530 lines
19 KiB
Python
530 lines
19 KiB
Python
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"""
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Unit tests for the basin hopping global minimization algorithm.
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"""
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import copy
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from numpy.testing import (assert_almost_equal, assert_equal, assert_,
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assert_allclose)
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import pytest
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from pytest import raises as assert_raises
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import numpy as np
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from numpy import cos, sin
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from scipy.optimize import basinhopping, OptimizeResult
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from scipy.optimize._basinhopping import (
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Storage, RandomDisplacement, Metropolis, AdaptiveStepsize)
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def func1d(x):
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f = cos(14.5 * x - 0.3) + (x + 0.2) * x
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df = np.array(-14.5 * sin(14.5 * x - 0.3) + 2. * x + 0.2)
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return f, df
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def func2d_nograd(x):
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f = cos(14.5 * x[0] - 0.3) + (x[1] + 0.2) * x[1] + (x[0] + 0.2) * x[0]
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return f
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def func2d(x):
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f = cos(14.5 * x[0] - 0.3) + (x[1] + 0.2) * x[1] + (x[0] + 0.2) * x[0]
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df = np.zeros(2)
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df[0] = -14.5 * sin(14.5 * x[0] - 0.3) + 2. * x[0] + 0.2
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df[1] = 2. * x[1] + 0.2
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return f, df
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def func2d_easyderiv(x):
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f = 2.0*x[0]**2 + 2.0*x[0]*x[1] + 2.0*x[1]**2 - 6.0*x[0]
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df = np.zeros(2)
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df[0] = 4.0*x[0] + 2.0*x[1] - 6.0
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df[1] = 2.0*x[0] + 4.0*x[1]
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return f, df
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class MyTakeStep1(RandomDisplacement):
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"""use a copy of displace, but have it set a special parameter to
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make sure it's actually being used."""
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def __init__(self):
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self.been_called = False
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super().__init__()
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def __call__(self, x):
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self.been_called = True
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return super().__call__(x)
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def myTakeStep2(x):
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"""redo RandomDisplacement in function form without the attribute stepsize
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to make sure everything still works ok
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"""
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s = 0.5
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x += np.random.uniform(-s, s, np.shape(x))
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return x
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class MyAcceptTest:
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"""pass a custom accept test
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This does nothing but make sure it's being used and ensure all the
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possible return values are accepted
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"""
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def __init__(self):
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self.been_called = False
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self.ncalls = 0
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self.testres = [False, 'force accept', True, np.bool_(True),
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np.bool_(False), [], {}, 0, 1]
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def __call__(self, **kwargs):
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self.been_called = True
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self.ncalls += 1
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if self.ncalls - 1 < len(self.testres):
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return self.testres[self.ncalls - 1]
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else:
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return True
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class MyCallBack:
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"""pass a custom callback function
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This makes sure it's being used. It also returns True after 10
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steps to ensure that it's stopping early.
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"""
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def __init__(self):
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self.been_called = False
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self.ncalls = 0
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def __call__(self, x, f, accepted):
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self.been_called = True
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self.ncalls += 1
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if self.ncalls == 10:
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return True
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class TestBasinHopping:
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def setup_method(self):
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""" Tests setup.
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Run tests based on the 1-D and 2-D functions described above.
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"""
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self.x0 = (1.0, [1.0, 1.0])
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self.sol = (-0.195, np.array([-0.195, -0.1]))
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self.tol = 3 # number of decimal places
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self.niter = 100
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self.disp = False
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# fix random seed
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np.random.seed(1234)
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self.kwargs = {"method": "L-BFGS-B", "jac": True}
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self.kwargs_nograd = {"method": "L-BFGS-B"}
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def test_TypeError(self):
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# test the TypeErrors are raised on bad input
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i = 1
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# if take_step is passed, it must be callable
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assert_raises(TypeError, basinhopping, func2d, self.x0[i],
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take_step=1)
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# if accept_test is passed, it must be callable
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assert_raises(TypeError, basinhopping, func2d, self.x0[i],
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accept_test=1)
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def test_input_validation(self):
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msg = 'target_accept_rate has to be in range \\(0, 1\\)'
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with assert_raises(ValueError, match=msg):
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basinhopping(func1d, self.x0[0], target_accept_rate=0.)
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with assert_raises(ValueError, match=msg):
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basinhopping(func1d, self.x0[0], target_accept_rate=1.)
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msg = 'stepwise_factor has to be in range \\(0, 1\\)'
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with assert_raises(ValueError, match=msg):
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basinhopping(func1d, self.x0[0], stepwise_factor=0.)
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with assert_raises(ValueError, match=msg):
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basinhopping(func1d, self.x0[0], stepwise_factor=1.)
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def test_1d_grad(self):
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# test 1-D minimizations with gradient
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i = 0
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res = basinhopping(func1d, self.x0[i], minimizer_kwargs=self.kwargs,
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niter=self.niter, disp=self.disp)
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assert_almost_equal(res.x, self.sol[i], self.tol)
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def test_2d(self):
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# test 2d minimizations with gradient
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i = 1
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res = basinhopping(func2d, self.x0[i], minimizer_kwargs=self.kwargs,
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niter=self.niter, disp=self.disp)
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assert_almost_equal(res.x, self.sol[i], self.tol)
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assert_(res.nfev > 0)
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def test_njev(self):
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# test njev is returned correctly
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i = 1
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minimizer_kwargs = self.kwargs.copy()
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# L-BFGS-B doesn't use njev, but BFGS does
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minimizer_kwargs["method"] = "BFGS"
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res = basinhopping(func2d, self.x0[i],
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minimizer_kwargs=minimizer_kwargs, niter=self.niter,
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disp=self.disp)
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assert_(res.nfev > 0)
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assert_equal(res.nfev, res.njev)
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def test_jac(self):
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# test Jacobian returned
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minimizer_kwargs = self.kwargs.copy()
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# BFGS returns a Jacobian
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minimizer_kwargs["method"] = "BFGS"
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res = basinhopping(func2d_easyderiv, [0.0, 0.0],
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minimizer_kwargs=minimizer_kwargs, niter=self.niter,
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disp=self.disp)
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assert_(hasattr(res.lowest_optimization_result, "jac"))
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# in this case, the Jacobian is just [df/dx, df/dy]
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_, jacobian = func2d_easyderiv(res.x)
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assert_almost_equal(res.lowest_optimization_result.jac, jacobian,
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self.tol)
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def test_2d_nograd(self):
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# test 2-D minimizations without gradient
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i = 1
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res = basinhopping(func2d_nograd, self.x0[i],
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minimizer_kwargs=self.kwargs_nograd,
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niter=self.niter, disp=self.disp)
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assert_almost_equal(res.x, self.sol[i], self.tol)
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@pytest.mark.fail_slow(5)
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def test_all_minimizers(self):
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# Test 2-D minimizations with gradient. Nelder-Mead, Powell, COBYLA, and
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# COBYQA don't accept jac=True, so aren't included here.
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i = 1
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methods = ['CG', 'BFGS', 'Newton-CG', 'L-BFGS-B', 'TNC', 'SLSQP']
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minimizer_kwargs = copy.copy(self.kwargs)
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for method in methods:
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minimizer_kwargs["method"] = method
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res = basinhopping(func2d, self.x0[i],
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minimizer_kwargs=minimizer_kwargs,
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niter=self.niter, disp=self.disp)
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assert_almost_equal(res.x, self.sol[i], self.tol)
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@pytest.mark.fail_slow(10)
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def test_all_nograd_minimizers(self):
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# Test 2-D minimizations without gradient. Newton-CG requires jac=True,
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# so not included here.
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i = 1
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methods = ['CG', 'BFGS', 'L-BFGS-B', 'TNC', 'SLSQP',
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'Nelder-Mead', 'Powell', 'COBYLA', 'COBYQA']
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minimizer_kwargs = copy.copy(self.kwargs_nograd)
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for method in methods:
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# COBYQA takes extensive amount of time on this problem
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niter = 10 if method == 'COBYQA' else self.niter
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minimizer_kwargs["method"] = method
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res = basinhopping(func2d_nograd, self.x0[i],
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minimizer_kwargs=minimizer_kwargs,
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niter=niter, disp=self.disp)
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tol = self.tol
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if method == 'COBYLA':
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tol = 2
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assert_almost_equal(res.x, self.sol[i], decimal=tol)
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def test_pass_takestep(self):
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# test that passing a custom takestep works
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# also test that the stepsize is being adjusted
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takestep = MyTakeStep1()
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initial_step_size = takestep.stepsize
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i = 1
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res = basinhopping(func2d, self.x0[i], minimizer_kwargs=self.kwargs,
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niter=self.niter, disp=self.disp,
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take_step=takestep)
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assert_almost_equal(res.x, self.sol[i], self.tol)
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assert_(takestep.been_called)
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# make sure that the build in adaptive step size has been used
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assert_(initial_step_size != takestep.stepsize)
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def test_pass_simple_takestep(self):
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# test that passing a custom takestep without attribute stepsize
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takestep = myTakeStep2
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i = 1
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res = basinhopping(func2d_nograd, self.x0[i],
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minimizer_kwargs=self.kwargs_nograd,
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niter=self.niter, disp=self.disp,
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take_step=takestep)
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assert_almost_equal(res.x, self.sol[i], self.tol)
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def test_pass_accept_test(self):
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# test passing a custom accept test
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# makes sure it's being used and ensures all the possible return values
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# are accepted.
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accept_test = MyAcceptTest()
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i = 1
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# there's no point in running it more than a few steps.
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basinhopping(func2d, self.x0[i], minimizer_kwargs=self.kwargs,
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niter=10, disp=self.disp, accept_test=accept_test)
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assert_(accept_test.been_called)
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def test_pass_callback(self):
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# test passing a custom callback function
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# This makes sure it's being used. It also returns True after 10 steps
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# to ensure that it's stopping early.
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callback = MyCallBack()
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i = 1
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# there's no point in running it more than a few steps.
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res = basinhopping(func2d, self.x0[i], minimizer_kwargs=self.kwargs,
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niter=30, disp=self.disp, callback=callback)
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assert_(callback.been_called)
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assert_("callback" in res.message[0])
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# One of the calls of MyCallBack is during BasinHoppingRunner
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# construction, so there are only 9 remaining before MyCallBack stops
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# the minimization.
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assert_equal(res.nit, 9)
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def test_minimizer_fail(self):
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# test if a minimizer fails
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i = 1
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self.kwargs["options"] = dict(maxiter=0)
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self.niter = 10
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res = basinhopping(func2d, self.x0[i], minimizer_kwargs=self.kwargs,
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niter=self.niter, disp=self.disp)
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# the number of failed minimizations should be the number of
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# iterations + 1
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assert_equal(res.nit + 1, res.minimization_failures)
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def test_niter_zero(self):
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# gh5915, what happens if you call basinhopping with niter=0
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i = 0
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basinhopping(func1d, self.x0[i], minimizer_kwargs=self.kwargs,
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niter=0, disp=self.disp)
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def test_seed_reproducibility(self):
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# seed should ensure reproducibility between runs
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minimizer_kwargs = {"method": "L-BFGS-B", "jac": True}
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f_1 = []
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def callback(x, f, accepted):
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f_1.append(f)
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basinhopping(func2d, [1.0, 1.0], minimizer_kwargs=minimizer_kwargs,
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niter=10, callback=callback, seed=10)
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f_2 = []
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def callback2(x, f, accepted):
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f_2.append(f)
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basinhopping(func2d, [1.0, 1.0], minimizer_kwargs=minimizer_kwargs,
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niter=10, callback=callback2, seed=10)
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assert_equal(np.array(f_1), np.array(f_2))
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def test_random_gen(self):
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# check that np.random.Generator can be used (numpy >= 1.17)
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rng = np.random.default_rng(1)
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minimizer_kwargs = {"method": "L-BFGS-B", "jac": True}
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res1 = basinhopping(func2d, [1.0, 1.0],
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minimizer_kwargs=minimizer_kwargs,
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niter=10, seed=rng)
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rng = np.random.default_rng(1)
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res2 = basinhopping(func2d, [1.0, 1.0],
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minimizer_kwargs=minimizer_kwargs,
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niter=10, seed=rng)
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assert_equal(res1.x, res2.x)
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def test_monotonic_basin_hopping(self):
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# test 1-D minimizations with gradient and T=0
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i = 0
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res = basinhopping(func1d, self.x0[i], minimizer_kwargs=self.kwargs,
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niter=self.niter, disp=self.disp, T=0)
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||
|
|
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)
|