"""
OpenMDAO Wrapper for the scipy.optimize.minimize family of local optimizers.
"""
import sys
from packaging.version import Version
import numpy as np
from scipy import __version__ as scipy_version
from scipy.optimize import minimize
from openmdao.core.constants import INF_BOUND
from openmdao.core.driver import Driver, RecordingDebugging
from openmdao.core.group import Group
from openmdao.utils.class_util import WeakMethodWrapper
from openmdao.utils.mpi import MPI
# Optimizers in scipy.minimize
_optimizers = {'Nelder-Mead', 'Powell', 'CG', 'BFGS', 'Newton-CG', 'L-BFGS-B',
'TNC', 'COBYLA', 'SLSQP'}
if Version(scipy_version) >= Version("1.1"): # Only available in newer versions
_optimizers.add('trust-constr')
# For 'basinhopping' and 'shgo' gradients are used only in the local minimization
_gradient_optimizers = {'CG', 'BFGS', 'Newton-CG', 'L-BFGS-B', 'TNC', 'SLSQP', 'dogleg',
'trust-ncg', 'trust-constr', 'basinhopping', 'shgo'}
_hessian_optimizers = {'trust-constr', 'trust-ncg'}
_bounds_optimizers = {'L-BFGS-B', 'TNC', 'SLSQP', 'trust-constr', 'dual_annealing', 'shgo',
'differential_evolution', 'basinhopping', 'Nelder-Mead'}
if Version(scipy_version) >= Version("1.11"):
# COBYLA supports bounds starting with SciPy Version 1.11
_bounds_optimizers |= {'COBYLA'}
_constraint_optimizers = {'COBYLA', 'SLSQP', 'trust-constr', 'shgo'}
_constraint_grad_optimizers = _gradient_optimizers & _constraint_optimizers
if Version(scipy_version) >= Version("1.4"):
_constraint_optimizers.add('differential_evolution')
_constraint_grad_optimizers.add('differential_evolution')
_eq_constraint_optimizers = {'SLSQP', 'trust-constr'}
_global_optimizers = {'differential_evolution', 'basinhopping'}
if Version(scipy_version) >= Version("1.2"): # Only available in newer versions
_global_optimizers |= {'shgo', 'dual_annealing'}
# Global optimizers and optimizers in minimize
_all_optimizers = _optimizers | _global_optimizers
# These require Hessian or Hessian-vector product, so they are not supported
# right now.
# dual-annealing and basinhopping not supported yet
_unsupported_optimizers = {'dogleg', 'trust-ncg'}
# With "old-style" a constraint is a dictionary, with "new-style" an object
# With "old-style" a bound is a tuple, with "new-style" a Bounds instance
# In principle now everything can work with "old-style"
# These settings have no effect to the optimizers implemented before SciPy 1.1
_supports_new_style = {'trust-constr'}
if Version(scipy_version) >= Version("1.4"):
_supports_new_style.add('differential_evolution')
_use_new_style = True # Recommended to set to True
CITATIONS = """
@article{Hwang_maud_2018
author = {Hwang, John T. and Martins, Joaquim R.R.A.},
title = "{A Computational Architecture for Coupling Heterogeneous
Numerical Models and Computing Coupled Derivatives}",
journal = "{ACM Trans. Math. Softw.}",
volume = {44},
number = {4},
month = jun,
year = {2018},
pages = {37:1--37:39},
articleno = {37},
numpages = {39},
doi = {10.1145/3182393},
publisher = {ACM},
"""
[docs]class ScipyOptimizeDriver(Driver):
"""
Driver wrapper for the scipy.optimize.minimize family of local optimizers.
Inequality constraints are supported by COBYLA and SLSQP,
but equality constraints are only supported by SLSQP. None of the other
optimizers support constraints.
ScipyOptimizeDriver supports the following:
equality_constraints
inequality_constraints
Parameters
----------
**kwargs : dict of keyword arguments
Keyword arguments that will be mapped into the Driver options.
Attributes
----------
fail : bool
Flag that indicates failure of most recent optimization.
iter_count : int
Counter for function evaluations.
_scipy_optimize_result : OptimizeResult
Result returned from scipy.optimize call.
opt_settings : dict
Dictionary of solver-specific options. See the scipy.optimize.minimize documentation.
_check_jac : bool
Used internally to control when to perform singular checks on computed total derivs.
_con_cache : dict
Cached result of constraint evaluations because scipy asks for them in a separate function.
_con_idx : dict
Used for constraint bookkeeping in the presence of 2-sided constraints.
_grad_cache : {}
Cached result of nonlinear constraint derivatives because scipy asks for them in a separate
function.
_exc_info : 3 item tuple
Storage for exception and traceback information.
_obj_and_nlcons : list
List of objective + nonlinear constraints. Used to compute total derivatives
for all except linear constraints.
_dvlist : list
Copy of _designvars.
_lincongrad_cache : np.ndarray
Pre-calculated gradients of linear constraints.
_desvar_array_cache : np.ndarray
Cached array for setting design variables.
"""
[docs] def __init__(self, **kwargs):
"""
Initialize the ScipyOptimizeDriver.
"""
super().__init__(**kwargs)
# What we support
self.supports['optimization'] = True
self.supports['inequality_constraints'] = True
self.supports['equality_constraints'] = True
self.supports['two_sided_constraints'] = True
self.supports['linear_constraints'] = True
self.supports['simultaneous_derivatives'] = True
# What we don't support
self.supports['multiple_objectives'] = False
self.supports['active_set'] = False
self.supports['integer_design_vars'] = False
self.supports['distributed_design_vars'] = False
self.supports._read_only = True
# The user places optimizer-specific settings in here.
self.opt_settings = {}
self._scipy_optimize_result = None
self._grad_cache = None
self._con_cache = None
self._con_idx = {}
self._obj_and_nlcons = None
self._dvlist = None
self._lincongrad_cache = None
self._desvar_array_cache = None
self.fail = False
self.iter_count = 0
self._check_jac = False
self._exc_info = None
self._total_jac_format = 'array'
self.cite = CITATIONS
def _declare_options(self):
"""
Declare options before kwargs are processed in the init method.
"""
self.options.declare('optimizer', 'SLSQP', values=_all_optimizers,
desc='Name of optimizer to use')
self.options.declare('tol', 1.0e-6, lower=0.0,
desc='Tolerance for termination. For detailed '
'control, use solver-specific options.')
self.options.declare('maxiter', 200, lower=0,
desc='Maximum number of iterations.')
self.options.declare('disp', True, types=bool,
desc='Set to False to prevent printing of Scipy convergence messages')
self.options.declare('singular_jac_behavior', default='warn',
values=['error', 'warn', 'ignore'],
desc='Defines behavior of a zero row/col check after first call to'
'compute_totals:'
'error - raise an error.'
'warn - raise a warning.'
"ignore - don't perform check.")
self.options.declare('singular_jac_tol', default=1e-16,
desc='Tolerance for zero row/column check.')
def _get_name(self):
"""
Get name of current optimizer.
Returns
-------
str
The name of the current optimizer.
"""
return "ScipyOptimize_" + self.options['optimizer']
def _setup_driver(self, problem):
"""
Prepare the driver for execution.
This is the final thing to run during setup.
Parameters
----------
problem : <Problem>
Pointer
"""
super()._setup_driver(problem)
opt = self.options['optimizer']
self.supports._read_only = False
self.supports['gradients'] = opt in _gradient_optimizers
self.supports['inequality_constraints'] = opt in _constraint_optimizers
self.supports['two_sided_constraints'] = opt in _constraint_optimizers
self.supports['equality_constraints'] = opt in _eq_constraint_optimizers
self.supports._read_only = True
self._check_jac = self.options['singular_jac_behavior'] in ['error', 'warn']
# Raises error if multiple objectives are not supported, but more objectives were defined.
if not self.supports['multiple_objectives'] and len(self._objs) > 1:
msg = '{} currently does not support multiple objectives.'
raise RuntimeError(msg.format(self.msginfo))
# Since COBYLA did not support bounds in versions of SciPy prior to 1.11, we need to
# add to the _cons metadata for any bounds that need to be translated into a constraint
if opt == 'COBYLA' and Version(scipy_version) < Version("1.11"):
for name, meta in self._designvars.items():
lower = meta['lower']
upper = meta['upper']
if isinstance(lower, np.ndarray) or lower > -INF_BOUND \
or isinstance(upper, np.ndarray) or upper < INF_BOUND:
self._cons[name] = meta.copy()
self._cons[name]['equals'] = None
self._cons[name]['linear'] = True
self._cons[name]['alias'] = None
[docs] def run(self):
"""
Optimize the problem using selected Scipy optimizer.
Returns
-------
bool
Failure flag; True if failed to converge, False is successful.
"""
self.result.reset()
prob = self._problem()
opt = self.options['optimizer']
model = prob.model
self.iter_count = 0
self._total_jac = None
self._total_jac_linear = None
self._desvar_array_cache = None
self._check_for_missing_objective()
self._check_for_invalid_desvar_values()
# Initial Run
with RecordingDebugging(self._get_name(), self.iter_count, self):
with model._relevance.nonlinear_active('iter'):
self._run_solve_nonlinear()
self.iter_count += 1
self._con_cache = self.get_constraint_values()
desvar_vals = self.get_design_var_values()
self._dvlist = list(self._designvars)
# maxiter and disp get passed into scipy with all the other options.
if 'maxiter' not in self.opt_settings: # lets you override the value in options
self.opt_settings['maxiter'] = self.options['maxiter']
self.opt_settings['disp'] = self.options['disp']
# Size Problem
ndesvar = 0
for desvar in self._designvars.values():
size = desvar['global_size'] if desvar['distributed'] else desvar['size']
ndesvar += size
x_init = np.empty(ndesvar)
# Initial Design Vars
i = 0
use_bounds = (opt in _bounds_optimizers)
if use_bounds:
bounds = []
else:
bounds = None
for name, meta in self._designvars.items():
size = meta['global_size'] if meta['distributed'] else meta['size']
x_init[i:i + size] = desvar_vals[name]
i += size
# Bounds if our optimizer supports them
if use_bounds:
meta_low = meta['lower']
meta_high = meta['upper']
for j in range(size):
if isinstance(meta_low, np.ndarray):
p_low = meta_low[j]
else:
p_low = meta_low
if isinstance(meta_high, np.ndarray):
p_high = meta_high[j]
else:
p_high = meta_high
bounds.append((p_low, p_high))
if use_bounds and (opt in _supports_new_style) and _use_new_style:
# For 'trust-constr' it is better to use the new type bounds, because it seems to work
# better (for the current examples in the tests) with the "keep_feasible" option
try:
from scipy.optimize import Bounds
from scipy.optimize._constraints import old_bound_to_new
except ImportError:
msg = ('The "trust-constr" optimizer is supported for SciPy 1.1.0 and above. '
'The installed version is {}')
raise ImportError(msg.format(scipy_version))
# Convert "old-style" bounds to "new_style" bounds
lower, upper = old_bound_to_new(bounds) # tuple, tuple
keep_feasible = self.opt_settings.get('keep_feasible_bounds', True)
bounds = Bounds(lb=lower, ub=upper, keep_feasible=keep_feasible)
# Constraints
constraints = []
nl_i = 1 # start at 1 since row 0 is the objective. Constraints start at row 1.
lin_i = 0 # counter for linear constraint jacobian
lincons = [] # list of linear constraints
self._obj_and_nlcons = list(self._objs)
if opt in _constraint_optimizers:
# get list of linear constraints and precalculate gradients for them (if any)
if opt in _constraint_grad_optimizers:
lincons = [name for name, meta in self._cons.items() if meta.get('linear')]
else:
lincons = []
if lincons:
lincongrad = self._lincongrad_cache = \
self._compute_totals(of=lincons, wrt=self._dvlist, return_format='array')
else:
self._lincongrad_cache = None
# map constraints to index and instantiate constraints for scipy
for name, meta in self._cons.items():
if meta['indices'] is not None:
meta['size'] = size = meta['indices'].indexed_src_size
else:
size = meta['global_size'] if meta['distributed'] else meta['size']
upper = meta['upper']
lower = meta['lower']
equals = meta['equals']
linear = name in lincons
if linear:
self._con_idx[name] = lin_i
lin_i += size
else:
self._obj_and_nlcons.append(name)
self._con_idx[name] = nl_i
nl_i += size
# In scipy constraint optimizers take constraints in two separate formats
if opt in _supports_new_style and _use_new_style:
# Type of constraints is list of NonlinearConstraint and/or LinearConstraint
try:
from scipy.optimize import NonlinearConstraint, LinearConstraint
except ImportError:
msg = ('The "trust-constr" optimizer is supported for SciPy 1.1.0 and'
'above. The installed version is {}')
raise ImportError(msg.format(scipy_version))
if equals is not None:
lb = ub = equals
else:
lb = lower
ub = upper
if linear:
# LinearConstraint
con = LinearConstraint(A=lincongrad[self._con_idx[name]],
lb=lower, ub=upper, keep_feasible=True)
else:
# NonlinearConstraint
# Loop over every index separately,
# because scipy calls each constraint by index.
for j in range(size):
# TODO add option for Hessian
# Double-sided constraints are accepted by the algorithm
args = [name, False, j]
con = NonlinearConstraint(
fun=signature_extender(
WeakMethodWrapper(self, '_con_val_func'), args),
lb=lb, ub=ub,
jac=signature_extender(
WeakMethodWrapper(self, '_congradfunc'), args)
)
constraints.append(con)
else:
# Type of constraints is list of dict
# Loop over every index separately,
# because scipy calls each constraint by index.
for j in range(size):
con_dict = {}
if meta['equals'] is not None:
con_dict['type'] = 'eq'
else:
con_dict['type'] = 'ineq'
con_dict['fun'] = WeakMethodWrapper(self, '_confunc')
if opt in _constraint_grad_optimizers:
con_dict['jac'] = WeakMethodWrapper(self, '_congradfunc')
con_dict['args'] = [name, False, j]
constraints.append(con_dict)
if isinstance(upper, np.ndarray):
upper = upper[j]
if isinstance(lower, np.ndarray):
lower = lower[j]
dblcon = (upper < INF_BOUND) and (lower > -INF_BOUND)
# Add extra constraint if double-sided
if dblcon:
dcon_dict = {}
dcon_dict['type'] = 'ineq'
dcon_dict['fun'] = WeakMethodWrapper(self, '_confunc')
if opt in _constraint_grad_optimizers:
dcon_dict['jac'] = WeakMethodWrapper(self, '_congradfunc')
dcon_dict['args'] = [name, True, j]
constraints.append(dcon_dict)
# Provide gradients for optimizers that support it
if opt in _gradient_optimizers:
jac = self._gradfunc
else:
jac = None
# Hessian calculation method for optimizers, which require it
if opt in _hessian_optimizers:
if 'hess' in self.opt_settings:
hess = self.opt_settings.pop('hess')
else:
# Defaults to BFGS, if not in opt_settings
from scipy.optimize import BFGS
hess = BFGS()
else:
hess = None
# compute dynamic simul deriv coloring if option is set
prob.get_total_coloring(self._coloring_info, run_model=False)
# optimize
try:
if opt in _optimizers:
if prob.comm.rank != 0:
self.opt_settings['disp'] = False
result = minimize(self._objfunc, x_init,
# args=(),
method=opt,
jac=jac,
hess=hess,
# hessp=None,
bounds=bounds,
constraints=constraints,
tol=self.options['tol'],
# callback=None,
options=self.opt_settings)
elif opt == 'basinhopping':
from scipy.optimize import basinhopping
def fun(x):
return self._objfunc(x), jac(x)
if 'minimizer_kwargs' not in self.opt_settings:
self.opt_settings['minimizer_kwargs'] = {"method": "L-BFGS-B", "jac": True}
self.opt_settings.pop('maxiter') # It does not have this argument
def accept_test(f_new, x_new, f_old, x_old):
# Used to implement bounds besides the original functionality
if bounds is not None:
bound_check = all([b[0] <= xi <= b[1] for xi, b in zip(x_new, bounds)])
user_test = self.opt_settings.pop('accept_test', None) # callable
# has to satisfy both the bounds and the acceptance test defined by the
# user
if user_test is not None:
test_res = user_test(f_new, x_new, f_old, x_old)
if test_res == 'force accept':
return test_res
else: # result is boolean
return bound_check and test_res
else: # no user acceptance test, check only the bounds
return bound_check
else:
return True
result = basinhopping(fun, x_init,
accept_test=accept_test,
**self.opt_settings)
elif opt == 'dual_annealing':
from scipy.optimize import dual_annealing
self.opt_settings.pop('disp') # It does not have this argument
# There is no "options" param, so "opt_settings" can be used to set the (many)
# keyword arguments
result = dual_annealing(self._objfunc,
bounds=bounds,
**self.opt_settings)
elif opt == 'differential_evolution':
from scipy.optimize import differential_evolution
# There is no "options" param, so "opt_settings" can be used to set the (many)
# keyword arguments
result = differential_evolution(self._objfunc, bounds=bounds,
constraints=constraints,
**self.opt_settings)
elif opt == 'shgo':
from scipy.optimize import shgo
kwargs = dict()
for option in ('minimizer_kwargs', 'sampling_method ', 'n', 'iters'):
if option in self.opt_settings:
kwargs[option] = self.opt_settings[option]
# Set the Jacobian and the Hessian to the value calculated in OpenMDAO
if 'minimizer_kwargs' not in kwargs or kwargs['minimizer_kwargs'] is None:
kwargs['minimizer_kwargs'] = {}
kwargs['minimizer_kwargs'].setdefault('jac', jac)
kwargs['minimizer_kwargs'].setdefault('hess', hess)
# Objective function tolerance
self.opt_settings['f_tol'] = self.options['tol']
result = shgo(self._objfunc,
bounds=bounds,
constraints=constraints,
options=self.opt_settings,
**kwargs)
else:
msg = 'Optimizer "{}" is not implemented yet. Choose from: {}'
raise NotImplementedError(msg.format(opt, _all_optimizers))
# If an exception was swallowed in one of our callbacks, we want to raise it
# rather than the cryptic message from scipy.
except Exception as msg:
if self._exc_info is None:
raise
if self._exc_info is not None:
self._reraise()
self._scipy_optimize_result = result
if hasattr(result, 'success'):
self.fail = not result.success
if self.fail:
if prob.comm.rank == 0:
print('Optimization FAILED.')
print(result.message)
print('-' * 35)
elif self.options['disp']:
if prob.comm.rank == 0:
print('Optimization Complete')
print('-' * 35)
else:
self.fail = True # It is not known, so the worst option is assumed
if prob.comm.rank == 0:
print('Optimization Complete (success not known)')
print(result.message)
print('-' * 35)
return self.fail
def _update_design_vars(self, x_new):
"""
Update the design variables in the model.
Parameters
----------
x_new : ndarray
Array containing input values at new design point.
"""
i = 0
for name, meta in self._designvars.items():
size = meta['size']
self.set_design_var(name, x_new[i:i + size])
i += size
def _objfunc(self, x_new):
"""
Evaluate and return the objective function.
Model is executed here.
Parameters
----------
x_new : ndarray
Array containing input values at new design point.
Returns
-------
float
Value of the objective function evaluated at the new design point.
"""
model = self._problem().model
try:
# Pass in new inputs
if MPI:
model.comm.Bcast(x_new, root=0)
if self._desvar_array_cache is None:
self._desvar_array_cache = np.empty(x_new.shape, dtype=x_new.dtype)
self._desvar_array_cache[:] = x_new
self._update_design_vars(x_new)
with RecordingDebugging(self._get_name(), self.iter_count, self):
self.iter_count += 1
with model._relevance.nonlinear_active('iter'):
self._run_solve_nonlinear()
# Get the objective function evaluations
for obj in self.get_objective_values().values():
f_new = obj
break
self._con_cache = self.get_constraint_values()
except Exception:
if self._exc_info is None: # only record the first one
self._exc_info = sys.exc_info()
return 0
# print("Functions calculated")
# rank = MPI.COMM_WORLD.rank if MPI else 0
# print(rank, ' xnew', x_new)
# print(rank, ' fnew', f_new)
return f_new
def _con_val_func(self, x_new, name, dbl, idx):
"""
Return the value of the constraint function requested in args.
The lower or upper bound is **not** subtracted from the value. Used for optimizers,
which take the bounds of the constraints (e.g. trust-constr)
Parameters
----------
x_new : ndarray
Array containing input values at new design point.
name : str
Name of the constraint to be evaluated.
dbl : bool
True if double sided constraint.
idx : float
Contains index into the constraint array.
Returns
-------
float
Value of the constraint function.
"""
if self.options['optimizer'] == 'differential_evolution':
# the DE opt will not have called this, so we do it here to update DV/resp values
self._objfunc(x_new)
return self._con_cache[name][idx]
def _confunc(self, x_new, name, dbl, idx):
"""
Return the value of the constraint function requested in args.
Note that this function is called for each constraint, so the model is only run when the
objective is evaluated.
Parameters
----------
x_new : ndarray
Array containing input values at new design point.
name : str
Name of the constraint to be evaluated.
dbl : bool
True if double sided constraint.
idx : float
Contains index into the constraint array.
Returns
-------
float
Value of the constraint function.
"""
if self._exc_info is not None:
self._reraise()
cons = self._con_cache
meta = self._cons[name]
# Equality constraints
equals = meta['equals']
if equals is not None:
if isinstance(equals, np.ndarray):
equals = equals[idx]
return cons[name][idx] - equals
# Note, scipy defines constraints to be satisfied when positive,
# which is the opposite of OpenMDAO.
upper = meta['upper']
if isinstance(upper, np.ndarray):
upper = upper[idx]
lower = meta['lower']
if isinstance(lower, np.ndarray):
lower = lower[idx]
if dbl or (lower <= -INF_BOUND):
return upper - cons[name][idx]
else:
return cons[name][idx] - lower
def _gradfunc(self, x_new):
"""
Evaluate and return the gradient for the objective.
Gradients for the constraints are also calculated and cached here.
Parameters
----------
x_new : ndarray
Array containing input values at new design point.
Returns
-------
ndarray
Gradient of objective with respect to input array.
"""
prob = self._problem()
model = prob.model
try:
grad = self._compute_totals(of=self._obj_and_nlcons, wrt=self._dvlist,
return_format=self._total_jac_format)
self._grad_cache = grad
# First time through, check for zero row/col.
if self._check_jac and self._total_jac is not None:
for subsys in model.system_iter(include_self=True, recurse=True, typ=Group):
if subsys._has_approx:
break
else:
raise_error = self.options['singular_jac_behavior'] == 'error'
self._total_jac.check_total_jac(raise_error=raise_error,
tol=self.options['singular_jac_tol'])
self._check_jac = False
except Exception:
if self._exc_info is None: # only record the first one
self._exc_info = sys.exc_info()
return np.array([[]])
# print("Gradients calculated for objective")
# print(' xnew', x_new)
# print(' grad', grad[0, :])
return grad[0, :]
def _congradfunc(self, x_new, name, dbl, idx):
"""
Return the cached gradient of the constraint function.
Note, scipy calls the constraints one at a time, so the gradient is cached when the
objective gradient is called.
Parameters
----------
x_new : ndarray
Array containing input values at new design point.
name : str
Name of the constraint to be evaluated.
dbl : bool
Denotes if a constraint is double-sided or not.
idx : float
Contains index into the constraint array.
Returns
-------
float
Gradient of the constraint function wrt all inputs.
"""
if self._exc_info is not None:
self._reraise()
meta = self._cons[name]
if meta['linear']:
grad = self._lincongrad_cache
else:
if self._grad_cache is None:
# _gradfunc has not been called, meaning gradients are not
# used for the objective but are needed for the constraints
self._gradfunc(x_new)
grad = self._grad_cache
grad_idx = self._con_idx[name] + idx
# print("Constraint Gradient returned")
# print(' xnew', x_new)
# print(' grad', name, 'idx', idx, grad[grad_idx, :])
# Equality constraints
if meta['equals'] is not None:
return grad[grad_idx, :]
# Note, scipy defines constraints to be satisfied when positive,
# which is the opposite of OpenMDAO.
lower = meta['lower']
if isinstance(lower, np.ndarray):
lower = lower[idx]
if dbl or (lower <= -INF_BOUND):
return -grad[grad_idx, :]
else:
return grad[grad_idx, :]
def _reraise(self):
"""
Reraise any exception encountered when scipy calls back into our method.
"""
exc_info = self._exc_info
self._exc_info = None # clear since we're done with it
raise exc_info[1].with_traceback(exc_info[2])
[docs]def signature_extender(fcn, extra_args):
"""
Closure function, which appends extra arguments to the original function call.
The first argument is the design vector. The possible extra arguments from the callback
of :func:`scipy.optimize.minimize` are not passed to the function.
Some algorithms take a sequence of :class:`~scipy.optimize.NonlinearConstraint` as input
for the constraints. For this class it is not possible to pass additional arguments.
With this function the signature will be correct for both scipy and the driver.
Parameters
----------
fcn : callable
Function, which takes the design vector as the first argument.
extra_args : tuple or list
Extra arguments for the function.
Returns
-------
callable
The function with the signature expected by the driver.
"""
def closure(x, *args):
return fcn(x, *extra_args)
return closure
