def test_multistart(subspace_dim, stepback):
lb, ub, x0 = finite_bounds_exlude_optimum()
fun = rosenboth
opt = Optimizer(fun,
ub=ub,
lb=lb,
verbose=logging.INFO,
options={
fides.Options.FATOL: 0,
fides.Options.SUBSPACE_DIM: subspace_dim,
fides.Options.STEPBACK_STRAT: stepback,
fides.Options.REFINE_STEPBACK: False,
fides.Options.MAXITER: 1e3
})
for _ in range(int(1e2)):
x0 = np.random.random(x0.shape) * (ub - lb) + lb
opt.minimize(x0)
assert opt.fval >= opt.fval_min
if opt.fval == opt.fval_min:
assert np.isclose(opt.grad, opt.grad_min).all()
assert np.isclose(opt.x, opt.x_min).all()
if np.all(ub > 1):
assert np.isclose(opt.x, [1, 1]).all()
assert np.isclose(opt.grad, np.zeros(opt.x.shape), atol=1e-6).all()
def test_wrong_x():
lb, ub, x0 = finite_bounds_exlude_optimum()
fun = rosen
opt = Optimizer(
fun, ub=ub, lb=lb, verbose=logging.INFO,
options={fides.Options.FATOL: 0},
hessian_update=DFP()
)
with pytest.raises(ValueError):
opt.minimize(np.expand_dims(x0, 1))
def test_wrong_dim(fun):
lb, ub, x0 = finite_bounds_exlude_optimum()
opt = Optimizer(
fun, ub=ub, lb=lb, verbose=logging.INFO,
options={fides.Options.FATOL: 0,
fides.Options.MAXITER: 1e3}
)
with pytest.raises(ValueError):
x0 = np.random.random(x0.shape) * (ub - lb) + lb
opt.minimize(x0)
def test_multistart_randomfail():
lb, ub, x0 = finite_bounds_exlude_optimum()
fun = rosenrandomfail
opt = Optimizer(
fun, ub=ub, lb=lb, verbose=logging.INFO,
options={fides.Options.FATOL: 0,
fides.Options.MAXITER: 1e3}
)
for _ in range(int(1e2)):
with pytest.raises(RuntimeError):
x0 = np.random.random(x0.shape) * (ub - lb) + lb
opt.minimize(x0)
def test_minimize_hess_approx(bounds_and_init, fun, happ, subspace_dim,
stepback, refine):
lb, ub, x0 = bounds_and_init
opt = Optimizer(
fun, ub=ub, lb=lb, verbose=logging.INFO,
hessian_update=happ if happ is not None else None,
options={fides.Options.FATOL: 0,
fides.Options.SUBSPACE_DIM: subspace_dim,
fides.Options.STEPBACK_STRAT: stepback,
fides.Options.MAXITER: 1e3,
fides.Options.REFINE_STEPBACK: refine, }
)
opt.minimize(x0)
assert opt.fval >= opt.fval_min
if opt.fval == opt.fval_min:
assert np.isclose(opt.grad, opt.grad_min).all()
assert np.isclose(opt.x, opt.x_min).all()
if np.all(ub > 1):
assert np.isclose(opt.x, [1, 1]).all()
assert np.isclose(opt.grad, np.zeros(opt.x.shape), atol=1e-6).all()
def test_maxiter_maxtime():
lb, ub, x0 = finite_bounds_exlude_optimum()
fun = rosengrad
opt = Optimizer(
fun, ub=ub, lb=lb, verbose=logging.INFO,
options={fides.Options.FATOL: 0},
hessian_update=DFP()
)
tstart = time.time()
opt.minimize(x0)
t_elapsed = time.time() - tstart
maxiter = opt.iteration - 1
maxtime = t_elapsed/10
opt.options[fides.Options.MAXITER] = maxiter
opt.minimize(x0)
assert opt.exitflag == fides.ExitFlag.MAXITER
del opt.options[fides.Options.MAXITER]
opt.options[fides.Options.MAXTIME] = maxtime
opt.minimize(x0)
assert opt.exitflag == fides.ExitFlag.MAXTIME
del opt.options[fides.Options.MAXTIME]
def test_history():
lb, ub, x0 = finite_bounds_exlude_optimum()
fun = fletcher
h5file = 'history.h5'
opt = Optimizer(
fun, ub=ub, lb=lb, verbose=logging.INFO,
options={fides.Options.FATOL: 0,
fides.Options.HISTORY_FILE: h5file},
hessian_update=GNSBFGS(),
resfun=True
)
opt.minimize(x0)
opt.minimize(x0)
with h5py.File(h5file, 'r') as f:
assert len(f.keys()) == 2 # one group per optimization
# create new optimizer to check we are appending
opt = Optimizer(
fun, ub=ub, lb=lb, verbose=logging.INFO,
options={fides.Options.FATOL: 0,
fides.Options.HISTORY_FILE: h5file},
hessian_update=GNSBFGS(),
resfun=True
)
opt.minimize(x0)
opt.minimize(x0)
opt.minimize(x0)
with h5py.File(h5file, 'r') as f:
assert len(f.keys()) == 5
os.remove(h5file)
def test_minimize_hess_approx(bounds_and_init, fun, happ, subspace_dim,
stepback):
lb, ub, x0 = bounds_and_init
if (x0 == 0).all() and fun is fletcher:
x0 += 1
kwargs = dict(
fun=fun, ub=ub, lb=lb, verbose=logging.WARNING,
hessian_update=happ if happ is not None else None,
options={fides.Options.FATOL: 0,
fides.Options.FRTOL: 1e-12 if fun is fletcher else 1e-8,
fides.Options.SUBSPACE_DIM: subspace_dim,
fides.Options.STEPBACK_STRAT: stepback,
fides.Options.MAXITER: 2e2},
resfun=happ.requires_resfun if happ is not None else False
)
if not (subspace_dim == fides.SubSpaceDim.STEIHAUG and
stepback == fides.StepBackStrategy.REFINE):
opt = Optimizer(**kwargs)
else:
with pytest.raises(ValueError):
Optimizer(**kwargs)
return
opt.minimize(x0)
assert opt.fval >= opt.fval_min
if fun is fletcher:
xsol = [0, 0]
else:
xsol = [1, 1]
if opt.fval == opt.fval_min:
assert np.isclose(opt.grad, opt.grad_min).all()
assert np.isclose(opt.x, opt.x_min).all()
if np.all(ub > 1) and not isinstance(happ, BB): # bad broyden is bad
assert np.isclose(opt.x, xsol,
atol=1e-4 if fun is fletcher else 1e-6).all()
assert np.isclose(opt.grad, np.zeros(opt.x.shape),
atol=1e-4 if fun is fletcher else 1e-6).all()
def fides(
criterion_and_derivative,
x,
lower_bounds,
upper_bounds,
*,
hessian_update_strategy="bfgs",
convergence_absolute_criterion_tolerance=CONVERGENCE_ABSOLUTE_CRITERION_TOLERANCE,
convergence_relative_criterion_tolerance=CONVERGENCE_RELATIVE_CRITERION_TOLERANCE,
convergence_absolute_params_tolerance=CONVERGENCE_ABSOLUTE_PARAMS_TOLERANCE,
convergence_absolute_gradient_tolerance=CONVERGENCE_ABSOLUTE_GRADIENT_TOLERANCE,
convergence_relative_gradient_tolerance=CONVERGENCE_RELATIVE_GRADIENT_TOLERANCE,
stopping_max_iterations=STOPPING_MAX_ITERATIONS,
stopping_max_seconds=np.inf,
trustregion_initial_radius=1.0,
trustregion_stepback_strategy="truncate",
trustregion_subspace_dimension="full",
trustregion_max_stepback_fraction=0.95,
trustregion_decrease_threshold=0.25,
trustregion_increase_threshold=0.75,
trustregion_decrease_factor=0.25,
trustregion_increase_factor=2.0,
):
"""Minimize a scalar function using the Fides Optimizer.
For details see :ref:`fides_algorithm`.
"""
if not IS_FIDES_INSTALLED:
raise NotInstalledError(
"The 'fides' algorithm requires the fides package to be installed. "
"You can install it with `pip install fides>=0.7.4`.")
fides_options = {
"delta_init": trustregion_initial_radius,
"eta": trustregion_increase_threshold,
"fatol": convergence_absolute_criterion_tolerance,
"frtol": convergence_relative_criterion_tolerance,
"gamma1": trustregion_decrease_factor,
"gamma2": trustregion_increase_factor,
"gatol": convergence_absolute_gradient_tolerance,
"grtol": convergence_relative_gradient_tolerance,
"maxiter": stopping_max_iterations,
"maxtime": stopping_max_seconds,
"mu": trustregion_decrease_threshold,
"stepback_strategy": trustregion_stepback_strategy,
"subspace_solver": trustregion_subspace_dimension,
"theta_max": trustregion_max_stepback_fraction,
"xtol": convergence_absolute_params_tolerance,
}
hessian_instance = _create_hessian_updater_from_user_input(
hessian_update_strategy)
opt = Optimizer(
fun=criterion_and_derivative,
lb=lower_bounds,
ub=upper_bounds,
verbose=logging.ERROR,
options=fides_options,
funargs=None,
hessian_update=hessian_instance,
resfun=False,
)
raw_res = opt.minimize(x)
res = _process_fides_res(raw_res, opt)
return res