526 lines
18 KiB
Python
526 lines
18 KiB
Python
"""
|
|
Unit tests for the basin hopping global minimization algorithm.
|
|
"""
|
|
import copy
|
|
|
|
from numpy.testing import (assert_almost_equal, assert_equal, assert_,
|
|
assert_allclose)
|
|
import pytest
|
|
from pytest import raises as assert_raises
|
|
import numpy as np
|
|
from numpy import cos, sin
|
|
|
|
from scipy.optimize import basinhopping, OptimizeResult
|
|
from scipy.optimize._basinhopping import (
|
|
Storage, RandomDisplacement, Metropolis, AdaptiveStepsize)
|
|
|
|
|
|
def func1d(x):
|
|
f = cos(14.5 * x - 0.3) + (x + 0.2) * x
|
|
df = np.array(-14.5 * sin(14.5 * x - 0.3) + 2. * x + 0.2)
|
|
return f, df
|
|
|
|
|
|
def func2d_nograd(x):
|
|
f = cos(14.5 * x[0] - 0.3) + (x[1] + 0.2) * x[1] + (x[0] + 0.2) * x[0]
|
|
return f
|
|
|
|
|
|
def func2d(x):
|
|
f = cos(14.5 * x[0] - 0.3) + (x[1] + 0.2) * x[1] + (x[0] + 0.2) * x[0]
|
|
df = np.zeros(2)
|
|
df[0] = -14.5 * sin(14.5 * x[0] - 0.3) + 2. * x[0] + 0.2
|
|
df[1] = 2. * x[1] + 0.2
|
|
return f, df
|
|
|
|
|
|
def func2d_easyderiv(x):
|
|
f = 2.0*x[0]**2 + 2.0*x[0]*x[1] + 2.0*x[1]**2 - 6.0*x[0]
|
|
df = np.zeros(2)
|
|
df[0] = 4.0*x[0] + 2.0*x[1] - 6.0
|
|
df[1] = 2.0*x[0] + 4.0*x[1]
|
|
|
|
return f, df
|
|
|
|
|
|
class MyTakeStep1(RandomDisplacement):
|
|
"""use a copy of displace, but have it set a special parameter to
|
|
make sure it's actually being used."""
|
|
def __init__(self):
|
|
self.been_called = False
|
|
super().__init__()
|
|
|
|
def __call__(self, x):
|
|
self.been_called = True
|
|
return super().__call__(x)
|
|
|
|
|
|
def myTakeStep2(x):
|
|
"""redo RandomDisplacement in function form without the attribute stepsize
|
|
to make sure everything still works ok
|
|
"""
|
|
s = 0.5
|
|
x += np.random.uniform(-s, s, np.shape(x))
|
|
return x
|
|
|
|
|
|
class MyAcceptTest:
|
|
"""pass a custom accept test
|
|
|
|
This does nothing but make sure it's being used and ensure all the
|
|
possible return values are accepted
|
|
"""
|
|
def __init__(self):
|
|
self.been_called = False
|
|
self.ncalls = 0
|
|
self.testres = [False, 'force accept', True, np.bool_(True),
|
|
np.bool_(False), [], {}, 0, 1]
|
|
|
|
def __call__(self, **kwargs):
|
|
self.been_called = True
|
|
self.ncalls += 1
|
|
if self.ncalls - 1 < len(self.testres):
|
|
return self.testres[self.ncalls - 1]
|
|
else:
|
|
return True
|
|
|
|
|
|
class MyCallBack:
|
|
"""pass a custom callback function
|
|
|
|
This makes sure it's being used. It also returns True after 10
|
|
steps to ensure that it's stopping early.
|
|
|
|
"""
|
|
def __init__(self):
|
|
self.been_called = False
|
|
self.ncalls = 0
|
|
|
|
def __call__(self, x, f, accepted):
|
|
self.been_called = True
|
|
self.ncalls += 1
|
|
if self.ncalls == 10:
|
|
return True
|
|
|
|
|
|
class TestBasinHopping:
|
|
|
|
def setup_method(self):
|
|
""" Tests setup.
|
|
|
|
Run tests based on the 1-D and 2-D functions described above.
|
|
"""
|
|
self.x0 = (1.0, [1.0, 1.0])
|
|
self.sol = (-0.195, np.array([-0.195, -0.1]))
|
|
|
|
self.tol = 3 # number of decimal places
|
|
|
|
self.niter = 100
|
|
self.disp = False
|
|
|
|
# fix random seed
|
|
np.random.seed(1234)
|
|
|
|
self.kwargs = {"method": "L-BFGS-B", "jac": True}
|
|
self.kwargs_nograd = {"method": "L-BFGS-B"}
|
|
|
|
def test_TypeError(self):
|
|
# test the TypeErrors are raised on bad input
|
|
i = 1
|
|
# if take_step is passed, it must be callable
|
|
assert_raises(TypeError, basinhopping, func2d, self.x0[i],
|
|
take_step=1)
|
|
# if accept_test is passed, it must be callable
|
|
assert_raises(TypeError, basinhopping, func2d, self.x0[i],
|
|
accept_test=1)
|
|
|
|
def test_input_validation(self):
|
|
msg = 'target_accept_rate has to be in range \\(0, 1\\)'
|
|
with assert_raises(ValueError, match=msg):
|
|
basinhopping(func1d, self.x0[0], target_accept_rate=0.)
|
|
with assert_raises(ValueError, match=msg):
|
|
basinhopping(func1d, self.x0[0], target_accept_rate=1.)
|
|
|
|
msg = 'stepwise_factor has to be in range \\(0, 1\\)'
|
|
with assert_raises(ValueError, match=msg):
|
|
basinhopping(func1d, self.x0[0], stepwise_factor=0.)
|
|
with assert_raises(ValueError, match=msg):
|
|
basinhopping(func1d, self.x0[0], stepwise_factor=1.)
|
|
|
|
def test_1d_grad(self):
|
|
# test 1-D minimizations with gradient
|
|
i = 0
|
|
res = basinhopping(func1d, self.x0[i], minimizer_kwargs=self.kwargs,
|
|
niter=self.niter, disp=self.disp)
|
|
assert_almost_equal(res.x, self.sol[i], self.tol)
|
|
|
|
def test_2d(self):
|
|
# test 2d minimizations with gradient
|
|
i = 1
|
|
res = basinhopping(func2d, self.x0[i], minimizer_kwargs=self.kwargs,
|
|
niter=self.niter, disp=self.disp)
|
|
assert_almost_equal(res.x, self.sol[i], self.tol)
|
|
assert_(res.nfev > 0)
|
|
|
|
def test_njev(self):
|
|
# test njev is returned correctly
|
|
i = 1
|
|
minimizer_kwargs = self.kwargs.copy()
|
|
# L-BFGS-B doesn't use njev, but BFGS does
|
|
minimizer_kwargs["method"] = "BFGS"
|
|
res = basinhopping(func2d, self.x0[i],
|
|
minimizer_kwargs=minimizer_kwargs, niter=self.niter,
|
|
disp=self.disp)
|
|
assert_(res.nfev > 0)
|
|
assert_equal(res.nfev, res.njev)
|
|
|
|
def test_jac(self):
|
|
# test Jacobian returned
|
|
minimizer_kwargs = self.kwargs.copy()
|
|
# BFGS returns a Jacobian
|
|
minimizer_kwargs["method"] = "BFGS"
|
|
|
|
res = basinhopping(func2d_easyderiv, [0.0, 0.0],
|
|
minimizer_kwargs=minimizer_kwargs, niter=self.niter,
|
|
disp=self.disp)
|
|
|
|
assert_(hasattr(res.lowest_optimization_result, "jac"))
|
|
|
|
# in this case, the Jacobian is just [df/dx, df/dy]
|
|
_, jacobian = func2d_easyderiv(res.x)
|
|
assert_almost_equal(res.lowest_optimization_result.jac, jacobian,
|
|
self.tol)
|
|
|
|
def test_2d_nograd(self):
|
|
# test 2-D minimizations without gradient
|
|
i = 1
|
|
res = basinhopping(func2d_nograd, self.x0[i],
|
|
minimizer_kwargs=self.kwargs_nograd,
|
|
niter=self.niter, disp=self.disp)
|
|
assert_almost_equal(res.x, self.sol[i], self.tol)
|
|
|
|
def test_all_minimizers(self):
|
|
# Test 2-D minimizations with gradient. Nelder-Mead, Powell, and COBYLA
|
|
# don't accept jac=True, so aren't included here.
|
|
i = 1
|
|
methods = ['CG', 'BFGS', 'Newton-CG', 'L-BFGS-B', 'TNC', 'SLSQP']
|
|
minimizer_kwargs = copy.copy(self.kwargs)
|
|
for method in methods:
|
|
minimizer_kwargs["method"] = method
|
|
res = basinhopping(func2d, self.x0[i],
|
|
minimizer_kwargs=minimizer_kwargs,
|
|
niter=self.niter, disp=self.disp)
|
|
assert_almost_equal(res.x, self.sol[i], self.tol)
|
|
|
|
def test_all_nograd_minimizers(self):
|
|
# Test 2-D minimizations without gradient. Newton-CG requires jac=True,
|
|
# so not included here.
|
|
i = 1
|
|
methods = ['CG', 'BFGS', 'L-BFGS-B', 'TNC', 'SLSQP',
|
|
'Nelder-Mead', 'Powell', 'COBYLA']
|
|
minimizer_kwargs = copy.copy(self.kwargs_nograd)
|
|
for method in methods:
|
|
minimizer_kwargs["method"] = method
|
|
res = basinhopping(func2d_nograd, self.x0[i],
|
|
minimizer_kwargs=minimizer_kwargs,
|
|
niter=self.niter, disp=self.disp)
|
|
tol = self.tol
|
|
if method == 'COBYLA':
|
|
tol = 2
|
|
assert_almost_equal(res.x, self.sol[i], decimal=tol)
|
|
|
|
def test_pass_takestep(self):
|
|
# test that passing a custom takestep works
|
|
# also test that the stepsize is being adjusted
|
|
takestep = MyTakeStep1()
|
|
initial_step_size = takestep.stepsize
|
|
i = 1
|
|
res = basinhopping(func2d, self.x0[i], minimizer_kwargs=self.kwargs,
|
|
niter=self.niter, disp=self.disp,
|
|
take_step=takestep)
|
|
assert_almost_equal(res.x, self.sol[i], self.tol)
|
|
assert_(takestep.been_called)
|
|
# make sure that the build in adaptive step size has been used
|
|
assert_(initial_step_size != takestep.stepsize)
|
|
|
|
def test_pass_simple_takestep(self):
|
|
# test that passing a custom takestep without attribute stepsize
|
|
takestep = myTakeStep2
|
|
i = 1
|
|
res = basinhopping(func2d_nograd, self.x0[i],
|
|
minimizer_kwargs=self.kwargs_nograd,
|
|
niter=self.niter, disp=self.disp,
|
|
take_step=takestep)
|
|
assert_almost_equal(res.x, self.sol[i], self.tol)
|
|
|
|
def test_pass_accept_test(self):
|
|
# test passing a custom accept test
|
|
# makes sure it's being used and ensures all the possible return values
|
|
# are accepted.
|
|
accept_test = MyAcceptTest()
|
|
i = 1
|
|
# there's no point in running it more than a few steps.
|
|
basinhopping(func2d, self.x0[i], minimizer_kwargs=self.kwargs,
|
|
niter=10, disp=self.disp, accept_test=accept_test)
|
|
assert_(accept_test.been_called)
|
|
|
|
def test_pass_callback(self):
|
|
# test passing a custom callback function
|
|
# This makes sure it's being used. It also returns True after 10 steps
|
|
# to ensure that it's stopping early.
|
|
callback = MyCallBack()
|
|
i = 1
|
|
# there's no point in running it more than a few steps.
|
|
res = basinhopping(func2d, self.x0[i], minimizer_kwargs=self.kwargs,
|
|
niter=30, disp=self.disp, callback=callback)
|
|
assert_(callback.been_called)
|
|
assert_("callback" in res.message[0])
|
|
# One of the calls of MyCallBack is during BasinHoppingRunner
|
|
# construction, so there are only 9 remaining before MyCallBack stops
|
|
# the minimization.
|
|
assert_equal(res.nit, 9)
|
|
|
|
def test_minimizer_fail(self):
|
|
# test if a minimizer fails
|
|
i = 1
|
|
self.kwargs["options"] = dict(maxiter=0)
|
|
self.niter = 10
|
|
res = basinhopping(func2d, self.x0[i], minimizer_kwargs=self.kwargs,
|
|
niter=self.niter, disp=self.disp)
|
|
# the number of failed minimizations should be the number of
|
|
# iterations + 1
|
|
assert_equal(res.nit + 1, res.minimization_failures)
|
|
|
|
def test_niter_zero(self):
|
|
# gh5915, what happens if you call basinhopping with niter=0
|
|
i = 0
|
|
basinhopping(func1d, self.x0[i], minimizer_kwargs=self.kwargs,
|
|
niter=0, disp=self.disp)
|
|
|
|
def test_seed_reproducibility(self):
|
|
# seed should ensure reproducibility between runs
|
|
minimizer_kwargs = {"method": "L-BFGS-B", "jac": True}
|
|
|
|
f_1 = []
|
|
|
|
def callback(x, f, accepted):
|
|
f_1.append(f)
|
|
|
|
basinhopping(func2d, [1.0, 1.0], minimizer_kwargs=minimizer_kwargs,
|
|
niter=10, callback=callback, seed=10)
|
|
|
|
f_2 = []
|
|
|
|
def callback2(x, f, accepted):
|
|
f_2.append(f)
|
|
|
|
basinhopping(func2d, [1.0, 1.0], minimizer_kwargs=minimizer_kwargs,
|
|
niter=10, callback=callback2, seed=10)
|
|
assert_equal(np.array(f_1), np.array(f_2))
|
|
|
|
def test_random_gen(self):
|
|
# check that np.random.Generator can be used (numpy >= 1.17)
|
|
rng = np.random.default_rng(1)
|
|
|
|
minimizer_kwargs = {"method": "L-BFGS-B", "jac": True}
|
|
|
|
res1 = basinhopping(func2d, [1.0, 1.0],
|
|
minimizer_kwargs=minimizer_kwargs,
|
|
niter=10, seed=rng)
|
|
|
|
rng = np.random.default_rng(1)
|
|
res2 = basinhopping(func2d, [1.0, 1.0],
|
|
minimizer_kwargs=minimizer_kwargs,
|
|
niter=10, seed=rng)
|
|
assert_equal(res1.x, res2.x)
|
|
|
|
def test_monotonic_basin_hopping(self):
|
|
# test 1-D minimizations with gradient and T=0
|
|
i = 0
|
|
res = basinhopping(func1d, self.x0[i], minimizer_kwargs=self.kwargs,
|
|
niter=self.niter, disp=self.disp, T=0)
|
|
assert_almost_equal(res.x, self.sol[i], self.tol)
|
|
|
|
|
|
class Test_Storage:
|
|
def setup_method(self):
|
|
self.x0 = np.array(1)
|
|
self.f0 = 0
|
|
|
|
minres = OptimizeResult(success=True)
|
|
minres.x = self.x0
|
|
minres.fun = self.f0
|
|
|
|
self.storage = Storage(minres)
|
|
|
|
def test_higher_f_rejected(self):
|
|
new_minres = OptimizeResult(success=True)
|
|
new_minres.x = self.x0 + 1
|
|
new_minres.fun = self.f0 + 1
|
|
|
|
ret = self.storage.update(new_minres)
|
|
minres = self.storage.get_lowest()
|
|
assert_equal(self.x0, minres.x)
|
|
assert_equal(self.f0, minres.fun)
|
|
assert_(not ret)
|
|
|
|
@pytest.mark.parametrize('success', [True, False])
|
|
def test_lower_f_accepted(self, success):
|
|
new_minres = OptimizeResult(success=success)
|
|
new_minres.x = self.x0 + 1
|
|
new_minres.fun = self.f0 - 1
|
|
|
|
ret = self.storage.update(new_minres)
|
|
minres = self.storage.get_lowest()
|
|
assert (self.x0 != minres.x) == success # can't use `is`
|
|
assert (self.f0 != minres.fun) == success # left side is NumPy bool
|
|
assert ret is success
|
|
|
|
|
|
class Test_RandomDisplacement:
|
|
def setup_method(self):
|
|
self.stepsize = 1.0
|
|
self.displace = RandomDisplacement(stepsize=self.stepsize)
|
|
self.N = 300000
|
|
self.x0 = np.zeros([self.N])
|
|
|
|
def test_random(self):
|
|
# the mean should be 0
|
|
# the variance should be (2*stepsize)**2 / 12
|
|
# note these tests are random, they will fail from time to time
|
|
x = self.displace(self.x0)
|
|
v = (2. * self.stepsize) ** 2 / 12
|
|
assert_almost_equal(np.mean(x), 0., 1)
|
|
assert_almost_equal(np.var(x), v, 1)
|
|
|
|
|
|
class Test_Metropolis:
|
|
def setup_method(self):
|
|
self.T = 2.
|
|
self.met = Metropolis(self.T)
|
|
self.res_new = OptimizeResult(success=True, fun=0.)
|
|
self.res_old = OptimizeResult(success=True, fun=1.)
|
|
|
|
def test_boolean_return(self):
|
|
# the return must be a bool, else an error will be raised in
|
|
# basinhopping
|
|
ret = self.met(res_new=self.res_new, res_old=self.res_old)
|
|
assert isinstance(ret, bool)
|
|
|
|
def test_lower_f_accepted(self):
|
|
assert_(self.met(res_new=self.res_new, res_old=self.res_old))
|
|
|
|
def test_accept(self):
|
|
# test that steps are randomly accepted for f_new > f_old
|
|
one_accept = False
|
|
one_reject = False
|
|
for i in range(1000):
|
|
if one_accept and one_reject:
|
|
break
|
|
res_new = OptimizeResult(success=True, fun=1.)
|
|
res_old = OptimizeResult(success=True, fun=0.5)
|
|
ret = self.met(res_new=res_new, res_old=res_old)
|
|
if ret:
|
|
one_accept = True
|
|
else:
|
|
one_reject = True
|
|
assert_(one_accept)
|
|
assert_(one_reject)
|
|
|
|
def test_GH7495(self):
|
|
# an overflow in exp was producing a RuntimeWarning
|
|
# create own object here in case someone changes self.T
|
|
met = Metropolis(2)
|
|
res_new = OptimizeResult(success=True, fun=0.)
|
|
res_old = OptimizeResult(success=True, fun=2000)
|
|
with np.errstate(over='raise'):
|
|
met.accept_reject(res_new=res_new, res_old=res_old)
|
|
|
|
def test_gh7799(self):
|
|
# gh-7799 reported a problem in which local search was successful but
|
|
# basinhopping returned an invalid solution. Show that this is fixed.
|
|
def func(x):
|
|
return (x**2-8)**2+(x+2)**2
|
|
|
|
x0 = -4
|
|
limit = 50 # Constrain to func value >= 50
|
|
con = {'type': 'ineq', 'fun': lambda x: func(x) - limit},
|
|
res = basinhopping(func, x0, 30, minimizer_kwargs={'constraints': con})
|
|
assert res.success
|
|
assert_allclose(res.fun, limit, rtol=1e-6)
|
|
|
|
def test_accept_gh7799(self):
|
|
# Metropolis should not accept the result of an unsuccessful new local
|
|
# search if the old local search was successful
|
|
|
|
met = Metropolis(0) # monotonic basin hopping
|
|
res_new = OptimizeResult(success=True, fun=0.)
|
|
res_old = OptimizeResult(success=True, fun=1.)
|
|
|
|
# if new local search was successful and energy is lower, accept
|
|
assert met(res_new=res_new, res_old=res_old)
|
|
# if new res is unsuccessful, don't accept - even if energy is lower
|
|
res_new.success = False
|
|
assert not met(res_new=res_new, res_old=res_old)
|
|
# ...unless the old res was unsuccessful, too. In that case, why not?
|
|
res_old.success = False
|
|
assert met(res_new=res_new, res_old=res_old)
|
|
|
|
def test_reject_all_gh7799(self):
|
|
# Test the behavior when there is no feasible solution
|
|
def fun(x):
|
|
return x@x
|
|
|
|
def constraint(x):
|
|
return x + 1
|
|
|
|
kwargs = {'constraints': {'type': 'eq', 'fun': constraint},
|
|
'bounds': [(0, 1), (0, 1)], 'method': 'slsqp'}
|
|
res = basinhopping(fun, x0=[2, 3], niter=10, minimizer_kwargs=kwargs)
|
|
assert not res.success
|
|
|
|
|
|
class Test_AdaptiveStepsize:
|
|
def setup_method(self):
|
|
self.stepsize = 1.
|
|
self.ts = RandomDisplacement(stepsize=self.stepsize)
|
|
self.target_accept_rate = 0.5
|
|
self.takestep = AdaptiveStepsize(takestep=self.ts, verbose=False,
|
|
accept_rate=self.target_accept_rate)
|
|
|
|
def test_adaptive_increase(self):
|
|
# if few steps are rejected, the stepsize should increase
|
|
x = 0.
|
|
self.takestep(x)
|
|
self.takestep.report(False)
|
|
for i in range(self.takestep.interval):
|
|
self.takestep(x)
|
|
self.takestep.report(True)
|
|
assert_(self.ts.stepsize > self.stepsize)
|
|
|
|
def test_adaptive_decrease(self):
|
|
# if few steps are rejected, the stepsize should increase
|
|
x = 0.
|
|
self.takestep(x)
|
|
self.takestep.report(True)
|
|
for i in range(self.takestep.interval):
|
|
self.takestep(x)
|
|
self.takestep.report(False)
|
|
assert_(self.ts.stepsize < self.stepsize)
|
|
|
|
def test_all_accepted(self):
|
|
# test that everything works OK if all steps were accepted
|
|
x = 0.
|
|
for i in range(self.takestep.interval + 1):
|
|
self.takestep(x)
|
|
self.takestep.report(True)
|
|
assert_(self.ts.stepsize > self.stepsize)
|
|
|
|
def test_all_rejected(self):
|
|
# test that everything works OK if all steps were rejected
|
|
x = 0.
|
|
for i in range(self.takestep.interval + 1):
|
|
self.takestep(x)
|
|
self.takestep.report(False)
|
|
assert_(self.ts.stepsize < self.stepsize)
|