def lbfgs_scipy(coords, pot, iprint=-1, tol=1e-3, nsteps=15000):
"""
a wrapper function for lbfgs routine in scipy
.. warn::
the scipy version of lbfgs uses linesearch based only on energy
which can make the minimization stop early. When the step size
is so small that the energy doesn't change to within machine precision (times the
parameter `factr`) the routine declares success and stops. This sounds fine, but
if the gradient is analytical the gradient can still be not converged. This is
because in the vicinity of the minimum the gradient changes much more rapidly then
the energy. Thus we want to make factr as small as possible. Unfortunately,
if we make it too small the routine realizes that the linesearch routine
isn't working and declares failure and exits.
So long story short, if your tolerance is very small (< 1e-6) this routine
will probably stop before truly reaching that tolerance. If you reduce `factr`
too much to mitigate this lbfgs will stop anyway, but declare failure misleadingly.
"""
import scipy.optimize
res = Result()
res.coords, res.energy, dictionary = scipy.optimize.fmin_l_bfgs_b(
pot.getEnergyGradient,
coords,
iprint=iprint,
pgtol=tol,
maxfun=nsteps,
factr=10.)
res.grad = dictionary["grad"]
res.nfev = dictionary["funcalls"]
warnflag = dictionary['warnflag']
# res.nsteps = dictionary['nit'] # new in scipy version 0.12
res.nsteps = res.nfev
res.message = dictionary['task']
res.success = True
if warnflag > 0:
print("warning: problem with quench: ", end=' ')
res.success = False
if warnflag == 1:
res.message = "too many function evaluations"
else:
res.message = str(dictionary['task'])
print(res.message)
# note: if the linesearch fails the lbfgs may fail without setting warnflag. Check
# tolerance exactly
if False:
if res.success:
maxV = np.max(np.abs(res.grad))
if maxV > tol:
print(
"warning: gradient seems too large", maxV, "tol =", tol,
". This is a known, but not understood issue of scipy_lbfgs"
)
print(res.message)
res.rms = res.grad.std()
return res
def ode_julia_naive(coords,
pot,
tol=1e-4,
nsteps=2000,
convergence_check=None,
solver_type=de.ROCK2(),
reltol=1e-5,
abstol=1e-5,
**kwargs):
class feval_pot:
""" wrapper class that makes sure the function is right
"""
def __init__(self):
self.nfev = 0
def get_negative_grad(self, x, p, t):
self.nfev += 1
return -pot.getEnergyGradient(x.copy())[1]
def get_energy_gradient(self, x):
self.nfev += 1
return pot.getEnergyGradient(x.copy())
function_evaluate_pot = feval_pot()
converged = False
n = 0
if convergence_check == None:
convergence_check = lambda g: np.max(g) < tol
# initialize ode problem
tspan = (0.0, 10.0)
# tspan
# tspan = (0.0, 10.0)
prob = de.ODEProblem(function_evaluate_pot.get_negative_grad, coords,
tspan)
integrator = de.init(prob, solver_type, reltol=reltol, abstol=abstol)
x_ = np.full(len(coords), np.nan)
while not converged and n < nsteps:
xold = x_
de.step_b(integrator)
x_ = integrator.u
n += 1
converged = convergence_check(de.get_du(integrator))
if converged:
print(de.get_du(integrator))
res = Result()
res.coords = x_
res.energy = pot.getEnergy(x_)
res.rms = 0
res.grad = 0
res.nfev = function_evaluate_pot.nfev
res.nsteps = n
res.success = converged
return res
def lbfgs_scipy(coords, pot, iprint=-1, tol=1e-3, nsteps=15000):
"""
a wrapper function for lbfgs routine in scipy
.. warn::
the scipy version of lbfgs uses linesearch based only on energy
which can make the minimization stop early. When the step size
is so small that the energy doesn't change to within machine precision (times the
parameter `factr`) the routine declares success and stops. This sounds fine, but
if the gradient is analytical the gradient can still be not converged. This is
because in the vicinity of the minimum the gradient changes much more rapidly then
the energy. Thus we want to make factr as small as possible. Unfortunately,
if we make it too small the routine realizes that the linesearch routine
isn't working and declares failure and exits.
So long story short, if your tolerance is very small (< 1e-6) this routine
will probably stop before truly reaching that tolerance. If you reduce `factr`
too much to mitigate this lbfgs will stop anyway, but declare failure misleadingly.
"""
if not hasattr(pot, "getEnergyGradient"):
# for compatibility with old quenchers.
# assume pot is a getEnergyGradient function
pot = _getEnergyGradientWrapper(pot)
import scipy.optimize
res = Result()
res.coords, res.energy, dictionary = scipy.optimize.fmin_l_bfgs_b(pot.getEnergyGradient,
coords, iprint=iprint, pgtol=tol, maxfun=nsteps, factr=10.)
res.grad = dictionary["grad"]
res.nfev = dictionary["funcalls"]
warnflag = dictionary['warnflag']
#res.nsteps = dictionary['nit'] # new in scipy version 0.12
res.nsteps = res.nfev
res.message = dictionary['task']
res.success = True
if warnflag > 0:
print "warning: problem with quench: ",
res.success = False
if warnflag == 1:
res.message = "too many function evaluations"
else:
res.message = str(dictionary['task'])
print res.message
#note: if the linesearch fails the lbfgs may fail without setting warnflag. Check
#tolerance exactly
if False:
if res.success:
maxV = np.max( np.abs(res.grad) )
if maxV > tol:
print "warning: gradient seems too large", maxV, "tol =", tol, ". This is a known, but not understood issue of scipy_lbfgs"
print res.message
res.rms = res.grad.std()
return res
def get_results(self):
res = Result()
with self.g.as_default(), self.g.device(self.device):
with self.session.as_default():
g, x = self.compute_gradients(self.model.gloss,
var_list=[self.model.x])[0]
g, x = self.process_grad(g, x)
res.energy = self.model.gloss.eval()
res.coords = x.eval()
res.grad = g.eval()
res.nfev = self.nfev.eval()
res.rms = self.rms.eval()
res.success = self.success.eval()
res.nsteps = self.neval
return res
def steepest_descent(x0,
pot,
iprint=-1,
dx=1e-4,
nsteps=100000,
tol=1e-3,
maxstep=-1.,
events=None):
"""steepest descent minimization
Notes
-----
this should never be used except for testing purposes. It is a bad implementation
of a terrible minimization routine. It will be very slow.
"""
N = len(x0)
x = x0.copy()
E, V = pot.getEnergyGradient(x)
funcalls = 1
for k in xrange(nsteps):
stp = -V * dx
if maxstep > 0:
stpsize = np.max(np.abs(V))
if stpsize > maxstep:
stp *= maxstep / stpsize
x += stp
E, V = pot.getEnergyGradient(x)
funcalls += 1
rms = np.linalg.norm(V) / np.sqrt(N)
if iprint > 0:
if funcalls % iprint == 0:
print "step %8d energy %20.12g rms gradient %20.12g" % (
funcalls, E, rms)
if events is not None:
for event in events:
event(energy=E, coords=x, rms=rms)
if rms < tol:
break
res = Result()
res.coords = x
res.energy = E
res.rms = rms
res.grad = V
res.nfev = funcalls
res.nsteps = k
res.success = res.rms <= tol
return res
def bfgs_scipy(coords, pot, iprint=-1, tol=1e-3, nsteps=5000, **kwargs):
"""
a wrapper function for the scipy BFGS algorithm
"""
import scipy.optimize
ret = scipy.optimize.fmin_bfgs(pot.getEnergy, coords, fprime=pot.getGradient,
gtol=tol, full_output=True, disp=iprint>0,
maxiter=nsteps, **kwargs)
res = Result()
res.coords = ret[0]
res.energy = ret[1]
res.grad = ret[2]
res.rms = np.linalg.norm(res.grad) / np.sqrt(len(res.grad))
res.nfev = ret[4] + ret[5]
res.nsteps = res.nfev # not correct, but no better information
res.success = np.max(np.abs(res.grad)) < tol
return res
def run(self, fmax=1e-3, steps=100000):
"""Run structure optimization algorithm.
This method will return when the forces on all individual
atoms are less than *fmax* or when the number of steps exceeds
*steps*."""
self.fmax = fmax
step = 0
res = Result()
res.success = False
while step < steps:
E, f = self.potential.getEnergyGradient(self.coords)
self.nfev += 1
#self.call_observers()
#print E
if self.alternate_stop_criterion is None:
i_am_done = self.converged(f)
else:
i_am_done = self.alternate_stop_criterion(energy=E, gradient=f,
tol=self.fmax)
if i_am_done:
res.success = True
break
self.step(-f)
self.nsteps += 1
rms = np.linalg.norm(f)/np.sqrt(len(f))
if self.iprint > 0:
if step % self.iprint == 0:
self.logger.info("fire: %s E %s rms %s", step, E, rms)
for event in self.events:
event(coords=self.coords, energy=E, rms=rms)
step += 1
res.nsteps = step
res.nfev = self.nfev
res.coords = self.coords
res.energy = E
res.grad = -f
res.rms = np.linalg.norm(res.grad)/np.sqrt(len(res.grad))
self.result = res
return res
def run(self, fmax=1e-3, steps=100000):
"""Run structure optimization algorithm.
This method will return when the forces on all individual
atoms are less than *fmax* or when the number of steps exceeds
*steps*.
"""
self.fmax = fmax
step = 0
res = Result()
res.success = False
while step < steps:
E, f = self.potential.getEnergyGradient(self.coords)
self.nfev += 1
if self.alternate_stop_criterion is None:
i_am_done = self.converged(f)
else:
i_am_done = self.alternate_stop_criterion(energy=E,
gradient=f,
tol=self.fmax)
if i_am_done:
res.success = True
break
self.step(-f)
self.nsteps += 1
rms = np.linalg.norm(f) / np.sqrt(len(f))
if self.iprint > 0:
if step % self.iprint == 0:
self.logger.info("fire: %s E %s rms %s", step, E, rms)
for event in self.events:
event(coords=self.coords, energy=E, rms=rms)
step += 1
res.nsteps = step
res.nfev = self.nfev
res.coords = self.coords
res.energy = E
res.grad = -f
res.rms = np.linalg.norm(res.grad) / np.sqrt(len(res.grad))
self.result = res
return res
def steepest_descent(x0, pot, iprint=-1, dx=1e-4, nsteps=100000,
tol=1e-3, maxstep=-1., events=None):
"""steepest descent minimization
Notes
-----
this should never be used except for testing purposes. It is a bad implementation
of a terrible minimization routine. It will be very slow.
"""
N = len(x0)
x = x0.copy()
E, V = pot.getEnergyGradient(x)
funcalls = 1
for k in range(nsteps):
stp = -V * dx
if maxstep > 0:
stpsize = np.max(np.abs(V))
if stpsize > maxstep:
stp *= maxstep / stpsize
x += stp
E, V = pot.getEnergyGradient(x)
funcalls += 1
rms = np.linalg.norm(V) / np.sqrt(N)
if iprint > 0:
if funcalls % iprint == 0:
print("step %8d energy %20.12g rms gradient %20.12g" % (funcalls, E, rms))
if events is not None:
for event in events:
event(energy=E, coords=x, rms=rms)
if rms < tol:
break
res = Result()
res.coords = x
res.energy = E
res.rms = rms
res.grad = V
res.nfev = funcalls
res.nsteps = k
res.success = res.rms <= tol
return res
def bfgs_scipy(coords, pot, iprint=-1, tol=1e-3, nsteps=5000, **kwargs):
"""
a wrapper function for the scipy BFGS algorithm
"""
import scipy.optimize
ret = scipy.optimize.fmin_bfgs(pot.getEnergy,
coords,
fprime=pot.getGradient,
gtol=tol,
full_output=True,
disp=iprint > 0,
maxiter=nsteps,
**kwargs)
res = Result()
res.coords = ret[0]
res.energy = ret[1]
res.grad = ret[2]
res.rms = np.linalg.norm(res.grad) / np.sqrt(len(res.grad))
res.nfev = ret[4] + ret[5]
res.nsteps = res.nfev # not correct, but no better information
res.success = np.max(np.abs(res.grad)) < tol
return res
def steepest_descent(x0, pot, iprint=-1, dx=1e-4, nsteps=100000,
tol=1e-3, maxstep=-1., events=None):
if not hasattr(pot, "getEnergyGradient"):
# for compatibility with old quenchers.
# assume pot is a getEnergyGradient function
pot = _getEnergyGradientWrapper(pot)
N = len(x0)
x=x0.copy()
E, V = pot.getEnergyGradient(x)
funcalls = 1
for k in xrange(nsteps):
stp = -V * dx
if maxstep > 0:
stpsize = np.max(np.abs(V))
if stpsize > maxstep:
stp *= maxstep / stpsize
x += stp
E, V = pot.getEnergyGradient(x)
funcalls += 1
rms = np.linalg.norm(V)/np.sqrt(N)
if iprint > 0:
if funcalls % iprint == 0:
print "step %8d energy %20.12g rms gradient %20.12g" % (funcalls, E, rms)
if events is not None:
for event in events:
event(energy=E, coords=x, rms=rms)
if rms < tol:
break
res = Result()
res.coords = x
res.energy = E
res.rms = rms
res.grad = V
res.nfev = funcalls
res.nsteps = k
res.success = res.rms <= tol
return res
def ode_julia_naive(coords,
pot,
tol=1e-4,
nsteps=20000,
convergence_check=None,
solver_type=de.CVODE_BDF(),
rtol=1e-4,
atol=1e-4,
**kwargs):
class feval_pot:
""" wrapper class that interfaces base potential to functions for ode solver
"""
def __init__(self):
self.nfev = 0
self.nhev = 0
def get_negative_grad(self, x, p, t):
"""
negative grad is f(u, p, t)
"""
self.nfev += 1
return -pot.getEnergyGradient(x.copy())[1]
def get_energy_gradient(self, x):
self.nfev += 1
return pot.getEnergyGradient(x.copy())
def get_jacobian(self, x, p, t):
self.nhev += 1
return -pot.getEnergyGradientHessian(x.copy())[2]
function_evaluate_pot = feval_pot()
converged = False
n = 0
if convergence_check == None:
convergence_check = lambda g: np.linalg.norm(g) < tol
# odefunc = de.ODEFunction(function_evaluate_pot.get_negative_grad, function_evaluate_pot.get_jacobian)
# initialize ode problem
tspan = (0, 10000.0)
f_bound = de.ODEFunction(function_evaluate_pot.get_negative_grad)
# f_free = de.ODEFunction(get_negative_grad,jac = get_jacobian)
prob = de.ODEProblem(f_bound, coords, tspan)
solver = Main.eval("CVODE_BDF(linear_solver=:GMRES)")
integrator = de.init(prob, solver, reltol=rtol, abstol=atol)
x_ = np.full(len(coords), np.nan)
while not converged and n < nsteps:
xold = x_
de.step_b(integrator)
x_ = integrator.u
n += 1
converged = convergence_check(de.get_du(integrator))
res = Result()
res.coords = x_
res.energy = pot.getEnergy(x_)
res.grad = 0
res.nfev = function_evaluate_pot.nfev
res.nsteps = n
res.nhev = function_evaluate_pot.nhev
res.success = converged
# res.nhev = function_evaluate_pot.nhev
return res
def run(self):
"""The main loop of the algorithm"""
coords = np.copy(self.coords)
res = Result() # return object
res.message = []
self._compute_gradients(coords)
iend = 0
for i in xrange(self.nsteps):
iend = i
# get the lowest eigenvalue and eigenvector
self.overlap = self._getLowestEigenVector(coords, i)
overlap = self.overlap
if self.eigenval < 0:
self.negatives_before_check -= 1
# determine whether everything looks OK.
all_ok = self.eigenval < 0 or not self.check_negative
if not all_ok:
if i == 0:
# we need to accept because we haven't saved the state yet
# Also, demand_initial_negative_vec will stop later if needed
all_ok = True
if not all_ok:
if self.negatives_before_check > 0 and not self.demand_initial_negative_vec:
print " positive before check. setting all ok"
all_ok = True
# if everything is OK, then continue, else revert the step
if all_ok:
self._saveState(coords)
self.reduce_step = 0
else:
self.npositive += 1
if self.npositive > self.npositive_max:
logger.warning(
"positive eigenvalue found too many times. ending %s",
self.npositive)
res.message.append(
"positive eigenvalue found too many times %d" %
self.npositive)
break
if self.verbosity > 2:
logger.info(
"the eigenvalue turned positive. %s %s", self.eigenval,
"Resetting last good values and taking smaller steps")
coords = self._resetState()
self.reduce_step += 1
# step uphill along the direction of the lowest eigenvector
coords = self._stepUphill(coords)
# minimize the coordinates in the space perpendicular to the lowest eigenvector
tangent_ret = self._minimizeTangentSpace(
coords, energy=self.get_energy(), gradient=self.get_gradient())
coords = tangent_ret.coords
tangentrms = tangent_ret.rms
# check if we are done and print some stuff
# self._compute_gradients(coords) # this is unnecessary
E = self.get_energy()
grad = self.get_gradient()
rms = np.linalg.norm(grad) * self.rmsnorm
gradpar = np.dot(grad, self.eigenvec) / np.linalg.norm(
self.eigenvec)
if self.iprint > 0:
if (i + 1) % self.iprint == 0:
ostring = "findTS: %3d E %9g rms %8g eigenvalue %9g rms perp %8g grad par %9g overlap %g" % (
i, E, rms, self.eigenval, tangentrms, gradpar, overlap)
extra = " Evec search: %d rms %g" % (
self.leig_result.nfev, self.leig_result.rms)
extra += " Tverse search: %d step %g" % (
self.tangent_result.nfev, self.tangent_move_step)
extra += " Uphill step:%g" % (self.uphill_step_size, )
logger.info("%s %s", ostring, extra)
if callable(self.event):
self.event(energy=E,
coords=coords,
rms=rms,
eigenval=self.eigenval,
stepnum=i)
if rms < self.tol:
break
if self.nfail >= self.nfail_max:
logger.warning(
"stopping findTransitionState. too many failures in eigenvector search %s",
self.nfail)
res.message.append(
"too many failures in eigenvector search %d" % self.nfail)
break
if i == 0 and self.eigenval > 0.:
if self.verbosity > 1:
logger.warning(
"initial eigenvalue is positive - increase NEB spring constant?"
)
if self.demand_initial_negative_vec:
logger.warning(
" aborting transition state search")
res.message.append("initial eigenvalue is positive %f" %
self.eigenval)
break
# done. do one last eigenvector search because coords may have changed
self._getLowestEigenVector(coords, iend)
# print some data
if self.verbosity > 0 or self.iprint > 0:
logger.info("findTransitionState done: %s %s %s %s %s", iend, E,
rms, "eigenvalue", self.eigenval)
success = True
# check if results make sense
if self.eigenval >= 0.:
if self.verbosity > 2:
logger.info(
"warning: transition state is ending with positive eigenvalue %s",
self.eigenval)
success = False
if rms > self.tol:
if self.verbosity > 2:
logger.info(
"warning: transition state search appears to have failed: rms %s",
rms)
success = False
if iend >= self.nsteps:
res.message.append("maximum iterations reached %d" % iend)
# update nfev with the number of calls from the transverse walker
if self._transverse_walker is not None:
twres = self._transverse_walker.get_result()
self.nfev += twres.nfev
res.coords = coords
res.energy = E
res.eigenval = self.eigenval
res.eigenvec = self.eigenvec
res.grad = grad
res.rms = rms
res.nsteps = iend
res.success = success
res.nfev = self.nfev
return res
def run(self):
"""The main loop of the algorithm"""
coords = np.copy(self.coords)
res = Result() # return object
res.message = []
# if starting with positive curvature, disable negative eigenvalue check
# this will be reenabled as soon as the eigenvector becomes negative
negative_before_check = 10
self._compute_gradients(coords)
for i in xrange(self.nsteps):
# get the lowest eigenvalue and eigenvector
self.overlap = self._getLowestEigenVector(coords, i)
overlap = self.overlap
#print self.eigenval
if self.eigenval < 0:
negative_before_check -= 1
# check to make sure the eigenvector is ok
if (i == 0 or self.eigenval <= 0 or not self.check_negative or
(negative_before_check > 0 and not self.demand_initial_negative_vec)):
self._saveState(coords)
self.reduce_step = 0
else:
self.npositive += 1
if self.npositive > self.npositive_max:
logger.warning( "positive eigenvalue found too many times. ending %s", self.npositive)
res.message.append( "positive eigenvalue found too many times %d" % self.npositive )
break
if self.verbosity > 2:
logger.info("the eigenvalue turned positive. %s %s", self.eigenval, "Resetting last good values and taking smaller steps")
coords = self._resetState()
self.reduce_step += 1
# step uphill along the direction of the lowest eigenvector
coords = self._stepUphill(coords)
# minimize the coordinates in the space perpendicular to the lowest eigenvector
tangent_ret = self._minimizeTangentSpace(coords, energy=self.get_energy(), gradient=self.get_gradient())
coords = tangent_ret.coords
tangentrms = tangent_ret.rms
# check if we are done and print some stuff
# self._compute_gradients(coords) # this is unnecessary
E = self.get_energy()
grad = self.get_gradient()
rms = np.linalg.norm(grad) * self.rmsnorm
gradpar = np.dot(grad, self.eigenvec) / np.linalg.norm(self.eigenvec)
if self.iprint > 0:
if (i+1) % self.iprint == 0:
ostring = "findTS: %3d E %9g rms %8g eigenvalue %9g rms perp %8g grad par %9g overlap %g" % (
i, E, rms, self.eigenval, tangentrms, gradpar, overlap)
extra = " Evec search: %d rms %g" % (self.leig_result.nfev, self.leig_result.rms)
extra += " Tverse search: %d step %g" % (self.tangent_result.nfev,
self.tangent_move_step)
extra += " Uphill step:%g" % (self.uphill_step_size,)
logger.info("%s %s", ostring, extra)
if callable(self.event):
self.event(energy=E, coords=coords, rms=rms, eigenval=self.eigenval, stepnum=i)
if rms < self.tol:
break
if self.nfail >= self.nfail_max:
logger.warning("stopping findTransitionState. too many failures in eigenvector search %s", self.nfail)
res.message.append( "too many failures in eigenvector search %d" % self.nfail )
break
if i == 0 and self.eigenval > 0.:
if self.verbosity > 1:
logger.warning("initial eigenvalue is positive - increase NEB spring constant?")
if self.demand_initial_negative_vec:
logger.warning(" aborting transition state search")
res.message.append( "initial eigenvalue is positive %f" % self.eigenval )
break
# done. do one last eigenvector search because coords may have changed
self._getLowestEigenVector(coords, i)
# print some data
if self.verbosity > 0 or self.iprint > 0:
logger.info("findTransitionState done: %s %s %s %s %s", i, E, rms, "eigenvalue", self.eigenval)
success = True
# check if results make sense
if self.eigenval >= 0.:
if self.verbosity > 2:
logger.info( "warning: transition state is ending with positive eigenvalue %s", self.eigenval)
success = False
if rms > self.tol:
if self.verbosity > 2:
logger.info("warning: transition state search appears to have failed: rms %s", rms)
success = False
if i >= self.nsteps:
res.message.append( "maximum iterations reached %d" % i )
# update nfev with the number of calls from the transverse walker
if self._transverse_walker is not None:
twres = self._transverse_walker.get_result()
self.nfev += twres.nfev
#return results
res.coords = coords
res.energy = E
res.eigenval = self.eigenval
res.eigenvec = self.eigenvec
res.grad = grad
res.rms = rms
res.nsteps = i
res.success = success
res.nfev = self.nfev
return res
def ode_scipy_naive(coords,
pot,
t_bound=1000,
tol=1e-4,
nsteps=20000,
convergence_check=None,
solver_type='rk45',
**kwargs):
""" This uses rk45 in a minimizer like approach to find the ode
The idea is to solve for the path
dx/dt = - \\grad{E}
Parameters
----------
coords: array
coords input for the quench
pot: array
potential class that has a
getenergygradient function that we need for stepping
nsteps: int
maximum number of steps
tol: float
gives a tolerance for making sure that we have found the minima
kwargs: ...
extra arguments for the integrator
Return
----------
result container with steps and function evaluations
"""
class feval_pot:
""" wrapper class that calculates function evaluations
and makes sure to point the gradient in the right direction
"""
def __init__(self):
self.nfev = 0
def get_gradient(self, t, x):
self.nfev += 1
return -pot.getEnergyGradient(x.copy())[1]
def get_energy_gradient(self, x):
self.nfev += 1
return pot.getEnergyGradient(x.copy())
# This code seems to work for these two solvers
# if solver_type == 'RK23':
# solver = RK23_LS
# else:
# solver = RK23_LS
solver = Radau
# def get_gradient(t, x):
# # gets just the gradient from the potential
# return pot.getEnergyGradient(x)[1]
function_evaluate_pot = feval_pot()
solver = solver(
function_evaluate_pot.get_gradient,
# function_evaluate_pot.get_energy_gradient,
0,
coords,
t_bound,
rtol=1e-3,
atol=1e-3)
# min_step = 10 * np.abs(np.nextafter(t, self.direction * np.inf) - t)
converged = False
n = 0
if convergence_check == None:
convergence_check = lambda g: np.linalg.norm(g) < tol
x_ = np.full(len(coords), np.nan)
while not converged and n < nsteps:
xold = x_
solver.step()
x_ = solver.dense_output().y_old
n += 1
converged = convergence_check(pot.getEnergyGradient(x_)[1])
res = Result()
res.coords = x_
res.nfev = function_evaluate_pot.nfev
print(res.nfev)
res.coords = x_
res.energy = pot.getEnergy(x_)
res.rms = 0
res.grad = 0
res.nsteps = n
res.success = converged
return res