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"""
Unit tests for the basin hopping global minimization algorithm.
"""
from __future__ import division, print_function, absolute_import
import copy
from numpy.testing import assert_almost_equal, assert_equal, assert_
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(MyTakeStep1, self).__init__()
def __call__(self, x):
self.been_called = True
return super(MyTakeStep1, self).__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(object):
"""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(object):
"""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(object):
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_1d_grad(self):
# test 1d 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 2d 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 2d 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 2d 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 built 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])
assert_equal(res.nit, 10)
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_monotonic_basin_hopping(self):
# test 1d 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(object):
def setup_method(self):
self.x0 = np.array(1)
self.f0 = 0
minres = OptimizeResult()
minres.x = self.x0
minres.fun = self.f0
self.storage = Storage(minres)
def test_higher_f_rejected(self):
new_minres = OptimizeResult()
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)
def test_lower_f_accepted(self):
new_minres = OptimizeResult()
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)
assert_(self.f0 != minres.fun)
assert_(ret)
class Test_RandomDisplacement(object):
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(object):
def setup_method(self):
self.T = 2.
self.met = Metropolis(self.T)
def test_boolean_return(self):
# the return must be a bool. else an error will be raised in
# basinhopping
ret = self.met(f_new=0., f_old=1.)
assert isinstance(ret, bool)
def test_lower_f_accepted(self):
assert_(self.met(f_new=0., f_old=1.))
def test_KeyError(self):
# should raise KeyError if kwargs f_old or f_new is not passed
assert_raises(KeyError, self.met, f_old=1.)
assert_raises(KeyError, self.met, f_new=1.)
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
ret = self.met(f_new=1., f_old=0.5)
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)
with np.errstate(over='raise'):
met.accept_reject(0, 2000)
class Test_AdaptiveStepsize(object):
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)