665069027765277e-05,
+             0.11060694607065294, 211.28835951100046, 690933.608546013,
+             4486577387.093535, 6.734021094824451e-05, 0.10915848194710433,
+             234.24338803525194, 860487.9079859136, 6276829044.8032465,
+             5.9191625040287665e-05, 0.10776821865668373, 259.7454711820425,
+             1071699.0387579766, 8780430224.544102, 5.1856803674907676e-05,
+             0.10606444911641115, 287.1843540288165, 1331126.3723998806,
+             12251687131.5685, 4.503421404759231e-05, 0.10347361247668461,
+             314.7338642485931, 1638796.0697522392, 16944331963.203278,
+             3.90470387455642e-05, 0.1007804070023012, 344.3427560918527,
+             2014064.4865519698, 23392351979.057854, 3.46557661636393e-05,
+             0.10046706610839032, 385.56603915081587, 2533036.2523656,
+             33044724430.235435, 3.148745865254635e-05, 0.1025441570117926,
+             442.09038234164746, 3262712.3882769793, 47815050050.199135,
+             2.9790762078715404e-05, 0.1089845379379672, 527.8068231298969,
+             4375751.903321453, 72035815708.42941, 2.8772639817606534e-05,
+             0.11823636789048445, 643.2048194503195, 5989838.001888927,
+             110764084330.93005, 2.7951691815106586e-05, 0.12903432664913705,
+             788.5500418523591, 8249371.000613411, 171368308481.2427,
+             2.6844392423114212e-05, 0.1392060709754626, 955.6296403631383,
+             11230229.319931043, 262063016295.25085, 2.499458273851386e-05,
+             0.14559344445184325, 1122.7022399726002, 14820229.698461473,
+             388475270970.9214, 2.337386729019776e-05, 0.15294300496886065,
+             1324.8158105672455, 19644861.137128454, 578442936182.7473,
+             2.0081014872174113e-05, 0.14760215298210377, 1436.2385042492353,
+             23923681.729276657, 791311658718.4193, 1.773374462991839e-05,
+             0.14642752940923615, 1600.5596278736678, 29949429.82503553,
+             1112815989293.9326, 1.5303115839590797e-05, 0.14194150045081785,
+             1742.873058605698, 36634451.931305364, 1529085389160.7544,
+             1.3148448731163076e-05, 0.13699368732998807, 1889.5284359054356,
+             44614279.74469635, 2091762812969.9607, 1.1739194407590062e-05,
+             0.13739553134643406, 2128.794599579694, 56462810.11822766,
+             2973783283306.8145, 1.0293367506254706e-05, 0.13533033372723272,
+             2355.372854690074, 70176508.28667311, 4151852759764.441,
+             9.678312586863569e-06, 0.14293577249119244, 2794.531827932675,
+             93528671.31952812, 6215821967224.52, -1.174086323572049e-05,
+             0.1429501325944908, 3139.4804810720925, 118031680.16618933,
+             -6466892421886.174, -2.1188265307407812e-05, 0.1477108290912869,
+             3644.1133424610953, 153900132.62392554, -4828013117542.036,
+             -8.614483025123122e-05, 0.16037100755883044, 4444.386620899393,
+             210846007.89660168, -1766340937974.433, 4.981445776141726e-05,
+             0.16053420251962536, 4997.558254401547, 266327328.4755411,
+             3862250287024.725, 1.8500019169456637e-05, 0.15448417164977674,
+             5402.289867444643, 323399508.1475582, 12152445411933.408,
+             -5.647882376069748e-05, 0.1406372975946189, 5524.633133597753,
+             371512945.9909363, -4162951345292.1514, 2.8048523486337994e-05,
+             0.13183417571186926, 5817.462495763679, 439447252.3728975,
+             9294740538175.03]).reshape(89, 5)
+        b = np.ones(89, dtype=np.float64)
+        sol, rnorm = nnls(A, b)
+        assert_allclose(sol, np.array([0.61124315, 8.22262829, 0., 0., 0.]))
+        assert_allclose(rnorm, 1.0556460808977297)

venv/lib/python3.10/site-packages/scipy/optimize/tests/test_nonlin.py

@@ -0,0 +1,534 @@
+""" Unit tests for nonlinear solvers
+Author: Ondrej Certik
+May 2007
+"""
+from numpy.testing import assert_
+import pytest
+
+from scipy.optimize import _nonlin as nonlin, root
+from scipy.sparse import csr_array
+from numpy import diag, dot
+from numpy.linalg import inv
+import numpy as np
+import scipy
+
+from .test_minpack import pressure_network
+
+SOLVERS = {'anderson': nonlin.anderson,
+           'diagbroyden': nonlin.diagbroyden,
+           'linearmixing': nonlin.linearmixing,
+           'excitingmixing': nonlin.excitingmixing,
+           'broyden1': nonlin.broyden1,
+           'broyden2': nonlin.broyden2,
+           'krylov': nonlin.newton_krylov}
+MUST_WORK = {'anderson': nonlin.anderson, 'broyden1': nonlin.broyden1,
+             'broyden2': nonlin.broyden2, 'krylov': nonlin.newton_krylov}
+
+# ----------------------------------------------------------------------------
+# Test problems
+# ----------------------------------------------------------------------------
+
+
+def F(x):
+    x = np.asarray(x).T
+    d = diag([3, 2, 1.5, 1, 0.5])
+    c = 0.01
+    f = -d @ x - c * float(x.T @ x) * x
+    return f
+
+
+F.xin = [1, 1, 1, 1, 1]
+F.KNOWN_BAD = {}
+F.JAC_KSP_BAD = {}
+F.ROOT_JAC_KSP_BAD = {}
+
+
+def F2(x):
+    return x
+
+
+F2.xin = [1, 2, 3, 4, 5, 6]
+F2.KNOWN_BAD = {'linearmixing': nonlin.linearmixing,
+                'excitingmixing': nonlin.excitingmixing}
+F2.JAC_KSP_BAD = {}
+F2.ROOT_JAC_KSP_BAD = {}
+
+
+def F2_lucky(x):
+    return x
+
+
+F2_lucky.xin = [0, 0, 0, 0, 0, 0]
+F2_lucky.KNOWN_BAD = {}
+F2_lucky.JAC_KSP_BAD = {}
+F2_lucky.ROOT_JAC_KSP_BAD = {}
+
+
+def F3(x):
+    A = np.array([[-2, 1, 0.], [1, -2, 1], [0, 1, -2]])
+    b = np.array([1, 2, 3.])
+    return A @ x - b
+
+
+F3.xin = [1, 2, 3]
+F3.KNOWN_BAD = {}
+F3.JAC_KSP_BAD = {}
+F3.ROOT_JAC_KSP_BAD = {}
+
+
+def F4_powell(x):
+    A = 1e4
+    return [A*x[0]*x[1] - 1, np.exp(-x[0]) + np.exp(-x[1]) - (1 + 1/A)]
+
+
+F4_powell.xin = [-1, -2]
+F4_powell.KNOWN_BAD = {'linearmixing': nonlin.linearmixing,
+                       'excitingmixing': nonlin.excitingmixing,
+                       'diagbroyden': nonlin.diagbroyden}
+# In the extreme case, it does not converge for nolinear problem solved by
+# MINRES and root problem solved by GMRES/BiCGStab/CGS/MINRES/TFQMR when using
+# Krylov method to approximate Jacobian
+F4_powell.JAC_KSP_BAD = {'minres'}
+F4_powell.ROOT_JAC_KSP_BAD = {'gmres', 'bicgstab', 'cgs', 'minres', 'tfqmr'}
+
+
+def F5(x):
+    return pressure_network(x, 4, np.array([.5, .5, .5, .5]))
+
+
+F5.xin = [2., 0, 2, 0]
+F5.KNOWN_BAD = {'excitingmixing': nonlin.excitingmixing,
+                'linearmixing': nonlin.linearmixing,
+                'diagbroyden': nonlin.diagbroyden}
+# In the extreme case, the Jacobian inversion yielded zero vector for nonlinear
+# problem solved by CGS/MINRES and it does not converge for root problem solved
+# by MINRES and when using Krylov method to approximate Jacobian
+F5.JAC_KSP_BAD = {'cgs', 'minres'}
+F5.ROOT_JAC_KSP_BAD = {'minres'}
+
+
+def F6(x):
+    x1, x2 = x
+    J0 = np.array([[-4.256, 14.7],
+                   [0.8394989, 0.59964207]])
+    v = np.array([(x1 + 3) * (x2**5 - 7) + 3*6,
+                  np.sin(x2 * np.exp(x1) - 1)])
+    return -np.linalg.solve(J0, v)
+
+
+F6.xin = [-0.5, 1.4]
+F6.KNOWN_BAD = {'excitingmixing': nonlin.excitingmixing,
+                'linearmixing': nonlin.linearmixing,
+                'diagbroyden': nonlin.diagbroyden}
+F6.JAC_KSP_BAD = {}
+F6.ROOT_JAC_KSP_BAD = {}
+
+
+# ----------------------------------------------------------------------------
+# Tests
+# ----------------------------------------------------------------------------
+
+
+class TestNonlin:
+    """
+    Check the Broyden methods for a few test problems.
+
+    broyden1, broyden2, and newton_krylov must succeed for
+    all functions. Some of the others don't -- tests in KNOWN_BAD are skipped.
+
+    """
+
+    def _check_nonlin_func(self, f, func, f_tol=1e-2):
+        # Test all methods mentioned in the class `KrylovJacobian`
+        if func == SOLVERS['krylov']:
+            for method in ['gmres', 'bicgstab', 'cgs', 'minres', 'tfqmr']:
+                if method in f.JAC_KSP_BAD:
+                    continue
+
+                x = func(f, f.xin, method=method, line_search=None,
+                         f_tol=f_tol, maxiter=200, verbose=0)
+                assert_(np.absolute(f(x)).max() < f_tol)
+
+        x = func(f, f.xin, f_tol=f_tol, maxiter=200, verbose=0)
+        assert_(np.absolute(f(x)).max() < f_tol)
+
+    def _check_root(self, f, method, f_tol=1e-2):
+        # Test Krylov methods
+        if method == 'krylov':
+            for jac_method in ['gmres', 'bicgstab', 'cgs', 'minres', 'tfqmr']:
+                if jac_method in f.ROOT_JAC_KSP_BAD:
+                    continue
+
+                res = root(f, f.xin, method=method,
+                           options={'ftol': f_tol, 'maxiter': 200,
+                                    'disp': 0,
+                                    'jac_options': {'method': jac_method}})
+                assert_(np.absolute(res.fun).max() < f_tol)
+
+        res = root(f, f.xin, method=method,
+                   options={'ftol': f_tol, 'maxiter': 200, 'disp': 0})
+        assert_(np.absolute(res.fun).max() < f_tol)
+
+    @pytest.mark.xfail
+    def _check_func_fail(self, *a, **kw):
+        pass
+
+    @pytest.mark.filterwarnings('ignore::DeprecationWarning')
+    def test_problem_nonlin(self):
+        for f in [F, F2, F2_lucky, F3, F4_powell, F5, F6]:
+            for func in SOLVERS.values():
+                if func in f.KNOWN_BAD.values():
+                    if func in MUST_WORK.values():
+                        self._check_func_fail(f, func)
+                    continue
+                self._check_nonlin_func(f, func)
+
+    @pytest.mark.filterwarnings('ignore::DeprecationWarning')
+    @pytest.mark.parametrize("method", ['lgmres', 'gmres', 'bicgstab', 'cgs',
+                                        'minres', 'tfqmr'])
+    def test_tol_norm_called(self, method):
+        # Check that supplying tol_norm keyword to nonlin_solve works
+        self._tol_norm_used = False
+
+        def local_norm_func(x):
+            self._tol_norm_used = True
+            return np.absolute(x).max()
+
+        nonlin.newton_krylov(F, F.xin, method=method, f_tol=1e-2,
+                             maxiter=200, verbose=0,
+                             tol_norm=local_norm_func)
+        assert_(self._tol_norm_used)
+
+    @pytest.mark.filterwarnings('ignore::DeprecationWarning')
+    def test_problem_root(self):
+        for f in [F, F2, F2_lucky, F3, F4_powell, F5, F6]:
+            for meth in SOLVERS:
+                if meth in f.KNOWN_BAD:
+                    if meth in MUST_WORK:
+                        self._check_func_fail(f, meth)
+                    continue
+                self._check_root(f, meth)
+
+    def test_no_convergence(self):
+        def wont_converge(x):
+            return 1e3 + x
+        
+        with pytest.raises(scipy.optimize.NoConvergence):
+            nonlin.newton_krylov(wont_converge, xin=[0], maxiter=1)
+
+
+class TestSecant:
+    """Check that some Jacobian approximations satisfy the secant condition"""
+
+    xs = [np.array([1., 2., 3., 4., 5.]),
+          np.array([2., 3., 4., 5., 1.]),
+          np.array([3., 4., 5., 1., 2.]),
+          np.array([4., 5., 1., 2., 3.]),
+          np.array([9., 1., 9., 1., 3.]),
+          np.array([0., 1., 9., 1., 3.]),
+          np.array([5., 5., 7., 1., 1.]),
+          np.array([1., 2., 7., 5., 1.]),]
+    fs = [x**2 - 1 for x in xs]
+
+    def _check_secant(self, jac_cls, npoints=1, **kw):
+        """
+        Check that the given Jacobian approximation satisfies secant
+        conditions for last `npoints` points.
+        """
+        jac = jac_cls(**kw)
+        jac.setup(self.xs[0], self.fs[0], None)
+        for j, (x, f) in enumerate(zip(self.xs[1:], self.fs[1:])):
+            jac.update(x, f)
+
+            for k in range(min(npoints, j+1)):
+                dx = self.xs[j-k+1] - self.xs[j-k]
+                df = self.fs[j-k+1] - self.fs[j-k]
+                assert_(np.allclose(dx, jac.solve(df)))
+
+            # Check that the `npoints` secant bound is strict
+            if j >= npoints:
+                dx = self.xs[j-npoints+1] - self.xs[j-npoints]
+                df = self.fs[j-npoints+1] - self.fs[j-npoints]
+                assert_(not np.allclose(dx, jac.solve(df)))
+
+    def test_broyden1(self):
+        self._check_secant(nonlin.BroydenFirst)
+
+    def test_broyden2(self):
+        self._check_secant(nonlin.BroydenSecond)
+
+    def test_broyden1_update(self):
+        # Check that BroydenFirst update works as for a dense matrix
+        jac = nonlin.BroydenFirst(alpha=0.1)
+        jac.setup(self.xs[0], self.fs[0], None)
+
+        B = np.identity(5) * (-1/0.1)
+
+        for last_j, (x, f) in enumerate(zip(self.xs[1:], self.fs[1:])):
+            df = f - self.fs[last_j]
+            dx = x - self.xs[last_j]
+            B += (df - dot(B, dx))[:, None] * dx[None, :] / dot(dx, dx)
+            jac.update(x, f)
+            assert_(np.allclose(jac.todense(), B, rtol=1e-10, atol=1e-13))
+
+    def test_broyden2_update(self):
+        # Check that BroydenSecond update works as for a dense matrix
+        jac = nonlin.BroydenSecond(alpha=0.1)
+        jac.setup(self.xs[0], self.fs[0], None)
+
+        H = np.identity(5) * (-0.1)
+
+        for last_j, (x, f) in enumerate(zip(self.xs[1:], self.fs[1:])):
+            df = f - self.fs[last_j]
+            dx = x - self.xs[last_j]
+            H += (dx - dot(H, df))[:, None] * df[None, :] / dot(df, df)
+            jac.update(x, f)
+            assert_(np.allclose(jac.todense(), inv(H), rtol=1e-10, atol=1e-13))
+
+    def test_anderson(self):
+        # Anderson mixing (with w0=0) satisfies secant conditions
+        # for the last M iterates, see [Ey]_
+        #
+        # .. [Ey] V. Eyert, J. Comp. Phys., 124, 271 (1996).
+        self._check_secant(nonlin.Anderson, M=3, w0=0, npoints=3)
+
+
+class TestLinear:
+    """Solve a linear equation;
+    some methods find the exact solution in a finite number of steps"""
+
+    def _check(self, jac, N, maxiter, complex=False, **kw):
+        np.random.seed(123)
+
+        A = np.random.randn(N, N)
+        if complex:
+            A = A + 1j*np.random.randn(N, N)
+        b = np.random.randn(N)
+        if complex:
+            b = b + 1j*np.random.randn(N)
+
+        def func(x):
+            return dot(A, x) - b
+
+        sol = nonlin.nonlin_solve(func, np.zeros(N), jac, maxiter=maxiter,
+                                  f_tol=1e-6, line_search=None, verbose=0)
+        assert_(np.allclose(dot(A, sol), b, atol=1e-6))
+
+    def test_broyden1(self):
+        # Broyden methods solve linear systems exactly in 2*N steps
+        self._check(nonlin.BroydenFirst(alpha=1.0), 20, 41, False)
+        self._check(nonlin.BroydenFirst(alpha=1.0), 20, 41, True)
+
+    def test_broyden2(self):
+        # Broyden methods solve linear systems exactly in 2*N steps
+        self._check(nonlin.BroydenSecond(alpha=1.0), 20, 41, False)
+        self._check(nonlin.BroydenSecond(alpha=1.0), 20, 41, True)
+
+    def test_anderson(self):
+        # Anderson is rather similar to Broyden, if given enough storage space
+        self._check(nonlin.Anderson(M=50, alpha=1.0), 20, 29, False)
+        self._check(nonlin.Anderson(M=50, alpha=1.0), 20, 29, True)
+
+    def test_krylov(self):
+        # Krylov methods solve linear systems exactly in N inner steps
+        self._check(nonlin.KrylovJacobian, 20, 2, False, inner_m=10)
+        self._check(nonlin.KrylovJacobian, 20, 2, True, inner_m=10)
+
+    def _check_autojac(self, A, b):
+        def func(x):
+            return A.dot(x) - b
+
+        def jac(v):
+            return A
+
+        sol = nonlin.nonlin_solve(func, np.zeros(b.shape[0]), jac, maxiter=2,
+                                  f_tol=1e-6, line_search=None, verbose=0)
+        np.testing.assert_allclose(A @ sol, b, atol=1e-6)
+        # test jac input as array -- not a function
+        sol = nonlin.nonlin_solve(func, np.zeros(b.shape[0]), A, maxiter=2,
+                                  f_tol=1e-6, line_search=None, verbose=0)
+        np.testing.assert_allclose(A @ sol, b, atol=1e-6)
+
+    def test_jac_sparse(self):
+        A = csr_array([[1, 2], [2, 1]])
+        b = np.array([1, -1])
+        self._check_autojac(A, b)
+        self._check_autojac((1 + 2j) * A, (2 + 2j) * b)
+
+    def test_jac_ndarray(self):
+        A = np.array([[1, 2], [2, 1]])
+        b = np.array([1, -1])
+        self._check_autojac(A, b)
+        self._check_autojac((1 + 2j) * A, (2 + 2j) * b)
+
+
+class TestJacobianDotSolve:
+    """
+    Check that solve/dot methods in Jacobian approximations are consistent
+    """
+
+    def _func(self, x):
+        return x**2 - 1 + np.dot(self.A, x)
+
+    def _check_dot(self, jac_cls, complex=False, tol=1e-6, **kw):
+        np.random.seed(123)
+
+        N = 7
+
+        def rand(*a):
+            q = np.random.rand(*a)
+            if complex:
+                q = q + 1j*np.random.rand(*a)
+            return q
+
+        def assert_close(a, b, msg):
+            d = abs(a - b).max()
+            f = tol + abs(b).max()*tol
+            if d > f:
+                raise AssertionError(f'{msg}: err {d:g}')
+
+        self.A = rand(N, N)
+
+        # initialize
+        x0 = np.random.rand(N)
+        jac = jac_cls(**kw)
+        jac.setup(x0, self._func(x0), self._func)
+
+        # check consistency
+        for k in range(2*N):
+            v = rand(N)
+
+            if hasattr(jac, '__array__'):
+                Jd = np.array(jac)
+                if hasattr(jac, 'solve'):
+                    Gv = jac.solve(v)
+                    Gv2 = np.linalg.solve(Jd, v)
+                    assert_close(Gv, Gv2, 'solve vs array')
+                if hasattr(jac, 'rsolve'):
+                    Gv = jac.rsolve(v)
+                    Gv2 = np.linalg.solve(Jd.T.conj(), v)
+                    assert_close(Gv, Gv2, 'rsolve vs array')
+                if hasattr(jac, 'matvec'):
+                    Jv = jac.matvec(v)
+                    Jv2 = np.dot(Jd, v)
+                    assert_close(Jv, Jv2, 'dot vs array')
+                if hasattr(jac, 'rmatvec'):
+                    Jv = jac.rmatvec(v)
+                    Jv2 = np.dot(Jd.T.conj(), v)
+                    assert_close(Jv, Jv2, 'rmatvec vs array')
+
+            if hasattr(jac, 'matvec') and hasattr(jac, 'solve'):
+                Jv = jac.matvec(v)
+                Jv2 = jac.solve(jac.matvec(Jv))
+                assert_close(Jv, Jv2, 'dot vs solve')
+
+            if hasattr(jac, 'rmatvec') and hasattr(jac, 'rsolve'):
+                Jv = jac.rmatvec(v)
+                Jv2 = jac.rmatvec(jac.rsolve(Jv))
+                assert_close(Jv, Jv2, 'rmatvec vs rsolve')
+
+            x = rand(N)
+            jac.update(x, self._func(x))
+
+    def test_broyden1(self):
+        self._check_dot(nonlin.BroydenFirst, complex=False)
+        self._check_dot(nonlin.BroydenFirst, complex=True)
+
+    def test_broyden2(self):
+        self._check_dot(nonlin.BroydenSecond, complex=False)
+        self._check_dot(nonlin.BroydenSecond, complex=True)
+
+    def test_anderson(self):
+        self._check_dot(nonlin.Anderson, complex=False)
+        self._check_dot(nonlin.Anderson, complex=True)
+
+    def test_diagbroyden(self):
+        self._check_dot(nonlin.DiagBroyden, complex=False)
+        self._check_dot(nonlin.DiagBroyden, complex=True)
+
+    def test_linearmixing(self):
+        self._check_dot(nonlin.LinearMixing, complex=False)
+        self._check_dot(nonlin.LinearMixing, complex=True)
+
+    def test_excitingmixing(self):
+        self._check_dot(nonlin.ExcitingMixing, complex=False)
+        self._check_dot(nonlin.ExcitingMixing, complex=True)
+
+    def test_krylov(self):
+        self._check_dot(nonlin.KrylovJacobian, complex=False, tol=1e-3)
+        self._check_dot(nonlin.KrylovJacobian, complex=True, tol=1e-3)
+
+
+class TestNonlinOldTests:
+    """ Test case for a simple constrained entropy maximization problem
+    (the machine translation example of Berger et al in
+    Computational Linguistics, vol 22, num 1, pp 39--72, 1996.)
+    """
+
+    def test_broyden1(self):
+        x = nonlin.broyden1(F, F.xin, iter=12, alpha=1)
+        assert_(nonlin.norm(x) < 1e-9)
+        assert_(nonlin.norm(F(x)) < 1e-9)
+
+    def test_broyden2(self):
+        x = nonlin.broyden2(F, F.xin, iter=12, alpha=1)
+        assert_(nonlin.norm(x) < 1e-9)
+        assert_(nonlin.norm(F(x)) < 1e-9)
+
+    def test_anderson(self):
+        x = nonlin.anderson(F, F.xin, iter=12, alpha=0.03, M=5)
+        assert_(nonlin.norm(x) < 0.33)
+
+    def test_linearmixing(self):
+        x = nonlin.linearmixing(F, F.xin, iter=60, alpha=0.5)
+        assert_(nonlin.norm(x) < 1e-7)
+        assert_(nonlin.norm(F(x)) < 1e-7)
+
+    def test_exciting(self):
+        x = nonlin.excitingmixing(F, F.xin, iter=20, alpha=0.5)
+        assert_(nonlin.norm(x) < 1e-5)
+        assert_(nonlin.norm(F(x)) < 1e-5)
+
+    def test_diagbroyden(self):
+        x = nonlin.diagbroyden(F, F.xin, iter=11, alpha=1)
+        assert_(nonlin.norm(x) < 1e-8)
+        assert_(nonlin.norm(F(x)) < 1e-8)
+
+    def test_root_broyden1(self):
+        res = root(F, F.xin, method='broyden1',
+                   options={'nit': 12, 'jac_options': {'alpha': 1}})
+        assert_(nonlin.norm(res.x) < 1e-9)
+        assert_(nonlin.norm(res.fun) < 1e-9)
+
+    def test_root_broyden2(self):
+        res = root(F, F.xin, method='broyden2',
+                   options={'nit': 12, 'jac_options': {'alpha': 1}})
+        assert_(nonlin.norm(res.x) < 1e-9)
+        assert_(nonlin.norm(res.fun) < 1e-9)
+
+    def test_root_anderson(self):
+        res = root(F, F.xin, method='anderson',
+                   options={'nit': 12,
+                            'jac_options': {'alpha': 0.03, 'M': 5}})
+        assert_(nonlin.norm(res.x) < 0.33)
+
+    def test_root_linearmixing(self):
+        res = root(F, F.xin, method='linearmixing',
+                   options={'nit': 60,
+                            'jac_options': {'alpha': 0.5}})
+        assert_(nonlin.norm(res.x) < 1e-7)
+        assert_(nonlin.norm(res.fun) < 1e-7)
+
+    def test_root_excitingmixing(self):
+        res = root(F, F.xin, method='excitingmixing',
+                   options={'nit': 20,
+                            'jac_options': {'alpha': 0.5}})
+        assert_(nonlin.norm(res.x) < 1e-5)
+        assert_(nonlin.norm(res.fun) < 1e-5)
+
+    def test_root_diagbroyden(self):
+        res = root(F, F.xin, method='diagbroyden',
+                   options={'nit': 11,
+                            'jac_options': {'alpha': 1}})
+        assert_(nonlin.norm(res.x) < 1e-8)
+        assert_(nonlin.norm(res.fun) < 1e-8)

venv/lib/python3.10/site-packages/scipy/optimize/tests/test_trustregion.py

@@ -0,0 +1,112 @@
+"""
+Unit tests for trust-region optimization routines.
+
+To run it in its simplest form::
+  nosetests test_optimize.py
+
+"""
+import pytest
+import numpy as np
+from numpy.testing import assert_, assert_equal, assert_allclose
+from scipy.optimize import (minimize, rosen, rosen_der, rosen_hess,
+                            rosen_hess_prod)
+
+
+class Accumulator:
+    """ This is for testing callbacks."""
+    def __init__(self):
+        self.count = 0
+        self.accum = None
+
+    def __call__(self, x):
+        self.count += 1
+        if self.accum is None:
+            self.accum = np.array(x)
+        else:
+            self.accum += x
+
+
+class TestTrustRegionSolvers:
+
+    def setup_method(self):
+        self.x_opt = [1.0, 1.0]
+        self.easy_guess = [2.0, 2.0]
+        self.hard_guess = [-1.2, 1.0]
+
+    def test_dogleg_accuracy(self):
+        # test the accuracy and the return_all option
+        x0 = self.hard_guess
+        r = minimize(rosen, x0, jac=rosen_der, hess=rosen_hess, tol=1e-8,
+                     method='dogleg', options={'return_all': True},)
+        assert_allclose(x0, r['allvecs'][0])
+        assert_allclose(r['x'], r['allvecs'][-1])
+        assert_allclose(r['x'], self.x_opt)
+
+    def test_dogleg_callback(self):
+        # test the callback mechanism and the maxiter and return_all options
+        accumulator = Accumulator()
+        maxiter = 5
+        r = minimize(rosen, self.hard_guess, jac=rosen_der, hess=rosen_hess,
+                     callback=accumulator, method='dogleg',
+                     options={'return_all': True, 'maxiter': maxiter},)
+        assert_equal(accumulator.count, maxiter)
+        assert_equal(len(r['allvecs']), maxiter+1)
+        assert_allclose(r['x'], r['allvecs'][-1])
+        assert_allclose(sum(r['allvecs'][1:]), accumulator.accum)
+
+    def test_dogleg_user_warning(self):
+        with pytest.warns(RuntimeWarning,
+                          match=r'Maximum number of iterations'):
+            minimize(rosen, self.hard_guess, jac=rosen_der,
+                     hess=rosen_hess, method='dogleg',
+                     options={'disp': True, 'maxiter': 1}, )
+
+    def test_solver_concordance(self):
+        # Assert that dogleg uses fewer iterations than ncg on the Rosenbrock
+        # test function, although this does not necessarily mean
+        # that dogleg is faster or better than ncg even for this function
+        # and especially not for other test functions.
+        f = rosen
+        g = rosen_der
+        h = rosen_hess
+        for x0 in (self.easy_guess, self.hard_guess):
+            r_dogleg = minimize(f, x0, jac=g, hess=h, tol=1e-8,
+                                method='dogleg', options={'return_all': True})
+            r_trust_ncg = minimize(f, x0, jac=g, hess=h, tol=1e-8,
+                                   method='trust-ncg',
+                                   options={'return_all': True})
+            r_trust_krylov = minimize(f, x0, jac=g, hess=h, tol=1e-8,
+                                   method='trust-krylov',
+                                   options={'return_all': True})
+            r_ncg = minimize(f, x0, jac=g, hess=h, tol=1e-8,
+                             method='newton-cg', options={'return_all': True})
+            r_iterative = minimize(f, x0, jac=g, hess=h, tol=1e-8,
+                                   method='trust-exact',
+                                   options={'return_all': True})
+            assert_allclose(self.x_opt, r_dogleg['x'])
+            assert_allclose(self.x_opt, r_trust_ncg['x'])
+            assert_allclose(self.x_opt, r_trust_krylov['x'])
+            assert_allclose(self.x_opt, r_ncg['x'])
+            assert_allclose(self.x_opt, r_iterative['x'])
+            assert_(len(r_dogleg['allvecs']) < len(r_ncg['allvecs']))
+
+    def test_trust_ncg_hessp(self):
+        for x0 in (self.easy_guess, self.hard_guess, self.x_opt):
+            r = minimize(rosen, x0, jac=rosen_der, hessp=rosen_hess_prod,
+                         tol=1e-8, method='trust-ncg')
+            assert_allclose(self.x_opt, r['x'])
+
+    def test_trust_ncg_start_in_optimum(self):
+        r = minimize(rosen, x0=self.x_opt, jac=rosen_der, hess=rosen_hess,
+                     tol=1e-8, method='trust-ncg')
+        assert_allclose(self.x_opt, r['x'])
+
+    def test_trust_krylov_start_in_optimum(self):
+        r = minimize(rosen, x0=self.x_opt, jac=rosen_der, hess=rosen_hess,
+                     tol=1e-8, method='trust-krylov')
+        assert_allclose(self.x_opt, r['x'])
+
+    def test_trust_exact_start_in_optimum(self):
+        r = minimize(rosen, x0=self.x_opt, jac=rosen_der, hess=rosen_hess,
+                     tol=1e-8, method='trust-exact')
+        assert_allclose(self.x_opt, r['x'])

venv/lib/python3.10/site-packages/scipy/optimize/tests/test_trustregion_exact.py

@@ -0,0 +1,352 @@
+"""
+Unit tests for trust-region iterative subproblem.
+
+To run it in its simplest form::
+  nosetests test_optimize.py
+
+"""
+import numpy as np
+from scipy.optimize._trustregion_exact import (
+    estimate_smallest_singular_value,
+    singular_leading_submatrix,
+    IterativeSubproblem)
+from scipy.linalg import (svd, get_lapack_funcs, det, qr, norm)
+from numpy.testing import (assert_array_equal,
+                           assert_equal, assert_array_almost_equal)
+
+
+def random_entry(n, min_eig, max_eig, case):
+
+    # Generate random matrix
+    rand = np.random.uniform(-1, 1, (n, n))
+
+    # QR decomposition
+    Q, _, _ = qr(rand, pivoting='True')
+
+    # Generate random eigenvalues
+    eigvalues = np.random.uniform(min_eig, max_eig, n)
+    eigvalues = np.sort(eigvalues)[::-1]
+
+    # Generate matrix
+    Qaux = np.multiply(eigvalues, Q)
+    A = np.dot(Qaux, Q.T)
+
+    # Generate gradient vector accordingly
+    # to the case is being tested.
+    if case == 'hard':
+        g = np.zeros(n)
+        g[:-1] = np.random.uniform(-1, 1, n-1)
+        g = np.dot(Q, g)
+    elif case == 'jac_equal_zero':
+        g = np.zeros(n)
+    else:
+        g = np.random.uniform(-1, 1, n)
+
+    return A, g
+
+
+class TestEstimateSmallestSingularValue:
+
+    def test_for_ill_condiotioned_matrix(self):
+
+        # Ill-conditioned triangular matrix
+        C = np.array([[1, 2, 3, 4],
+                      [0, 0.05, 60, 7],
+                      [0, 0, 0.8, 9],
+                      [0, 0, 0, 10]])
+
+        # Get svd decomposition
+        U, s, Vt = svd(C)
+
+        # Get smallest singular value and correspondent right singular vector.
+        smin_svd = s[-1]
+        zmin_svd = Vt[-1, :]
+
+        # Estimate smallest singular value
+        smin, zmin = estimate_smallest_singular_value(C)
+
+        # Check the estimation
+        assert_array_almost_equal(smin, smin_svd, decimal=8)
+        assert_array_almost_equal(abs(zmin), abs(zmin_svd), decimal=8)
+
+
+class TestSingularLeadingSubmatrix:
+
+    def test_for_already_singular_leading_submatrix(self):
+
+        # Define test matrix A.
+        # Note that the leading 2x2 submatrix is singular.
+        A = np.array([[1, 2, 3],
+                      [2, 4, 5],
+                      [3, 5, 6]])
+
+        # Get Cholesky from lapack functions
+        cholesky, = get_lapack_funcs(('potrf',), (A,))
+
+        # Compute Cholesky Decomposition
+        c, k = cholesky(A, lower=False, overwrite_a=False, clean=True)
+
+        delta, v = singular_leading_submatrix(A, c, k)
+
+        A[k-1, k-1] += delta
+
+        # Check if the leading submatrix is singular.
+        assert_array_almost_equal(det(A[:k, :k]), 0)
+
+        # Check if `v` fulfil the specified properties
+        quadratic_term = np.dot(v, np.dot(A, v))
+        assert_array_almost_equal(quadratic_term, 0)
+
+    def test_for_simetric_indefinite_matrix(self):
+
+        # Define test matrix A.
+        # Note that the leading 5x5 submatrix is indefinite.
+        A = np.asarray([[1, 2, 3, 7, 8],
+                        [2, 5, 5, 9, 0],
+                        [3, 5, 11, 1, 2],
+                        [7, 9, 1, 7, 5],
+                        [8, 0, 2, 5, 8]])
+
+        # Get Cholesky from lapack functions
+        cholesky, = get_lapack_funcs(('potrf',), (A,))
+
+        # Compute Cholesky Decomposition
+        c, k = cholesky(A, lower=False, overwrite_a=False, clean=True)
+
+        delta, v = singular_leading_submatrix(A, c, k)
+
+        A[k-1, k-1] += delta
+
+        # Check if the leading submatrix is singular.
+        assert_array_almost_equal(det(A[:k, :k]), 0)
+
+        # Check if `v` fulfil the specified properties
+        quadratic_term = np.dot(v, np.dot(A, v))
+        assert_array_almost_equal(quadratic_term, 0)
+
+    def test_for_first_element_equal_to_zero(self):
+
+        # Define test matrix A.
+        # Note that the leading 2x2 submatrix is singular.
+        A = np.array([[0, 3, 11],
+                      [3, 12, 5],
+                      [11, 5, 6]])
+
+        # Get Cholesky from lapack functions
+        cholesky, = get_lapack_funcs(('potrf',), (A,))
+
+        # Compute Cholesky Decomposition
+        c, k = cholesky(A, lower=False, overwrite_a=False, clean=True)
+
+        delta, v = singular_leading_submatrix(A, c, k)
+
+        A[k-1, k-1] += delta
+
+        # Check if the leading submatrix is singular
+        assert_array_almost_equal(det(A[:k, :k]), 0)
+
+        # Check if `v` fulfil the specified properties
+        quadratic_term = np.dot(v, np.dot(A, v))
+        assert_array_almost_equal(quadratic_term, 0)
+
+
+class TestIterativeSubproblem:
+
+    def test_for_the_easy_case(self):
+
+        # `H` is chosen such that `g` is not orthogonal to the
+        # eigenvector associated with the smallest eigenvalue `s`.
+        H = [[10, 2, 3, 4],
+             [2, 1, 7, 1],
+             [3, 7, 1, 7],
+             [4, 1, 7, 2]]
+        g = [1, 1, 1, 1]
+
+        # Trust Radius
+        trust_radius = 1
+
+        # Solve Subproblem
+        subprob = IterativeSubproblem(x=0,
+                                      fun=lambda x: 0,
+                                      jac=lambda x: np.array(g),
+                                      hess=lambda x: np.array(H),
+                                      k_easy=1e-10,
+                                      k_hard=1e-10)
+        p, hits_boundary = subprob.solve(trust_radius)
+
+        assert_array_almost_equal(p, [0.00393332, -0.55260862,
+                                      0.67065477, -0.49480341])
+        assert_array_almost_equal(hits_boundary, True)
+
+    def test_for_the_hard_case(self):
+
+        # `H` is chosen such that `g` is orthogonal to the
+        # eigenvector associated with the smallest eigenvalue `s`.
+        H = [[10, 2, 3, 4],
+             [2, 1, 7, 1],
+             [3, 7, 1, 7],
+             [4, 1, 7, 2]]
+        g = [6.4852641521327437, 1, 1, 1]
+        s = -8.2151519874416614
+
+        # Trust Radius
+        trust_radius = 1
+
+        # Solve Subproblem
+        subprob = IterativeSubproblem(x=0,
+                                      fun=lambda x: 0,
+                                      jac=lambda x: np.array(g),
+                                      hess=lambda x: np.array(H),
+                                      k_easy=1e-10,
+                                      k_hard=1e-10)
+        p, hits_boundary = subprob.solve(trust_radius)
+
+        assert_array_almost_equal(-s, subprob.lambda_current)
+
+    def test_for_interior_convergence(self):
+
+        H = [[1.812159, 0.82687265, 0.21838879, -0.52487006, 0.25436988],
+             [0.82687265, 2.66380283, 0.31508988, -0.40144163, 0.08811588],
+             [0.21838879, 0.31508988, 2.38020726, -0.3166346, 0.27363867],
+             [-0.52487006, -0.40144163, -0.3166346, 1.61927182, -0.42140166],
+             [0.25436988, 0.08811588, 0.27363867, -0.42140166, 1.33243101]]
+
+        g = [0.75798952, 0.01421945, 0.33847612, 0.83725004, -0.47909534]
+
+        # Solve Subproblem
+        subprob = IterativeSubproblem(x=0,
+                                      fun=lambda x: 0,
+                                      jac=lambda x: np.array(g),
+                                      hess=lambda x: np.array(H))
+        p, hits_boundary = subprob.solve(1.1)
+
+        assert_array_almost_equal(p, [-0.68585435, 0.1222621, -0.22090999,
+                                      -0.67005053, 0.31586769])
+        assert_array_almost_equal(hits_boundary, False)
+        assert_array_almost_equal(subprob.lambda_current, 0)
+        assert_array_almost_equal(subprob.niter, 1)
+
+    def test_for_jac_equal_zero(self):
+
+        H = [[0.88547534, 2.90692271, 0.98440885, -0.78911503, -0.28035809],
+             [2.90692271, -0.04618819, 0.32867263, -0.83737945, 0.17116396],
+             [0.98440885, 0.32867263, -0.87355957, -0.06521957, -1.43030957],
+             [-0.78911503, -0.83737945, -0.06521957, -1.645709, -0.33887298],
+             [-0.28035809, 0.17116396, -1.43030957, -0.33887298, -1.68586978]]
+
+        g = [0, 0, 0, 0, 0]
+
+        # Solve Subproblem
+        subprob = IterativeSubproblem(x=0,
+                                      fun=lambda x: 0,
+                                      jac=lambda x: np.array(g),
+                                      hess=lambda x: np.array(H),
+                                      k_easy=1e-10,
+                                      k_hard=1e-10)
+        p, hits_boundary = subprob.solve(1.1)
+
+        assert_array_almost_equal(p, [0.06910534, -0.01432721,
+                                      -0.65311947, -0.23815972,
+                                      -0.84954934])
+        assert_array_almost_equal(hits_boundary, True)
+
+    def test_for_jac_very_close_to_zero(self):
+
+        H = [[0.88547534, 2.90692271, 0.98440885, -0.78911503, -0.28035809],
+             [2.90692271, -0.04618819, 0.32867263, -0.83737945, 0.17116396],
+             [0.98440885, 0.32867263, -0.87355957, -0.06521957, -1.43030957],
+             [-0.78911503, -0.83737945, -0.06521957, -1.645709, -0.33887298],
+             [-0.28035809, 0.17116396, -1.43030957, -0.33887298, -1.68586978]]
+
+        g = [0, 0, 0, 0, 1e-15]
+
+        # Solve Subproblem
+        subprob = IterativeSubproblem(x=0,
+                                      fun=lambda x: 0,
+                                      jac=lambda x: np.array(g),
+                                      hess=lambda x: np.array(H),
+                                      k_easy=1e-10,
+                                      k_hard=1e-10)
+        p, hits_boundary = subprob.solve(1.1)
+
+        assert_array_almost_equal(p, [0.06910534, -0.01432721,
+                                      -0.65311947, -0.23815972,
+                                      -0.84954934])
+        assert_array_almost_equal(hits_boundary, True)
+
+    def test_for_random_entries(self):
+        # Seed
+        np.random.seed(1)
+
+        # Dimension
+        n = 5
+
+        for case in ('easy', 'hard', 'jac_equal_zero'):
+
+            eig_limits = [(-20, -15),
+                          (-10, -5),
+                          (-10, 0),
+                          (-5, 5),
+                          (-10, 10),
+                          (0, 10),
+                          (5, 10),
+                          (15, 20)]
+
+            for min_eig, max_eig in eig_limits:
+                # Generate random symmetric matrix H with
+                # eigenvalues between min_eig and max_eig.
+                H, g = random_entry(n, min_eig, max_eig, case)
+
+                # Trust radius
+                trust_radius_list = [0.1, 0.3, 0.6, 0.8, 1, 1.2, 3.3, 5.5, 10]
+
+                for trust_radius in trust_radius_list:
+                    # Solve subproblem with very high accuracy
+                    subprob_ac = IterativeSubproblem(0,
+                                                     lambda x: 0,
+                                                     lambda x: g,
+                                                     lambda x: H,
+                                                     k_easy=1e-10,
+                                                     k_hard=1e-10)
+
+                    p_ac, hits_boundary_ac = subprob_ac.solve(trust_radius)
+
+                    # Compute objective function value
+                    J_ac = 1/2*np.dot(p_ac, np.dot(H, p_ac))+np.dot(g, p_ac)
+
+                    stop_criteria = [(0.1, 2),
+                                     (0.5, 1.1),
+                                     (0.9, 1.01)]
+
+                    for k_opt, k_trf in stop_criteria:
+
+                        # k_easy and k_hard computed in function
+                        # of k_opt and k_trf accordingly to
+                        # Conn, A. R., Gould, N. I., & Toint, P. L. (2000).
+                        # "Trust region methods". Siam. p. 197.
+                        k_easy = min(k_trf-1,
+                                     1-np.sqrt(k_opt))
+                        k_hard = 1-k_opt
+
+                        # Solve subproblem
+                        subprob = IterativeSubproblem(0,
+                                                      lambda x: 0,
+                                                      lambda x: g,
+                                                      lambda x: H,
+                                                      k_easy=k_easy,
+                                                      k_hard=k_hard)
+                        p, hits_boundary = subprob.solve(trust_radius)
+
+                        # Compute objective function value
+                        J = 1/2*np.dot(p, np.dot(H, p))+np.dot(g, p)
+
+                        # Check if it respect k_trf
+                        if hits_boundary:
+                            assert_array_equal(np.abs(norm(p)-trust_radius) <=
+                                               (k_trf-1)*trust_radius, True)
+                        else:
+                            assert_equal(norm(p) <= trust_radius, True)
+
+                        # Check if it respect k_opt
+                        assert_equal(J <= k_opt*J_ac, True)
+