742 lines
29 KiB
Python
742 lines
29 KiB
Python
"""
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basinhopping: The basinhopping global optimization algorithm
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"""
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import numpy as np
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import math
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import scipy.optimize
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from scipy._lib._util import check_random_state
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__all__ = ['basinhopping']
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class Storage:
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"""
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Class used to store the lowest energy structure
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"""
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def __init__(self, minres):
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self._add(minres)
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def _add(self, minres):
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self.minres = minres
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self.minres.x = np.copy(minres.x)
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def update(self, minres):
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if minres.fun < self.minres.fun:
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self._add(minres)
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return True
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else:
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return False
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def get_lowest(self):
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return self.minres
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class BasinHoppingRunner:
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"""This class implements the core of the basinhopping algorithm.
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x0 : ndarray
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The starting coordinates.
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minimizer : callable
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The local minimizer, with signature ``result = minimizer(x)``.
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The return value is an `optimize.OptimizeResult` object.
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step_taking : callable
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This function displaces the coordinates randomly. Signature should
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be ``x_new = step_taking(x)``. Note that `x` may be modified in-place.
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accept_tests : list of callables
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Each test is passed the kwargs `f_new`, `x_new`, `f_old` and
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`x_old`. These tests will be used to judge whether or not to accept
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the step. The acceptable return values are True, False, or ``"force
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accept"``. If any of the tests return False then the step is rejected.
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If ``"force accept"``, then this will override any other tests in
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order to accept the step. This can be used, for example, to forcefully
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escape from a local minimum that ``basinhopping`` is trapped in.
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disp : bool, optional
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Display status messages.
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"""
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def __init__(self, x0, minimizer, step_taking, accept_tests, disp=False):
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self.x = np.copy(x0)
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self.minimizer = minimizer
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self.step_taking = step_taking
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self.accept_tests = accept_tests
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self.disp = disp
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self.nstep = 0
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# initialize return object
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self.res = scipy.optimize.OptimizeResult()
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self.res.minimization_failures = 0
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# do initial minimization
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minres = minimizer(self.x)
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if not minres.success:
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self.res.minimization_failures += 1
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if self.disp:
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print("warning: basinhopping: local minimization failure")
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self.x = np.copy(minres.x)
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self.energy = minres.fun
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if self.disp:
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print("basinhopping step %d: f %g" % (self.nstep, self.energy))
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# initialize storage class
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self.storage = Storage(minres)
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if hasattr(minres, "nfev"):
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self.res.nfev = minres.nfev
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if hasattr(minres, "njev"):
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self.res.njev = minres.njev
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if hasattr(minres, "nhev"):
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self.res.nhev = minres.nhev
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def _monte_carlo_step(self):
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"""Do one Monte Carlo iteration
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Randomly displace the coordinates, minimize, and decide whether
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or not to accept the new coordinates.
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"""
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# Take a random step. Make a copy of x because the step_taking
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# algorithm might change x in place
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x_after_step = np.copy(self.x)
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x_after_step = self.step_taking(x_after_step)
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# do a local minimization
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minres = self.minimizer(x_after_step)
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x_after_quench = minres.x
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energy_after_quench = minres.fun
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if not minres.success:
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self.res.minimization_failures += 1
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if self.disp:
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print("warning: basinhopping: local minimization failure")
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if hasattr(minres, "nfev"):
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self.res.nfev += minres.nfev
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if hasattr(minres, "njev"):
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self.res.njev += minres.njev
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if hasattr(minres, "nhev"):
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self.res.nhev += minres.nhev
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# accept the move based on self.accept_tests. If any test is False,
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# then reject the step. If any test returns the special string
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# 'force accept', then accept the step regardless. This can be used
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# to forcefully escape from a local minimum if normal basin hopping
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# steps are not sufficient.
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accept = True
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for test in self.accept_tests:
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testres = test(f_new=energy_after_quench, x_new=x_after_quench,
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f_old=self.energy, x_old=self.x)
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if testres == 'force accept':
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accept = True
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break
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elif testres is None:
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raise ValueError("accept_tests must return True, False, or "
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"'force accept'")
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elif not testres:
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accept = False
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# Report the result of the acceptance test to the take step class.
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# This is for adaptive step taking
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if hasattr(self.step_taking, "report"):
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self.step_taking.report(accept, f_new=energy_after_quench,
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x_new=x_after_quench, f_old=self.energy,
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x_old=self.x)
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return accept, minres
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def one_cycle(self):
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"""Do one cycle of the basinhopping algorithm
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"""
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self.nstep += 1
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new_global_min = False
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accept, minres = self._monte_carlo_step()
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if accept:
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self.energy = minres.fun
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self.x = np.copy(minres.x)
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new_global_min = self.storage.update(minres)
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# print some information
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if self.disp:
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self.print_report(minres.fun, accept)
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if new_global_min:
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print("found new global minimum on step %d with function"
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" value %g" % (self.nstep, self.energy))
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# save some variables as BasinHoppingRunner attributes
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self.xtrial = minres.x
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self.energy_trial = minres.fun
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self.accept = accept
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return new_global_min
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def print_report(self, energy_trial, accept):
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"""print a status update"""
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minres = self.storage.get_lowest()
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print("basinhopping step %d: f %g trial_f %g accepted %d "
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" lowest_f %g" % (self.nstep, self.energy, energy_trial,
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accept, minres.fun))
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class AdaptiveStepsize:
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"""
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Class to implement adaptive stepsize.
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This class wraps the step taking class and modifies the stepsize to
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ensure the true acceptance rate is as close as possible to the target.
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Parameters
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----------
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takestep : callable
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The step taking routine. Must contain modifiable attribute
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takestep.stepsize
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accept_rate : float, optional
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The target step acceptance rate
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interval : int, optional
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Interval for how often to update the stepsize
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factor : float, optional
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The step size is multiplied or divided by this factor upon each
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update.
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verbose : bool, optional
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Print information about each update
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"""
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def __init__(self, takestep, accept_rate=0.5, interval=50, factor=0.9,
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verbose=True):
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self.takestep = takestep
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self.target_accept_rate = accept_rate
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self.interval = interval
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self.factor = factor
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self.verbose = verbose
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self.nstep = 0
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self.nstep_tot = 0
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self.naccept = 0
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def __call__(self, x):
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return self.take_step(x)
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def _adjust_step_size(self):
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old_stepsize = self.takestep.stepsize
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accept_rate = float(self.naccept) / self.nstep
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if accept_rate > self.target_accept_rate:
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# We're accepting too many steps. This generally means we're
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# trapped in a basin. Take bigger steps.
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self.takestep.stepsize /= self.factor
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else:
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# We're not accepting enough steps. Take smaller steps.
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self.takestep.stepsize *= self.factor
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if self.verbose:
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print("adaptive stepsize: acceptance rate %f target %f new "
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"stepsize %g old stepsize %g" % (accept_rate,
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self.target_accept_rate, self.takestep.stepsize,
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old_stepsize))
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def take_step(self, x):
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self.nstep += 1
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self.nstep_tot += 1
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if self.nstep % self.interval == 0:
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self._adjust_step_size()
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return self.takestep(x)
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def report(self, accept, **kwargs):
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"called by basinhopping to report the result of the step"
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if accept:
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self.naccept += 1
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class RandomDisplacement:
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"""Add a random displacement of maximum size `stepsize` to each coordinate.
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Calling this updates `x` in-place.
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Parameters
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----------
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stepsize : float, optional
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Maximum stepsize in any dimension
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random_gen : {None, int, `numpy.random.Generator`,
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`numpy.random.RandomState`}, optional
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If `seed` is None (or `np.random`), the `numpy.random.RandomState`
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singleton is used.
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If `seed` is an int, a new ``RandomState`` instance is used,
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seeded with `seed`.
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If `seed` is already a ``Generator`` or ``RandomState`` instance then
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that instance is used.
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"""
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def __init__(self, stepsize=0.5, random_gen=None):
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self.stepsize = stepsize
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self.random_gen = check_random_state(random_gen)
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def __call__(self, x):
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x += self.random_gen.uniform(-self.stepsize, self.stepsize,
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np.shape(x))
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return x
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class MinimizerWrapper:
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"""
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wrap a minimizer function as a minimizer class
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"""
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def __init__(self, minimizer, func=None, **kwargs):
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self.minimizer = minimizer
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self.func = func
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self.kwargs = kwargs
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def __call__(self, x0):
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if self.func is None:
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return self.minimizer(x0, **self.kwargs)
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else:
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return self.minimizer(self.func, x0, **self.kwargs)
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class Metropolis:
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"""Metropolis acceptance criterion.
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Parameters
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----------
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T : float
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The "temperature" parameter for the accept or reject criterion.
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random_gen : {None, int, `numpy.random.Generator`,
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`numpy.random.RandomState`}, optional
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If `seed` is None (or `np.random`), the `numpy.random.RandomState`
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singleton is used.
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If `seed` is an int, a new ``RandomState`` instance is used,
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seeded with `seed`.
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If `seed` is already a ``Generator`` or ``RandomState`` instance then
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that instance is used.
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Random number generator used for acceptance test.
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"""
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def __init__(self, T, random_gen=None):
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# Avoid ZeroDivisionError since "MBH can be regarded as a special case
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# of the BH framework with the Metropolis criterion, where temperature
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# T = 0." (Reject all steps that increase energy.)
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self.beta = 1.0 / T if T != 0 else float('inf')
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self.random_gen = check_random_state(random_gen)
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def accept_reject(self, energy_new, energy_old):
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"""
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If new energy is lower than old, it will always be accepted.
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If new is higher than old, there is a chance it will be accepted,
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less likely for larger differences.
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"""
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with np.errstate(invalid='ignore'):
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# The energy values being fed to Metropolis are 1-length arrays, and if
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# they are equal, their difference is 0, which gets multiplied by beta,
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# which is inf, and array([0]) * float('inf') causes
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#
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# RuntimeWarning: invalid value encountered in multiply
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#
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# Ignore this warning so when the algorithm is on a flat plane, it always
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# accepts the step, to try to move off the plane.
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prod = -(energy_new - energy_old) * self.beta
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w = math.exp(min(0, prod))
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rand = self.random_gen.uniform()
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return w >= rand
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def __call__(self, **kwargs):
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"""
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f_new and f_old are mandatory in kwargs
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"""
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return bool(self.accept_reject(kwargs["f_new"],
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kwargs["f_old"]))
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def basinhopping(func, x0, niter=100, T=1.0, stepsize=0.5,
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minimizer_kwargs=None, take_step=None, accept_test=None,
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callback=None, interval=50, disp=False, niter_success=None,
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seed=None, *, target_accept_rate=0.5, stepwise_factor=0.9):
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"""Find the global minimum of a function using the basin-hopping algorithm.
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Basin-hopping is a two-phase method that combines a global stepping
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algorithm with local minimization at each step. Designed to mimic
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the natural process of energy minimization of clusters of atoms, it works
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well for similar problems with "funnel-like, but rugged" energy landscapes
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[5]_.
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As the step-taking, step acceptance, and minimization methods are all
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customizable, this function can also be used to implement other two-phase
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methods.
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Parameters
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----------
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func : callable ``f(x, *args)``
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Function to be optimized. ``args`` can be passed as an optional item
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in the dict `minimizer_kwargs`
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x0 : array_like
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Initial guess.
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niter : integer, optional
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The number of basin-hopping iterations. There will be a total of
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``niter + 1`` runs of the local minimizer.
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T : float, optional
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The "temperature" parameter for the acceptance or rejection criterion.
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Higher "temperatures" mean that larger jumps in function value will be
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accepted. For best results `T` should be comparable to the
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separation (in function value) between local minima.
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stepsize : float, optional
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Maximum step size for use in the random displacement.
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minimizer_kwargs : dict, optional
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Extra keyword arguments to be passed to the local minimizer
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`scipy.optimize.minimize` Some important options could be:
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method : str
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The minimization method (e.g. ``"L-BFGS-B"``)
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args : tuple
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Extra arguments passed to the objective function (`func`) and
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its derivatives (Jacobian, Hessian).
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take_step : callable ``take_step(x)``, optional
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Replace the default step-taking routine with this routine. The default
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step-taking routine is a random displacement of the coordinates, but
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other step-taking algorithms may be better for some systems.
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`take_step` can optionally have the attribute ``take_step.stepsize``.
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If this attribute exists, then `basinhopping` will adjust
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``take_step.stepsize`` in order to try to optimize the global minimum
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search.
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accept_test : callable, ``accept_test(f_new=f_new, x_new=x_new, f_old=fold, x_old=x_old)``, optional
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Define a test which will be used to judge whether to accept the
|
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step. This will be used in addition to the Metropolis test based on
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"temperature" `T`. The acceptable return values are True,
|
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False, or ``"force accept"``. If any of the tests return False
|
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then the step is rejected. If the latter, then this will override any
|
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other tests in order to accept the step. This can be used, for example,
|
|
to forcefully escape from a local minimum that `basinhopping` is
|
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trapped in.
|
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callback : callable, ``callback(x, f, accept)``, optional
|
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A callback function which will be called for all minima found. ``x``
|
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and ``f`` are the coordinates and function value of the trial minimum,
|
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and ``accept`` is whether that minimum was accepted. This can
|
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be used, for example, to save the lowest N minima found. Also,
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`callback` can be used to specify a user defined stop criterion by
|
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optionally returning True to stop the `basinhopping` routine.
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interval : integer, optional
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interval for how often to update the `stepsize`
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disp : bool, optional
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Set to True to print status messages
|
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niter_success : integer, optional
|
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Stop the run if the global minimum candidate remains the same for this
|
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number of iterations.
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seed : {None, int, `numpy.random.Generator`, `numpy.random.RandomState`}, optional
|
|
|
|
If `seed` is None (or `np.random`), the `numpy.random.RandomState`
|
|
singleton is used.
|
|
If `seed` is an int, a new ``RandomState`` instance is used,
|
|
seeded with `seed`.
|
|
If `seed` is already a ``Generator`` or ``RandomState`` instance then
|
|
that instance is used.
|
|
Specify `seed` for repeatable minimizations. The random numbers
|
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generated with this seed only affect the default Metropolis
|
|
`accept_test` and the default `take_step`. If you supply your own
|
|
`take_step` and `accept_test`, and these functions use random
|
|
number generation, then those functions are responsible for the state
|
|
of their random number generator.
|
|
target_accept_rate : float, optional
|
|
The target acceptance rate that is used to adjust the `stepsize`.
|
|
If the current acceptance rate is greater than the target,
|
|
then the `stepsize` is increased. Otherwise, it is decreased.
|
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Range is (0, 1). Default is 0.5.
|
|
|
|
.. versionadded:: 1.8.0
|
|
|
|
stepwise_factor : float, optional
|
|
The `stepsize` is multiplied or divided by this stepwise factor upon
|
|
each update. Range is (0, 1). Default is 0.9.
|
|
|
|
.. versionadded:: 1.8.0
|
|
|
|
Returns
|
|
-------
|
|
res : OptimizeResult
|
|
The optimization result represented as a `OptimizeResult` object.
|
|
Important attributes are: ``x`` the solution array, ``fun`` the value
|
|
of the function at the solution, and ``message`` which describes the
|
|
cause of the termination. The ``OptimizeResult`` object returned by the
|
|
selected minimizer at the lowest minimum is also contained within this
|
|
object and can be accessed through the ``lowest_optimization_result``
|
|
attribute. See `OptimizeResult` for a description of other attributes.
|
|
|
|
See Also
|
|
--------
|
|
minimize :
|
|
The local minimization function called once for each basinhopping step.
|
|
`minimizer_kwargs` is passed to this routine.
|
|
|
|
Notes
|
|
-----
|
|
Basin-hopping is a stochastic algorithm which attempts to find the global
|
|
minimum of a smooth scalar function of one or more variables [1]_ [2]_ [3]_
|
|
[4]_. The algorithm in its current form was described by David Wales and
|
|
Jonathan Doye [2]_ http://www-wales.ch.cam.ac.uk/.
|
|
|
|
The algorithm is iterative with each cycle composed of the following
|
|
features
|
|
|
|
1) random perturbation of the coordinates
|
|
|
|
2) local minimization
|
|
|
|
3) accept or reject the new coordinates based on the minimized function
|
|
value
|
|
|
|
The acceptance test used here is the Metropolis criterion of standard Monte
|
|
Carlo algorithms, although there are many other possibilities [3]_.
|
|
|
|
This global minimization method has been shown to be extremely efficient
|
|
for a wide variety of problems in physics and chemistry. It is
|
|
particularly useful when the function has many minima separated by large
|
|
barriers. See the `Cambridge Cluster Database
|
|
<https://www-wales.ch.cam.ac.uk/CCD.html>`_ for databases of molecular
|
|
systems that have been optimized primarily using basin-hopping. This
|
|
database includes minimization problems exceeding 300 degrees of freedom.
|
|
|
|
See the free software program `GMIN <https://www-wales.ch.cam.ac.uk/GMIN>`_
|
|
for a Fortran implementation of basin-hopping. This implementation has many
|
|
variations of the procedure described above, including more
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advanced step taking algorithms and alternate acceptance criterion.
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For stochastic global optimization there is no way to determine if the true
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global minimum has actually been found. Instead, as a consistency check,
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the algorithm can be run from a number of different random starting points
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to ensure the lowest minimum found in each example has converged to the
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global minimum. For this reason, `basinhopping` will by default simply
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run for the number of iterations `niter` and return the lowest minimum
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found. It is left to the user to ensure that this is in fact the global
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minimum.
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Choosing `stepsize`: This is a crucial parameter in `basinhopping` and
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depends on the problem being solved. The step is chosen uniformly in the
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region from x0-stepsize to x0+stepsize, in each dimension. Ideally, it
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should be comparable to the typical separation (in argument values) between
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local minima of the function being optimized. `basinhopping` will, by
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default, adjust `stepsize` to find an optimal value, but this may take
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many iterations. You will get quicker results if you set a sensible
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initial value for ``stepsize``.
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Choosing `T`: The parameter `T` is the "temperature" used in the
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Metropolis criterion. Basinhopping steps are always accepted if
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``func(xnew) < func(xold)``. Otherwise, they are accepted with
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probability::
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exp( -(func(xnew) - func(xold)) / T )
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So, for best results, `T` should to be comparable to the typical
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difference (in function values) between local minima. (The height of
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"walls" between local minima is irrelevant.)
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If `T` is 0, the algorithm becomes Monotonic Basin-Hopping, in which all
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steps that increase energy are rejected.
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.. versionadded:: 0.12.0
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References
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----------
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.. [1] Wales, David J. 2003, Energy Landscapes, Cambridge University Press,
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Cambridge, UK.
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.. [2] Wales, D J, and Doye J P K, Global Optimization by Basin-Hopping and
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the Lowest Energy Structures of Lennard-Jones Clusters Containing up to
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110 Atoms. Journal of Physical Chemistry A, 1997, 101, 5111.
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.. [3] Li, Z. and Scheraga, H. A., Monte Carlo-minimization approach to the
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multiple-minima problem in protein folding, Proc. Natl. Acad. Sci. USA,
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1987, 84, 6611.
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.. [4] Wales, D. J. and Scheraga, H. A., Global optimization of clusters,
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crystals, and biomolecules, Science, 1999, 285, 1368.
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.. [5] Olson, B., Hashmi, I., Molloy, K., and Shehu1, A., Basin Hopping as
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a General and Versatile Optimization Framework for the Characterization
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of Biological Macromolecules, Advances in Artificial Intelligence,
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Volume 2012 (2012), Article ID 674832, :doi:`10.1155/2012/674832`
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Examples
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--------
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The following example is a 1-D minimization problem, with many
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local minima superimposed on a parabola.
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>>> import numpy as np
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>>> from scipy.optimize import basinhopping
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>>> func = lambda x: np.cos(14.5 * x - 0.3) + (x + 0.2) * x
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>>> x0 = [1.]
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Basinhopping, internally, uses a local minimization algorithm. We will use
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the parameter `minimizer_kwargs` to tell basinhopping which algorithm to
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use and how to set up that minimizer. This parameter will be passed to
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`scipy.optimize.minimize`.
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>>> minimizer_kwargs = {"method": "BFGS"}
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>>> ret = basinhopping(func, x0, minimizer_kwargs=minimizer_kwargs,
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... niter=200)
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>>> print("global minimum: x = %.4f, f(x) = %.4f" % (ret.x, ret.fun))
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global minimum: x = -0.1951, f(x) = -1.0009
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Next consider a 2-D minimization problem. Also, this time, we
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will use gradient information to significantly speed up the search.
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>>> def func2d(x):
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... f = np.cos(14.5 * x[0] - 0.3) + (x[1] + 0.2) * x[1] + (x[0] +
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... 0.2) * x[0]
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... df = np.zeros(2)
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... df[0] = -14.5 * np.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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We'll also use a different local minimization algorithm. Also, we must tell
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the minimizer that our function returns both energy and gradient (Jacobian).
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>>> minimizer_kwargs = {"method":"L-BFGS-B", "jac":True}
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>>> x0 = [1.0, 1.0]
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>>> ret = basinhopping(func2d, x0, minimizer_kwargs=minimizer_kwargs,
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... niter=200)
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>>> print("global minimum: x = [%.4f, %.4f], f(x) = %.4f" % (ret.x[0],
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... ret.x[1],
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... ret.fun))
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global minimum: x = [-0.1951, -0.1000], f(x) = -1.0109
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Here is an example using a custom step-taking routine. Imagine you want
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the first coordinate to take larger steps than the rest of the coordinates.
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This can be implemented like so:
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>>> class MyTakeStep:
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... def __init__(self, stepsize=0.5):
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... self.stepsize = stepsize
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... self.rng = np.random.default_rng()
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... def __call__(self, x):
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... s = self.stepsize
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... x[0] += self.rng.uniform(-2.*s, 2.*s)
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... x[1:] += self.rng.uniform(-s, s, x[1:].shape)
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... return x
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Since ``MyTakeStep.stepsize`` exists basinhopping will adjust the magnitude
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of `stepsize` to optimize the search. We'll use the same 2-D function as
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before
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>>> mytakestep = MyTakeStep()
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>>> ret = basinhopping(func2d, x0, minimizer_kwargs=minimizer_kwargs,
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... niter=200, take_step=mytakestep)
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>>> print("global minimum: x = [%.4f, %.4f], f(x) = %.4f" % (ret.x[0],
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... ret.x[1],
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... ret.fun))
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global minimum: x = [-0.1951, -0.1000], f(x) = -1.0109
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Now, let's do an example using a custom callback function which prints the
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value of every minimum found
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>>> def print_fun(x, f, accepted):
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... print("at minimum %.4f accepted %d" % (f, int(accepted)))
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We'll run it for only 10 basinhopping steps this time.
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>>> rng = np.random.default_rng()
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>>> ret = basinhopping(func2d, x0, minimizer_kwargs=minimizer_kwargs,
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... niter=10, callback=print_fun, seed=rng)
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at minimum 0.4159 accepted 1
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at minimum -0.4317 accepted 1
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at minimum -1.0109 accepted 1
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at minimum -0.9073 accepted 1
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at minimum -0.4317 accepted 0
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at minimum -0.1021 accepted 1
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at minimum -0.7425 accepted 1
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at minimum -0.9073 accepted 1
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at minimum -0.4317 accepted 0
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at minimum -0.7425 accepted 1
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at minimum -0.9073 accepted 1
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The minimum at -1.0109 is actually the global minimum, found already on the
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8th iteration.
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"""
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if target_accept_rate <= 0. or target_accept_rate >= 1.:
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raise ValueError('target_accept_rate has to be in range (0, 1)')
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if stepwise_factor <= 0. or stepwise_factor >= 1.:
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raise ValueError('stepwise_factor has to be in range (0, 1)')
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x0 = np.array(x0)
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# set up the np.random generator
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rng = check_random_state(seed)
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# set up minimizer
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if minimizer_kwargs is None:
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minimizer_kwargs = dict()
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wrapped_minimizer = MinimizerWrapper(scipy.optimize.minimize, func,
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**minimizer_kwargs)
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|
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# set up step-taking algorithm
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if take_step is not None:
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if not callable(take_step):
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raise TypeError("take_step must be callable")
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# if take_step.stepsize exists then use AdaptiveStepsize to control
|
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# take_step.stepsize
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if hasattr(take_step, "stepsize"):
|
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take_step_wrapped = AdaptiveStepsize(
|
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take_step, interval=interval,
|
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accept_rate=target_accept_rate,
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factor=stepwise_factor,
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verbose=disp)
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else:
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take_step_wrapped = take_step
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else:
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# use default
|
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displace = RandomDisplacement(stepsize=stepsize, random_gen=rng)
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take_step_wrapped = AdaptiveStepsize(displace, interval=interval,
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accept_rate=target_accept_rate,
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factor=stepwise_factor,
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verbose=disp)
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|
|
# set up accept tests
|
|
accept_tests = []
|
|
if accept_test is not None:
|
|
if not callable(accept_test):
|
|
raise TypeError("accept_test must be callable")
|
|
accept_tests = [accept_test]
|
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|
|
# use default
|
|
metropolis = Metropolis(T, random_gen=rng)
|
|
accept_tests.append(metropolis)
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|
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if niter_success is None:
|
|
niter_success = niter + 2
|
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|
|
bh = BasinHoppingRunner(x0, wrapped_minimizer, take_step_wrapped,
|
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accept_tests, disp=disp)
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|
|
# The wrapped minimizer is called once during construction of
|
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# BasinHoppingRunner, so run the callback
|
|
if callable(callback):
|
|
callback(bh.storage.minres.x, bh.storage.minres.fun, True)
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|
|
# start main iteration loop
|
|
count, i = 0, 0
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message = ["requested number of basinhopping iterations completed"
|
|
" successfully"]
|
|
for i in range(niter):
|
|
new_global_min = bh.one_cycle()
|
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|
|
if callable(callback):
|
|
# should we pass a copy of x?
|
|
val = callback(bh.xtrial, bh.energy_trial, bh.accept)
|
|
if val is not None:
|
|
if val:
|
|
message = ["callback function requested stop early by"
|
|
"returning True"]
|
|
break
|
|
|
|
count += 1
|
|
if new_global_min:
|
|
count = 0
|
|
elif count > niter_success:
|
|
message = ["success condition satisfied"]
|
|
break
|
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|
|
# prepare return object
|
|
res = bh.res
|
|
res.lowest_optimization_result = bh.storage.get_lowest()
|
|
res.x = np.copy(res.lowest_optimization_result.x)
|
|
res.fun = res.lowest_optimization_result.fun
|
|
res.message = message
|
|
res.nit = i + 1
|
|
res.success = res.lowest_optimization_result.success
|
|
return res
|