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How to use suppressed_stdout method in Test_junkie

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test_optimize.py

Source:test_optimize.py

1"""2Unit tests for optimization routines from optimize.py3Authors:4   Ed Schofield, Nov 20055   Andrew Straw, April 20086To run it in its simplest form::7  nosetests test_optimize.py8"""9from __future__ import division, print_function, absolute_import10import warnings11import itertools12import numpy as np13from numpy.testing import (assert_raises, assert_allclose, assert_equal,14                           assert_, TestCase, run_module_suite, dec,15                           assert_almost_equal, assert_warns,16                           assert_array_less)17from scipy._lib._testutils import suppressed_stdout18from scipy import optimize19def test_check_grad():20    # Verify if check_grad is able to estimate the derivative of the21    # logistic function.22    def logit(x):23        return 1 / (1 + np.exp(-x))24    def der_logit(x):25        return np.exp(-x) / (1 + np.exp(-x))**226    x0 = np.array([1.5])27    r = optimize.check_grad(logit, der_logit, x0)28    assert_almost_equal(r, 0)29    r = optimize.check_grad(logit, der_logit, x0, epsilon=1e-6)30    assert_almost_equal(r, 0)31    # Check if the epsilon parameter is being considered.32    r = abs(optimize.check_grad(logit, der_logit, x0, epsilon=1e-1) - 0)33    assert_(r > 1e-7)34class CheckOptimize(object):35    """ Base test case for a simple constrained entropy maximization problem36    (the machine translation example of Berger et al in37    Computational Linguistics, vol 22, num 1, pp 39--72, 1996.)38    """39    def setUp(self):40        self.F = np.array([[1,1,1],[1,1,0],[1,0,1],[1,0,0],[1,0,0]])41        self.K = np.array([1., 0.3, 0.5])42        self.startparams = np.zeros(3, np.float64)43        self.solution = np.array([0., -0.524869316, 0.487525860])44        self.maxiter = 100045        self.funccalls = 046        self.gradcalls = 047        self.trace = []48    def func(self, x):49        self.funccalls += 150        if self.funccalls > 6000:51            raise RuntimeError("too many iterations in optimization routine")52        log_pdot = np.dot(self.F, x)53        logZ = np.log(sum(np.exp(log_pdot)))54        f = logZ - np.dot(self.K, x)55        self.trace.append(x)56        return f57    def grad(self, x):58        self.gradcalls += 159        log_pdot = np.dot(self.F, x)60        logZ = np.log(sum(np.exp(log_pdot)))61        p = np.exp(log_pdot - logZ)62        return np.dot(self.F.transpose(), p) - self.K63    def hess(self, x):64        log_pdot = np.dot(self.F, x)65        logZ = np.log(sum(np.exp(log_pdot)))66        p = np.exp(log_pdot - logZ)67        return np.dot(self.F.T,68                      np.dot(np.diag(p), self.F - np.dot(self.F.T, p)))69    def hessp(self, x, p):70        return np.dot(self.hess(x), p)71class CheckOptimizeParameterized(CheckOptimize):72    @suppressed_stdout73    def test_cg(self):74        # conjugate gradient optimization routine75        if self.use_wrapper:76            opts = {'maxiter': self.maxiter, 'disp': self.disp,77                    'return_all': False}78            res = optimize.minimize(self.func, self.startparams, args=(),79                                    method='CG', jac=self.grad,80                                    options=opts)81            params, fopt, func_calls, grad_calls, warnflag = \82                res['x'], res['fun'], res['nfev'], res['njev'], res['status']83        else:84            retval = optimize.fmin_cg(self.func, self.startparams,85                                      self.grad, (), maxiter=self.maxiter,86                                      full_output=True, disp=self.disp,87                                      retall=False)88            (params, fopt, func_calls, grad_calls, warnflag) = retval89        assert_allclose(self.func(params), self.func(self.solution),90                        atol=1e-6)91        # Ensure that function call counts are 'known good'; these are from92        # Scipy 0.7.0. Don't allow them to increase.93        assert_(self.funccalls == 9, self.funccalls)94        assert_(self.gradcalls == 7, self.gradcalls)95        # Ensure that the function behaves the same; this is from Scipy 0.7.096        assert_allclose(self.trace[2:4],97                        [[0, -0.5, 0.5],98                         [0, -5.05700028e-01, 4.95985862e-01]],99                        atol=1e-14, rtol=1e-7)100    @suppressed_stdout101    def test_bfgs(self):102        # Broyden-Fletcher-Goldfarb-Shanno optimization routine103        if self.use_wrapper:104            opts = {'maxiter': self.maxiter, 'disp': self.disp,105                    'return_all': False}106            res = optimize.minimize(self.func, self.startparams,107                                    jac=self.grad, method='BFGS', args=(),108                                    options=opts)109            params, fopt, gopt, Hopt, func_calls, grad_calls, warnflag = (110                    res['x'], res['fun'], res['jac'], res['hess_inv'],111                    res['nfev'], res['njev'], res['status'])112        else:113            retval = optimize.fmin_bfgs(self.func, self.startparams, self.grad,114                                        args=(), maxiter=self.maxiter,115                                        full_output=True, disp=self.disp,116                                        retall=False)117            (params, fopt, gopt, Hopt, func_calls, grad_calls, warnflag) = retval118        assert_allclose(self.func(params), self.func(self.solution),119                        atol=1e-6)120        # Ensure that function call counts are 'known good'; these are from121        # Scipy 0.7.0. Don't allow them to increase.122        assert_(self.funccalls == 10, self.funccalls)123        assert_(self.gradcalls == 8, self.gradcalls)124        # Ensure that the function behaves the same; this is from Scipy 0.7.0125        assert_allclose(self.trace[6:8],126                        [[0, -5.25060743e-01, 4.87748473e-01],127                         [0, -5.24885582e-01, 4.87530347e-01]],128                        atol=1e-14, rtol=1e-7)129    @suppressed_stdout130    def test_bfgs_infinite(self):131        # Test corner case where -Inf is the minimum.  See gh-2019.132        func = lambda x: -np.e**-x133        fprime = lambda x: -func(x)134        x0 = [0]135        olderr = np.seterr(over='ignore')136        try:137            if self.use_wrapper:138                opts = {'disp': self.disp}139                x = optimize.minimize(func, x0, jac=fprime, method='BFGS',140                                      args=(), options=opts)['x']141            else:142                x = optimize.fmin_bfgs(func, x0, fprime, disp=self.disp)143            assert_(not np.isfinite(func(x)))144        finally:145            np.seterr(**olderr)146    @suppressed_stdout147    def test_powell(self):148        # Powell (direction set) optimization routine149        if self.use_wrapper:150            opts = {'maxiter': self.maxiter, 'disp': self.disp,151                    'return_all': False}152            res = optimize.minimize(self.func, self.startparams, args=(),153                                    method='Powell', options=opts)154            params, fopt, direc, numiter, func_calls, warnflag = (155                    res['x'], res['fun'], res['direc'], res['nit'],156                    res['nfev'], res['status'])157        else:158            retval = optimize.fmin_powell(self.func, self.startparams,159                                          args=(), maxiter=self.maxiter,160                                          full_output=True, disp=self.disp,161                                          retall=False)162            (params, fopt, direc, numiter, func_calls, warnflag) = retval163        assert_allclose(self.func(params), self.func(self.solution),164                        atol=1e-6)165        # Ensure that function call counts are 'known good'; these are from166        # Scipy 0.7.0. Don't allow them to increase.167        #168        # However, some leeway must be added: the exact evaluation169        # count is sensitive to numerical error, and floating-point170        # computations are not bit-for-bit reproducible across171        # machines, and when using e.g. MKL, data alignment172        # etc. affect the rounding error.173        #174        assert_(self.funccalls <= 116 + 20, self.funccalls)175        assert_(self.gradcalls == 0, self.gradcalls)176        # Ensure that the function behaves the same; this is from Scipy 0.7.0177        assert_allclose(self.trace[34:39],178                        [[0.72949016, -0.44156936, 0.47100962],179                         [0.72949016, -0.44156936, 0.48052496],180                         [1.45898031, -0.88313872, 0.95153458],181                         [0.72949016, -0.44156936, 0.47576729],182                         [1.72949016, -0.44156936, 0.47576729]],183                        atol=1e-14, rtol=1e-7)184    @suppressed_stdout185    def test_neldermead(self):186        # Nelder-Mead simplex algorithm187        if self.use_wrapper:188            opts = {'maxiter': self.maxiter, 'disp': self.disp,189                    'return_all': False}190            res = optimize.minimize(self.func, self.startparams, args=(),191                                    method='Nelder-mead', options=opts)192            params, fopt, numiter, func_calls, warnflag, final_simplex = (193                    res['x'], res['fun'], res['nit'], res['nfev'],194                    res['status'], res['final_simplex'])195        else:196            retval = optimize.fmin(self.func, self.startparams,197                                        args=(), maxiter=self.maxiter,198                                        full_output=True, disp=self.disp,199                                        retall=False)200            (params, fopt, numiter, func_calls, warnflag) = retval201        assert_allclose(self.func(params), self.func(self.solution),202                        atol=1e-6)203        # Ensure that function call counts are 'known good'; these are from204        # Scipy 0.7.0. Don't allow them to increase.205        assert_(self.funccalls == 167, self.funccalls)206        assert_(self.gradcalls == 0, self.gradcalls)207        # Ensure that the function behaves the same; this is from Scipy 0.7.0208        assert_allclose(self.trace[76:78],209                        [[0.1928968, -0.62780447, 0.35166118],210                         [0.19572515, -0.63648426, 0.35838135]],211                        atol=1e-14, rtol=1e-7)212    @suppressed_stdout213    def test_neldermead_initial_simplex(self):214        # Nelder-Mead simplex algorithm215        simplex = np.zeros((4, 3))216        simplex[...] = self.startparams217        for j in range(3):218            simplex[j+1,j] += 0.1219        if self.use_wrapper:220            opts = {'maxiter': self.maxiter, 'disp': False,221                    'return_all': True, 'initial_simplex': simplex}222            res = optimize.minimize(self.func, self.startparams, args=(),223                                    method='Nelder-mead', options=opts)224            params, fopt, numiter, func_calls, warnflag = \225                    res['x'], res['fun'], res['nit'], res['nfev'], \226                    res['status']227            assert_allclose(res['allvecs'][0], simplex[0])228        else:229            retval = optimize.fmin(self.func, self.startparams,230                                        args=(), maxiter=self.maxiter,231                                        full_output=True, disp=False, retall=False,232                                        initial_simplex=simplex)233            (params, fopt, numiter, func_calls, warnflag) = retval234        assert_allclose(self.func(params), self.func(self.solution),235                        atol=1e-6)236        # Ensure that function call counts are 'known good'; these are from237        # Scipy 0.17.0. Don't allow them to increase.238        assert_(self.funccalls == 100, self.funccalls)239        assert_(self.gradcalls == 0, self.gradcalls)240        # Ensure that the function behaves the same; this is from Scipy 0.15.0241        assert_allclose(self.trace[50:52],242                        [[0.14687474, -0.5103282, 0.48252111],243                         [0.14474003, -0.5282084, 0.48743951]],244                        atol=1e-14, rtol=1e-7)245    @suppressed_stdout246    def test_neldermead_initial_simplex_bad(self):247        # Check it fails with a bad simplices248        bad_simplices = []249        simplex = np.zeros((3, 2))250        simplex[...] = self.startparams[:2]251        for j in range(2):252            simplex[j+1,j] += 0.1253        bad_simplices.append(simplex)254        simplex = np.zeros((3, 3))255        bad_simplices.append(simplex)256        for simplex in bad_simplices:257            if self.use_wrapper:258                opts = {'maxiter': self.maxiter, 'disp': False,259                        'return_all': False, 'initial_simplex': simplex}260                assert_raises(ValueError,261                              optimize.minimize, self.func, self.startparams, args=(),262                              method='Nelder-mead', options=opts)263            else:264                assert_raises(ValueError, optimize.fmin, self.func, self.startparams,265                              args=(), maxiter=self.maxiter,266                              full_output=True, disp=False, retall=False,267                              initial_simplex=simplex)268    @suppressed_stdout269    def test_ncg(self):270        # line-search Newton conjugate gradient optimization routine271        if self.use_wrapper:272            opts = {'maxiter': self.maxiter, 'disp': self.disp,273                    'return_all': False}274            retval = optimize.minimize(self.func, self.startparams,275                                       method='Newton-CG', jac=self.grad,276                                       args=(), options=opts)['x']277        else:278            retval = optimize.fmin_ncg(self.func, self.startparams, self.grad,279                                       args=(), maxiter=self.maxiter,280                                       full_output=False, disp=self.disp,281                                       retall=False)282        params = retval283        assert_allclose(self.func(params), self.func(self.solution),284                        atol=1e-6)285        # Ensure that function call counts are 'known good'; these are from286        # Scipy 0.7.0. Don't allow them to increase.287        assert_(self.funccalls == 7, self.funccalls)288        assert_(self.gradcalls <= 22, self.gradcalls)  # 0.13.0289        #assert_(self.gradcalls <= 18, self.gradcalls) # 0.9.0290        #assert_(self.gradcalls == 18, self.gradcalls) # 0.8.0291        #assert_(self.gradcalls == 22, self.gradcalls) # 0.7.0292        # Ensure that the function behaves the same; this is from Scipy 0.7.0293        assert_allclose(self.trace[3:5],294                        [[-4.35700753e-07, -5.24869435e-01, 4.87527480e-01],295                         [-4.35700753e-07, -5.24869401e-01, 4.87527774e-01]],296                        atol=1e-6, rtol=1e-7)297    @suppressed_stdout298    def test_ncg_hess(self):299        # Newton conjugate gradient with Hessian300        if self.use_wrapper:301            opts = {'maxiter': self.maxiter, 'disp': self.disp,302                    'return_all': False}303            retval = optimize.minimize(self.func, self.startparams,304                                       method='Newton-CG', jac=self.grad,305                                       hess=self.hess,306                                       args=(), options=opts)['x']307        else:308            retval = optimize.fmin_ncg(self.func, self.startparams, self.grad,309                                       fhess=self.hess,310                                       args=(), maxiter=self.maxiter,311                                       full_output=False, disp=self.disp,312                                       retall=False)313        params = retval314        assert_allclose(self.func(params), self.func(self.solution),315                        atol=1e-6)316        # Ensure that function call counts are 'known good'; these are from317        # Scipy 0.7.0. Don't allow them to increase.318        assert_(self.funccalls == 7, self.funccalls)319        assert_(self.gradcalls <= 18, self.gradcalls)  # 0.9.0320        # assert_(self.gradcalls == 18, self.gradcalls) # 0.8.0321        # assert_(self.gradcalls == 22, self.gradcalls) # 0.7.0322        # Ensure that the function behaves the same; this is from Scipy 0.7.0323        assert_allclose(self.trace[3:5],324                        [[-4.35700753e-07, -5.24869435e-01, 4.87527480e-01],325                         [-4.35700753e-07, -5.24869401e-01, 4.87527774e-01]],326                        atol=1e-6, rtol=1e-7)327    @suppressed_stdout328    def test_ncg_hessp(self):329        # Newton conjugate gradient with Hessian times a vector p.330        if self.use_wrapper:331            opts = {'maxiter': self.maxiter, 'disp': self.disp,332                    'return_all': False}333            retval = optimize.minimize(self.func, self.startparams,334                                       method='Newton-CG', jac=self.grad,335                                       hessp=self.hessp,336                                       args=(), options=opts)['x']337        else:338            retval = optimize.fmin_ncg(self.func, self.startparams, self.grad,339                                       fhess_p=self.hessp,340                                       args=(), maxiter=self.maxiter,341                                       full_output=False, disp=self.disp,342                                       retall=False)343        params = retval344        assert_allclose(self.func(params), self.func(self.solution),345                        atol=1e-6)346        # Ensure that function call counts are 'known good'; these are from347        # Scipy 0.7.0. Don't allow them to increase.348        assert_(self.funccalls == 7, self.funccalls)349        assert_(self.gradcalls <= 18, self.gradcalls)  # 0.9.0350        # assert_(self.gradcalls == 18, self.gradcalls) # 0.8.0351        # assert_(self.gradcalls == 22, self.gradcalls) # 0.7.0352        # Ensure that the function behaves the same; this is from Scipy 0.7.0353        assert_allclose(self.trace[3:5],354                        [[-4.35700753e-07, -5.24869435e-01, 4.87527480e-01],355                         [-4.35700753e-07, -5.24869401e-01, 4.87527774e-01]],356                        atol=1e-6, rtol=1e-7)357def test_neldermead_xatol_fatol():358    # gh4484359    # test we can call with fatol, xatol specified360    func = lambda x: x[0]**2 + x[1]**2361    optimize._minimize._minimize_neldermead(func, [1, 1], maxiter=2,362                                            xatol=1e-3, fatol=1e-3)363    assert_warns(DeprecationWarning,364                 optimize._minimize._minimize_neldermead,365                 func, [1, 1], xtol=1e-3, ftol=1e-3, maxiter=2)366class TestOptimizeWrapperDisp(CheckOptimizeParameterized):367    use_wrapper = True368    disp = True369class TestOptimizeWrapperNoDisp(CheckOptimizeParameterized):370    use_wrapper = True371    disp = False372class TestOptimizeNoWrapperDisp(CheckOptimizeParameterized):373    use_wrapper = False374    disp = True375class TestOptimizeNoWrapperNoDisp(CheckOptimizeParameterized):376    use_wrapper = False377    disp = False378class TestOptimizeSimple(CheckOptimize):379    def test_bfgs_nan(self):380        # Test corner case where nan is fed to optimizer.  See gh-2067.381        func = lambda x: x382        fprime = lambda x: np.ones_like(x)383        x0 = [np.nan]384        with np.errstate(over='ignore', invalid='ignore'):385            x = optimize.fmin_bfgs(func, x0, fprime, disp=False)386            assert_(np.isnan(func(x)))387    def test_bfgs_nan_return(self):388        # Test corner cases where fun returns NaN. See gh-4793.389        # First case: NaN from first call.390        func = lambda x: np.nan391        with np.errstate(invalid='ignore'):392            result = optimize.minimize(func, 0)393        assert_(np.isnan(result['fun']))394        assert_(result['success'] is False)395        # Second case: NaN from second call.396        func = lambda x: 0 if x == 0 else np.nan397        fprime = lambda x: np.ones_like(x)  # Steer away from zero.398        with np.errstate(invalid='ignore'):399            result = optimize.minimize(func, 0, jac=fprime)400        assert_(np.isnan(result['fun']))401        assert_(result['success'] is False)402    def test_bfgs_numerical_jacobian(self):403        # BFGS with numerical jacobian and a vector epsilon parameter.404        # define the epsilon parameter using a random vector405        epsilon = np.sqrt(np.finfo(float).eps) * np.random.rand(len(self.solution))406        params = optimize.fmin_bfgs(self.func, self.startparams,407                                    epsilon=epsilon, args=(),408                                    maxiter=self.maxiter, disp=False)409        assert_allclose(self.func(params), self.func(self.solution),410                        atol=1e-6)411    def test_bfgs_gh_2169(self):412        def f(x):413            if x < 0:414                return 1.79769313e+308415            else:416                return x + 1./x417        xs = optimize.fmin_bfgs(f, [10.], disp=False)418        assert_allclose(xs, 1.0, rtol=1e-4, atol=1e-4)419    def test_l_bfgs_b(self):420        # limited-memory bound-constrained BFGS algorithm421        retval = optimize.fmin_l_bfgs_b(self.func, self.startparams,422                                        self.grad, args=(),423                                        maxiter=self.maxiter)424        (params, fopt, d) = retval425        assert_allclose(self.func(params), self.func(self.solution),426                        atol=1e-6)427        # Ensure that function call counts are 'known good'; these are from428        # Scipy 0.7.0. Don't allow them to increase.429        assert_(self.funccalls == 7, self.funccalls)430        assert_(self.gradcalls == 5, self.gradcalls)431        # Ensure that the function behaves the same; this is from Scipy 0.7.0432        assert_allclose(self.trace[3:5],433                        [[0., -0.52489628, 0.48753042],434                         [0., -0.52489628, 0.48753042]],435                        atol=1e-14, rtol=1e-7)436    def test_l_bfgs_b_numjac(self):437        # L-BFGS-B with numerical jacobian438        retval = optimize.fmin_l_bfgs_b(self.func, self.startparams,439                                        approx_grad=True,440                                        maxiter=self.maxiter)441        (params, fopt, d) = retval442        assert_allclose(self.func(params), self.func(self.solution),443                        atol=1e-6)444    def test_l_bfgs_b_funjac(self):445        # L-BFGS-B with combined objective function and jacobian446        def fun(x):447            return self.func(x), self.grad(x)448        retval = optimize.fmin_l_bfgs_b(fun, self.startparams,449                                        maxiter=self.maxiter)450        (params, fopt, d) = retval451        assert_allclose(self.func(params), self.func(self.solution),452                        atol=1e-6)453    def test_minimize_l_bfgs_b(self):454        # Minimize with L-BFGS-B method455        opts = {'disp': False, 'maxiter': self.maxiter}456        r = optimize.minimize(self.func, self.startparams,457                              method='L-BFGS-B', jac=self.grad,458                              options=opts)459        assert_allclose(self.func(r.x), self.func(self.solution),460                        atol=1e-6)461        # approximate jacobian462        ra = optimize.minimize(self.func, self.startparams,463                               method='L-BFGS-B', options=opts)464        assert_allclose(self.func(ra.x), self.func(self.solution),465                        atol=1e-6)466        # check that function evaluations in approximate jacobian are counted467        assert_(ra.nfev > r.nfev)468    def test_minimize_l_bfgs_b_ftol(self):469        # Check that the `ftol` parameter in l_bfgs_b works as expected470        v0 = None471        for tol in [1e-1, 1e-4, 1e-7, 1e-10]:472            opts = {'disp': False, 'maxiter': self.maxiter, 'ftol': tol}473            sol = optimize.minimize(self.func, self.startparams,474                                    method='L-BFGS-B', jac=self.grad,475                                    options=opts)476            v = self.func(sol.x)477            if v0 is None:478                v0 = v479            else:480                assert_(v < v0)481            assert_allclose(v, self.func(self.solution), rtol=tol)482    def test_minimize_l_bfgs_maxls(self):483        # check that the maxls is passed down to the Fortran routine484        sol = optimize.minimize(optimize.rosen, np.array([-1.2,1.0]),485                                method='L-BFGS-B', jac=optimize.rosen_der,486                                options={'disp': False, 'maxls': 1})487        assert_(not sol.success)488    def test_minimize_l_bfgs_b_maxfun_interruption(self):489        # gh-6162490        f = optimize.rosen491        g = optimize.rosen_der492        values = []493        x0 = np.ones(7) * 1000494        def objfun(x):495            value = f(x)496            values.append(value)497            return value498        # Look for an interesting test case.499        # Request a maxfun that stops at a particularly bad function500        # evaluation somewhere between 100 and 300 evaluations.501        low, medium, high = 30, 100, 300502        optimize.fmin_l_bfgs_b(objfun, x0, fprime=g, maxfun=high)503        v, k = max((y, i) for i, y in enumerate(values[medium:]))504        maxfun = medium + k505        # If the minimization strategy is reasonable,506        # the minimize() result should not be worse than the best507        # of the first 30 function evaluations.508        target = min(values[:low])509        xmin, fmin, d = optimize.fmin_l_bfgs_b(f, x0, fprime=g, maxfun=maxfun)510        assert_array_less(fmin, target)511    def test_custom(self):512        # This function comes from the documentation example.513        def custmin(fun, x0, args=(), maxfev=None, stepsize=0.1,514                maxiter=100, callback=None, **options):515            bestx = x0516            besty = fun(x0)517            funcalls = 1518            niter = 0519            improved = True520            stop = False521            while improved and not stop and niter < maxiter:522                improved = False523                niter += 1524                for dim in range(np.size(x0)):525                    for s in [bestx[dim] - stepsize, bestx[dim] + stepsize]:526                        testx = np.copy(bestx)527                        testx[dim] = s528                        testy = fun(testx, *args)529                        funcalls += 1530                        if testy < besty:531                            besty = testy532                            bestx = testx533                            improved = True534                    if callback is not None:535                        callback(bestx)536                    if maxfev is not None and funcalls >= maxfev:537                        stop = True538                        break539            return optimize.OptimizeResult(fun=besty, x=bestx, nit=niter,540                                           nfev=funcalls, success=(niter > 1))541        x0 = [1.35, 0.9, 0.8, 1.1, 1.2]542        res = optimize.minimize(optimize.rosen, x0, method=custmin,543                                options=dict(stepsize=0.05))544        assert_allclose(res.x, 1.0, rtol=1e-4, atol=1e-4)545    def test_minimize_tol_parameter(self):546        # Check that the minimize() tol= argument does something547        def func(z):548            x, y = z549            return x**2*y**2 + x**4 + 1550        def dfunc(z):551            x, y = z552            return np.array([2*x*y**2 + 4*x**3, 2*x**2*y])553        for method in ['nelder-mead', 'powell', 'cg', 'bfgs',554                       'newton-cg', 'l-bfgs-b', 'tnc',555                       'cobyla', 'slsqp']:556            if method in ('nelder-mead', 'powell', 'cobyla'):557                jac = None558            else:559                jac = dfunc560            sol1 = optimize.minimize(func, [1, 1], jac=jac, tol=1e-10,561                                     method=method)562            sol2 = optimize.minimize(func, [1, 1], jac=jac, tol=1.0,563                                     method=method)564            assert_(func(sol1.x) < func(sol2.x),565                    "%s: %s vs. %s" % (method, func(sol1.x), func(sol2.x)))566    def test_no_increase(self):567        # Check that the solver doesn't return a value worse than the568        # initial point.569        def func(x):570            return (x - 1)**2571        def bad_grad(x):572            # purposefully invalid gradient function, simulates a case573            # where line searches start failing574            return 2*(x - 1) * (-1) - 2575        def check(method):576            x0 = np.array([2.0])577            f0 = func(x0)578            jac = bad_grad579            if method in ['nelder-mead', 'powell', 'cobyla']:580                jac = None581            sol = optimize.minimize(func, x0, jac=jac, method=method,582                                    options=dict(maxiter=20))583            assert_equal(func(sol.x), sol.fun)584            dec.knownfailureif(method == 'slsqp', "SLSQP returns slightly worse")(lambda: None)()585            assert_(func(sol.x) <= f0)586        for method in ['nelder-mead', 'powell', 'cg', 'bfgs',587                       'newton-cg', 'l-bfgs-b', 'tnc',588                       'cobyla', 'slsqp']:589            yield check, method590    def test_slsqp_respect_bounds(self):591        # Regression test for gh-3108592        def f(x):593            return sum((x - np.array([1., 2., 3., 4.]))**2)594        def cons(x):595            a = np.array([[-1, -1, -1, -1], [-3, -3, -2, -1]])596            return np.concatenate([np.dot(a, x) + np.array([5, 10]), x])597        x0 = np.array([0.5, 1., 1.5, 2.])598        res = optimize.minimize(f, x0, method='slsqp',599                                constraints={'type': 'ineq', 'fun': cons})600        assert_allclose(res.x, np.array([0., 2, 5, 8])/3, atol=1e-12)601    def test_minimize_automethod(self):602        def f(x):603            return x**2604        def cons(x):605            return x - 2606        x0 = np.array([10.])607        sol_0 = optimize.minimize(f, x0)608        sol_1 = optimize.minimize(f, x0, constraints=[{'type': 'ineq', 'fun': cons}])609        sol_2 = optimize.minimize(f, x0, bounds=[(5, 10)])610        sol_3 = optimize.minimize(f, x0, constraints=[{'type': 'ineq', 'fun': cons}], bounds=[(5, 10)])611        sol_4 = optimize.minimize(f, x0, constraints=[{'type': 'ineq', 'fun': cons}], bounds=[(1, 10)])612        for sol in [sol_0, sol_1, sol_2, sol_3, sol_4]:613            assert_(sol.success)614        assert_allclose(sol_0.x, 0, atol=1e-7)615        assert_allclose(sol_1.x, 2, atol=1e-7)616        assert_allclose(sol_2.x, 5, atol=1e-7)617        assert_allclose(sol_3.x, 5, atol=1e-7)618        assert_allclose(sol_4.x, 2, atol=1e-7)619    def test_minimize_coerce_args_param(self):620        # Regression test for gh-3503621        def Y(x, c):622            return np.sum((x-c)**2)623        def dY_dx(x, c=None):624            return 2*(x-c)625        c = np.array([3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5])626        xinit = np.random.randn(len(c))627        optimize.minimize(Y, xinit, jac=dY_dx, args=(c), method="BFGS")628    def test_initial_step_scaling(self):629        # Check that optimizer initial step is not huge even if the630        # function and gradients are631        scales = [1e-50, 1, 1e50]632        methods = ['CG', 'BFGS', 'L-BFGS-B', 'Newton-CG']633        def f(x):634            if first_step_size[0] is None and x[0] != x0[0]:635                first_step_size[0] = abs(x[0] - x0[0])636            if abs(x).max() > 1e4:637                raise AssertionError("Optimization stepped far away!")638            return scale*(x[0] - 1)**2639        def g(x):640            return np.array([scale*(x[0] - 1)])641        for scale, method in itertools.product(scales, methods):642            if method in ('CG', 'BFGS'):643                options = dict(gtol=scale*1e-8)644            else:645                options = dict()646            if scale < 1e-10 and method in ('L-BFGS-B', 'Newton-CG'):647                # XXX: return initial point if they see small gradient648                continue649            x0 = [-1.0]650            first_step_size = [None]651            res = optimize.minimize(f, x0, jac=g, method=method,652                                    options=options)653            err_msg = "{0} {1}: {2}: {3}".format(method, scale, first_step_size,654                                                 res)655            assert_(res.success, err_msg)656            assert_allclose(res.x, [1.0], err_msg=err_msg)657            assert_(res.nit <= 3, err_msg)658            if scale > 1e-10:659                if method in ('CG', 'BFGS'):660                    assert_allclose(first_step_size[0], 1.01, err_msg=err_msg)661                else:662                    # Newton-CG and L-BFGS-B use different logic for the first step,663                    # but are both scaling invariant with step sizes ~ 1664                    assert_(first_step_size[0] > 0.5 and first_step_size[0] < 3,665                            err_msg)666            else:667                # step size has upper bound of ||grad||, so line668                # search makes many small steps669                pass670class TestLBFGSBBounds(TestCase):671    def setUp(self):672        self.bounds = ((1, None), (None, None))673        self.solution = (1, 0)674    def fun(self, x, p=2.0):675        return 1.0 / p * (x[0]**p + x[1]**p)676    def jac(self, x, p=2.0):677        return x**(p - 1)678    def fj(self, x, p=2.0):679        return self.fun(x, p), self.jac(x, p)680    def test_l_bfgs_b_bounds(self):681        x, f, d = optimize.fmin_l_bfgs_b(self.fun, [0, -1],682                                         fprime=self.jac,683                                         bounds=self.bounds)684        assert_(d['warnflag'] == 0, d['task'])685        assert_allclose(x, self.solution, atol=1e-6)686    def test_l_bfgs_b_funjac(self):687        # L-BFGS-B with fun and jac combined and extra arguments688        x, f, d = optimize.fmin_l_bfgs_b(self.fj, [0, -1], args=(2.0, ),689                                         bounds=self.bounds)690        assert_(d['warnflag'] == 0, d['task'])691        assert_allclose(x, self.solution, atol=1e-6)692    def test_minimize_l_bfgs_b_bounds(self):693        # Minimize with method='L-BFGS-B' with bounds694        res = optimize.minimize(self.fun, [0, -1], method='L-BFGS-B',695                                jac=self.jac, bounds=self.bounds)696        assert_(res['success'], res['message'])697        assert_allclose(res.x, self.solution, atol=1e-6)698class TestOptimizeScalar(TestCase):699    def setUp(self):700        self.solution = 1.5701    def fun(self, x, a=1.5):702        """Objective function"""703        return (x - a)**2 - 0.8704    def test_brent(self):705        x = optimize.brent(self.fun)706        assert_allclose(x, self.solution, atol=1e-6)707        x = optimize.brent(self.fun, brack=(-3, -2))708        assert_allclose(x, self.solution, atol=1e-6)709        x = optimize.brent(self.fun, full_output=True)710        assert_allclose(x[0], self.solution, atol=1e-6)711        x = optimize.brent(self.fun, brack=(-15, -1, 15))712        assert_allclose(x, self.solution, atol=1e-6)713    def test_golden(self):714        x = optimize.golden(self.fun)715        assert_allclose(x, self.solution, atol=1e-6)716        x = optimize.golden(self.fun, brack=(-3, -2))717        assert_allclose(x, self.solution, atol=1e-6)718        x = optimize.golden(self.fun, full_output=True)719        assert_allclose(x[0], self.solution, atol=1e-6)720        x = optimize.golden(self.fun, brack=(-15, -1, 15))721        assert_allclose(x, self.solution, atol=1e-6)722    def test_fminbound(self):723        x = optimize.fminbound(self.fun, 0, 1)724        assert_allclose(x, 1, atol=1e-4)725        x = optimize.fminbound(self.fun, 1, 5)726        assert_allclose(x, self.solution, atol=1e-6)727        x = optimize.fminbound(self.fun, np.array([1]), np.array([5]))728        assert_allclose(x, self.solution, atol=1e-6)729        assert_raises(ValueError, optimize.fminbound, self.fun, 5, 1)730    def test_fminbound_scalar(self):731        try:732            optimize.fminbound(self.fun, np.zeros((1, 2)), 1)733            self.fail("exception not raised")734        except ValueError as e:735            assert_('must be scalar' in str(e))736        x = optimize.fminbound(self.fun, 1, np.array(5))737        assert_allclose(x, self.solution, atol=1e-6)738    def test_minimize_scalar(self):739        # combine all tests above for the minimize_scalar wrapper740        x = optimize.minimize_scalar(self.fun).x741        assert_allclose(x, self.solution, atol=1e-6)742        x = optimize.minimize_scalar(self.fun, method='Brent')743        assert_(x.success)744        x = optimize.minimize_scalar(self.fun, method='Brent',745                                     options=dict(maxiter=3))746        assert_(not x.success)747        x = optimize.minimize_scalar(self.fun, bracket=(-3, -2),748                                    args=(1.5, ), method='Brent').x749        assert_allclose(x, self.solution, atol=1e-6)750        x = optimize.minimize_scalar(self.fun, method='Brent',751                                    args=(1.5,)).x752        assert_allclose(x, self.solution, atol=1e-6)753        x = optimize.minimize_scalar(self.fun, bracket=(-15, -1, 15),754                                    args=(1.5, ), method='Brent').x755        assert_allclose(x, self.solution, atol=1e-6)756        x = optimize.minimize_scalar(self.fun, bracket=(-3, -2),757                                     args=(1.5, ), method='golden').x758        assert_allclose(x, self.solution, atol=1e-6)759        x = optimize.minimize_scalar(self.fun, method='golden',760                                     args=(1.5,)).x761        assert_allclose(x, self.solution, atol=1e-6)762        x = optimize.minimize_scalar(self.fun, bracket=(-15, -1, 15),763                                     args=(1.5, ), method='golden').x764        assert_allclose(x, self.solution, atol=1e-6)765        x = optimize.minimize_scalar(self.fun, bounds=(0, 1), args=(1.5,),766                                     method='Bounded').x767        assert_allclose(x, 1, atol=1e-4)768        x = optimize.minimize_scalar(self.fun, bounds=(1, 5), args=(1.5, ),769                                    method='bounded').x770        assert_allclose(x, self.solution, atol=1e-6)771        x = optimize.minimize_scalar(self.fun, bounds=(np.array([1]),772                                                      np.array([5])),773                                    args=(np.array([1.5]), ),774                                    method='bounded').x775        assert_allclose(x, self.solution, atol=1e-6)776        assert_raises(ValueError, optimize.minimize_scalar, self.fun,777                      bounds=(5, 1), method='bounded', args=(1.5, ))778        assert_raises(ValueError, optimize.minimize_scalar, self.fun,779                      bounds=(np.zeros(2), 1), method='bounded', args=(1.5, ))780        x = optimize.minimize_scalar(self.fun, bounds=(1, np.array(5)),781                                     method='bounded').x782        assert_allclose(x, self.solution, atol=1e-6)783    def test_minimize_scalar_custom(self):784        # This function comes from the documentation example.785        def custmin(fun, bracket, args=(), maxfev=None, stepsize=0.1,786                maxiter=100, callback=None, **options):787            bestx = (bracket[1] + bracket[0]) / 2.0788            besty = fun(bestx)789            funcalls = 1790            niter = 0791            improved = True792            stop = False793            while improved and not stop and niter < maxiter:794                improved = False795                niter += 1796                for testx in [bestx - stepsize, bestx + stepsize]:797                    testy = fun(testx, *args)798                    funcalls += 1799                    if testy < besty:800                        besty = testy801                        bestx = testx802                        improved = True803                if callback is not None:804                    callback(bestx)805                if maxfev is not None and funcalls >= maxfev:806                    stop = True807                    break808            return optimize.OptimizeResult(fun=besty, x=bestx, nit=niter,809                                           nfev=funcalls, success=(niter > 1))810        res = optimize.minimize_scalar(self.fun, bracket=(0, 4), method=custmin,811                                       options=dict(stepsize=0.05))812        assert_allclose(res.x, self.solution, atol=1e-6)813    def test_minimize_scalar_coerce_args_param(self):814        # Regression test for gh-3503815        optimize.minimize_scalar(self.fun, args=1.5)816def test_brent_negative_tolerance():817    assert_raises(ValueError, optimize.brent, np.cos, tol=-.01)818class TestNewtonCg(object):819    def test_rosenbrock(self):820        x0 = np.array([-1.2, 1.0])821        sol = optimize.minimize(optimize.rosen, x0,822                                jac=optimize.rosen_der,823                                hess=optimize.rosen_hess,824                                tol=1e-5,825                                method='Newton-CG')826        assert_(sol.success, sol.message)827        assert_allclose(sol.x, np.array([1, 1]), rtol=1e-4)828    def test_himmelblau(self):829        x0 = np.array(himmelblau_x0)830        sol = optimize.minimize(himmelblau,831                                x0,832                                jac=himmelblau_grad,833                                hess=himmelblau_hess,834                                method='Newton-CG',835                                tol=1e-6)836        assert_(sol.success, sol.message)837        assert_allclose(sol.x, himmelblau_xopt, rtol=1e-4)838        assert_allclose(sol.fun, himmelblau_min, atol=1e-4)839class TestRosen(TestCase):840    def test_hess(self):841        # Compare rosen_hess(x) times p with rosen_hess_prod(x,p).  See gh-1775842        x = np.array([3, 4, 5])843        p = np.array([2, 2, 2])844        hp = optimize.rosen_hess_prod(x, p)845        dothp = np.dot(optimize.rosen_hess(x), p)846        assert_equal(hp, dothp)847def himmelblau(p):848    """849    R^2 -> R^1 test function for optimization.  The function has four local850    minima where himmelblau(xopt) == 0.851    """852    x, y = p853    a = x*x + y - 11854    b = x + y*y - 7855    return a*a + b*b856def himmelblau_grad(p):857    x, y = p858    return np.array([4*x**3 + 4*x*y - 42*x + 2*y**2 - 14,859                     2*x**2 + 4*x*y + 4*y**3 - 26*y - 22])860def himmelblau_hess(p):861    x, y = p862    return np.array([[12*x**2 + 4*y - 42, 4*x + 4*y],863                     [4*x + 4*y, 4*x + 12*y**2 - 26]])864himmelblau_x0 = [-0.27, -0.9]865himmelblau_xopt = [3, 2]866himmelblau_min = 0.0867def test_minimize_multiple_constraints():868    # Regression test for gh-4240.869    def func(x):870        return np.array([25 - 0.2 * x[0] - 0.4 * x[1] - 0.33 * x[2]])871    def func1(x):872        return np.array([x[1]])873    def func2(x):874        return np.array([x[2]])875    cons = ({'type': 'ineq', 'fun': func},876            {'type': 'ineq', 'fun': func1},877            {'type': 'ineq', 'fun': func2})878    f = lambda x: -1 * (x[0] + x[1] + x[2])879    res = optimize.minimize(f, [0, 0, 0], method='SLSQP', constraints=cons)880    assert_allclose(res.x, [125, 0, 0], atol=1e-10)881class TestOptimizeResultAttributes(TestCase):882    # Test that all minimizers return an OptimizeResult containing883    # all the OptimizeResult attributes884    def setUp(self):885        self.x0 = [5, 5]886        self.func = optimize.rosen887        self.jac = optimize.rosen_der888        self.hess = optimize.rosen_hess889        self.hessp = optimize.rosen_hess_prod890        self.bounds = [(0., 10.), (0., 10.)]891    def test_attributes_present(self):892        methods = ['Nelder-Mead', 'Powell', 'CG', 'BFGS', 'Newton-CG',893                   'L-BFGS-B', 'TNC', 'COBYLA', 'SLSQP', 'dogleg',894                   'trust-ncg']895        attributes = ['nit', 'nfev', 'x', 'success', 'status', 'fun',896                      'message']897        skip = {'COBYLA': ['nit']}898        for method in methods:899            with warnings.catch_warnings():900                warnings.simplefilter("ignore")901                res = optimize.minimize(self.func, self.x0, method=method,902                                        jac=self.jac, hess=self.hess,903                                        hessp=self.hessp)904            for attribute in attributes:905                if method in skip and attribute in skip[method]:906                    continue907                assert_(hasattr(res, attribute))908                assert_(attribute in dir(res))909class TestBrute:910    # Test the "brute force" method911    def setUp(self):912        self.params = (2, 3, 7, 8, 9, 10, 44, -1, 2, 26, 1, -2, 0.5)913        self.rranges = (slice(-4, 4, 0.25), slice(-4, 4, 0.25))914        self.solution = np.array([-1.05665192, 1.80834843])915    def f1(self, z, *params):916        x, y = z917        a, b, c, d, e, f, g, h, i, j, k, l, scale = params918        return (a * x**2 + b * x * y + c * y**2 + d*x + e*y + f)919    def f2(self, z, *params):920        x, y = z921        a, b, c, d, e, f, g, h, i, j, k, l, scale = params922        return (-g*np.exp(-((x-h)**2 + (y-i)**2) / scale))923    def f3(self, z, *params):924        x, y = z925        a, b, c, d, e, f, g, h, i, j, k, l, scale = params926        return (-j*np.exp(-((x-k)**2 + (y-l)**2) / scale))927    def func(self, z, *params):928        return self.f1(z, *params) + self.f2(z, *params) + self.f3(z, *params)929    @suppressed_stdout930    def test_brute(self):931        # test fmin932        resbrute = optimize.brute(self.func, self.rranges, args=self.params,933                                  full_output=True, finish=optimize.fmin)934        assert_allclose(resbrute[0], self.solution, atol=1e-3)935        assert_allclose(resbrute[1], self.func(self.solution, *self.params),936                        atol=1e-3)937        # test minimize938        resbrute = optimize.brute(self.func, self.rranges, args=self.params,939                                  full_output=True,940                                  finish=optimize.minimize)941        assert_allclose(resbrute[0], self.solution, atol=1e-3)942        assert_allclose(resbrute[1], self.func(self.solution, *self.params),943                        atol=1e-3)944class TestIterationLimits(TestCase):945    # Tests that optimisation does not give up before trying requested946    # number of iterations or evaluations. And that it does not succeed947    # by exceeding the limits.948    def setUp(self):949        self.funcalls = 0950    def slow_func(self, v):951        self.funcalls += 1952        r,t = np.sqrt(v[0]**2+v[1]**2), np.arctan2(v[0],v[1])953        return np.sin(r*20 + t)+r*0.5954    def test_neldermead_limit(self):955        self.check_limits("Nelder-Mead", 200)956    def test_powell_limit(self):957        self.check_limits("powell", 1000)958    def check_limits(self, method, default_iters):959        for start_v in [[0.1,0.1], [1,1], [2,2]]:960            for mfev in [50, 500, 5000]:961                self.funcalls = 0962                res = optimize.minimize(self.slow_func, start_v,963                      method=method, options={"maxfev":mfev})964                assert_(self.funcalls == res["nfev"])965                if res["success"]:966                    assert_(res["nfev"] < mfev)967                else:968                    assert_(res["nfev"] >= mfev)969            for mit in [50, 500,5000]:970                res = optimize.minimize(self.slow_func, start_v,971                      method=method, options={"maxiter":mit})972                if res["success"]:973                    assert_(res["nit"] <= mit)974                else:975                    assert_(res["nit"] >= mit)976            for mfev,mit in [[50,50], [5000,5000],[5000,np.inf]]:977                self.funcalls = 0978                res = optimize.minimize(self.slow_func, start_v,979                      method=method, options={"maxiter":mit, "maxfev":mfev})980                assert_(self.funcalls == res["nfev"])981                if res["success"]:982                    assert_(res["nfev"] < mfev and res["nit"] <= mit)983                else:984                    assert_(res["nfev"] >= mfev or res["nit"] >= mit)985            for mfev,mit in [[np.inf,None], [None,np.inf]]:986                self.funcalls = 0987                res = optimize.minimize(self.slow_func, start_v,988                      method=method, options={"maxiter":mit, "maxfev":mfev})989                assert_(self.funcalls == res["nfev"])990                if res["success"]:991                    if mfev is None:992                        assert_(res["nfev"] < default_iters*2)993                    else:994                        assert_(res["nit"] <= default_iters*2)995                else:996                    assert_(res["nfev"] >= default_iters*2 or997                        res["nit"] >= default_iters*2)998if __name__ == "__main__":...

_testutils.py

Source:_testutils.py

...19        except (ValueError, KeyError):20            pass21        return dec.knownfailureif(True, msg)(func)22    return deco23def suppressed_stdout(f):24    import nose25    def pwrapper(*arg, **kwargs):26        oldstdout = sys.stdout27        sys.stdout = open(os.devnull, 'w')28        try:29            return f(*arg, **kwargs)30        finally:31            sys.stdout.close()32            sys.stdout = oldstdout33    return nose.tools.make_decorator(f)(pwrapper)34@decorator35def xslow(func, *a, **kw):36    try:37        v = int(os.environ.get('SCIPY_XSLOW', '0'))...

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