def step(self, f):
atoms = self.atoms
from ase.neb import NEB
assert not isinstance(atoms, NEB)
r = atoms.get_positions()
r = r.reshape(-1)
g = -f.reshape(-1) / self.alpha
p0 = self.p
self.update(r, g, self.r0, self.g0, p0)
#o,v = np.linalg.eigh(self.B)
e = self.func(r)
self.p = -np.dot(self.H, g)
p_size = np.sqrt((self.p**2).sum())
if self.nsteps != 0:
p0_size = np.sqrt((p0**2).sum())
delta_p = self.p / p_size + p0 / p0_size
if p_size <= np.sqrt(len(atoms) * 1e-10):
self.p /= (p_size / np.sqrt(len(atoms) * 1e-10))
ls = LineSearch()
self.alpha_k, e, self.e0, self.no_update = \
ls._line_search(self.func, self.fprime, r, self.p, g, e, self.e0,
maxstep=self.maxstep, c1=self.c1,
c2=self.c2, stpmax=self.stpmax)
if self.alpha_k is None:
raise RuntimeError("LineSearch failed!")
dr = self.alpha_k * self.p
atoms.set_positions((r + dr).reshape(len(atoms), -1))
self.r0 = r
self.g0 = g
self.dump((self.r0, self.g0, self.e0, self.task, self.H))
def step(self, f):
atoms = self.atoms
from ase.neb import NEB
if isinstance(atoms, NEB):
raise TypeError('NEB calculations cannot use the BFGSLineSearch'
' optimizer. Use BFGS or another optimizer.')
r = atoms.get_positions()
r = r.reshape(-1)
g = -f.reshape(-1) / self.alpha
p0 = self.p
self.update(r, g, self.r0, self.g0, p0)
#o,v = np.linalg.eigh(self.B)
e = self.func(r)
self.p = -np.dot(self.H,g)
p_size = np.sqrt((self.p **2).sum())
if self.nsteps != 0:
p0_size = np.sqrt((p0 **2).sum())
delta_p = self.p/p_size + p0/p0_size
if p_size <= np.sqrt(len(atoms) * 1e-10):
self.p /= (p_size / np.sqrt(len(atoms)*1e-10))
ls = LineSearch()
self.alpha_k, e, self.e0, self.no_update = \
ls._line_search(self.func, self.fprime, r, self.p, g, e, self.e0,
maxstep=self.maxstep, c1=self.c1,
c2=self.c2, stpmax=self.stpmax)
if self.alpha_k is None:
raise RuntimeError("LineSearch failed!")
dr = self.alpha_k * self.p
atoms.set_positions((r+dr).reshape(len(atoms),-1))
self.r0 = r
self.g0 = g
self.dump((self.r0, self.g0, self.e0, self.task, self.H))
def step(self, f=None):
atoms = self.atoms
if f is None:
f = atoms.get_forces()
from ase.neb import NEB
if isinstance(atoms, NEB):
raise TypeError('NEB calculations cannot use the BFGSLineSearch'
' optimizer. Use BFGS or another optimizer.')
r = atoms.get_positions()
r = r.reshape(-1)
g = -f.reshape(-1) / self.alpha
p0 = self.p
self.update(r, g, self.r0, self.g0, p0)
# o,v = np.linalg.eigh(self.B)
e = self.func(r)
self.p = -np.dot(self.H, g)
p_size = np.sqrt((self.p**2).sum())
if p_size <= np.sqrt(len(atoms) * 1e-10):
self.p /= (p_size / np.sqrt(len(atoms)*1e-10))
ls = LineSearch()
self.alpha_k, e, self.e0, self.no_update = \
ls._line_search(self.func, self.fprime, r, self.p, g, e, self.e0,
maxstep=self.maxstep, c1=self.c1,
c2=self.c2, stpmax=self.stpmax)
if self.alpha_k is None:
raise RuntimeError("LineSearch failed!")
dr = self.alpha_k * self.p
atoms.set_positions((r + dr).reshape(len(atoms), -1))
self.r0 = r
self.g0 = g
self.dump((self.r0, self.g0, self.e0, self.task, self.H))
def line_search(self, r, g, e):
self.p = self.p.ravel()
p_size = np.sqrt((self.p **2).sum())
if p_size <= np.sqrt(len(self.atoms) * 1e-10):
self.p /= (p_size / np.sqrt(len(self.atoms)*1e-10))
g = g.ravel()
r = r.ravel()
ls = LineSearch()
self.alpha_k, e, self.e0, self.no_update = \
ls._line_search(self.func, self.fprime, r, self.p, g, e, self.e0,
maxstep=self.maxstep, c1=.23,
c2=.46, stpmax=50.)
def line_search(self, r, g, e):
self.p = self.p.ravel()
p_size = np.sqrt((self.p **2).sum())
if p_size <= np.sqrt(len(self.atoms) * 1e-10):
self.p /= (p_size / np.sqrt(len(self.atoms) * 1e-10))
g = g.ravel()
r = r.ravel()
ls = LineSearch()
self.alpha_k, e, self.e0, self.no_update = \
ls._line_search(self.func, self.fprime, r, self.p, g, e, self.e0,
maxstep=self.maxstep, c1=.23,
c2=.46, stpmax=50.)
if self.alpha_k is None:
raise RuntimeError('LineSearch failed!')
def line_search(self, r, g, e, previously_reset_hessian):
self.p = self.p.ravel()
p_size = np.sqrt((self.p**2).sum())
if p_size <= np.sqrt(len(self.atoms) * 1e-10):
self.p /= (p_size / np.sqrt(len(self.atoms) * 1e-10))
g = g.ravel()
r = r.ravel()
if self.use_armijo:
try:
# CO: modified call to ls.run
# TODO: pass also the old slope to the linesearch
# so that the RumPath can extract a better starting guess?
# alternatively: we can adjust the rotation_factors
# out using some extrapolation tricks?
ls = LineSearchArmijo(self.func, c1=self.c1, tol=1e-14)
step, func_val, no_update = ls.run(
r,
self.p,
a_min=self.a_min,
func_start=e,
func_prime_start=g,
func_old=self.e0,
rigid_units=self.rigid_units,
rotation_factors=self.rotation_factors,
maxstep=self.maxstep)
self.e0 = e
self.e1 = func_val
self.alpha_k = step
except (ValueError, RuntimeError):
if not previously_reset_hessian:
warnings.warn(
'Armijo linesearch failed, resetting Hessian and '
'trying again')
self.reset_hessian()
self.alpha_k = 0.0
else:
raise RuntimeError(
'Armijo linesearch failed after reset of Hessian, '
'aborting')
else:
ls = LineSearch()
self.alpha_k, e, self.e0, self.no_update = \
ls._line_search(self.func, self.fprime, r, self.p, g,
e, self.e0, stpmin=self.a_min,
maxstep=self.maxstep, c1=self.c1,
c2=self.c2, stpmax=50.)
self.e1 = e
if self.alpha_k is None:
raise RuntimeError('Wolff lineSearch failed!')
def fmin_bfgs(
f,
x0,
fprime=None,
args=(),
gtol=1e-5,
norm=Inf,
epsilon=_epsilon,
maxiter=None,
full_output=0,
disp=1,
retall=0,
callback=None,
maxstep=0.2,
):
"""Minimize a function using the BFGS algorithm.
Parameters:
f : callable f(x,*args)
Objective function to be minimized.
x0 : ndarray
Initial guess.
fprime : callable f'(x,*args)
Gradient of f.
args : tuple
Extra arguments passed to f and fprime.
gtol : float
Gradient norm must be less than gtol before succesful termination.
norm : float
Order of norm (Inf is max, -Inf is min)
epsilon : int or ndarray
If fprime is approximated, use this value for the step size.
callback : callable
An optional user-supplied function to call after each
iteration. Called as callback(xk), where xk is the
current parameter vector.
Returns: (xopt, {fopt, gopt, Hopt, func_calls, grad_calls, warnflag}, <allvecs>)
xopt : ndarray
Parameters which minimize f, i.e. f(xopt) == fopt.
fopt : float
Minimum value.
gopt : ndarray
Value of gradient at minimum, f'(xopt), which should be near 0.
Bopt : ndarray
Value of 1/f''(xopt), i.e. the inverse hessian matrix.
func_calls : int
Number of function_calls made.
grad_calls : int
Number of gradient calls made.
warnflag : integer
1 : Maximum number of iterations exceeded.
2 : Gradient and/or function calls not changing.
allvecs : list
Results at each iteration. Only returned if retall is True.
*Other Parameters*:
maxiter : int
Maximum number of iterations to perform.
full_output : bool
If True,return fopt, func_calls, grad_calls, and warnflag
in addition to xopt.
disp : bool
Print convergence message if True.
retall : bool
Return a list of results at each iteration if True.
Notes:
Optimize the function, f, whose gradient is given by fprime
using the quasi-Newton method of Broyden, Fletcher, Goldfarb,
and Shanno (BFGS) See Wright, and Nocedal 'Numerical
Optimization', 1999, pg. 198.
*See Also*:
scikits.openopt : SciKit which offers a unified syntax to call
this and other solvers.
"""
x0 = asarray(x0).squeeze()
if x0.ndim == 0:
x0.shape = (1,)
if maxiter is None:
maxiter = len(x0) * 200
func_calls, f = wrap_function(f, args)
if fprime is None:
grad_calls, myfprime = wrap_function(approx_fprime, (f, epsilon))
else:
grad_calls, myfprime = wrap_function(fprime, args)
gfk = myfprime(x0)
k = 0
N = len(x0)
I = numpy.eye(N, dtype=int)
Hk = I
old_fval = f(x0)
old_old_fval = old_fval + 5000
xk = x0
if retall:
allvecs = [x0]
sk = [2 * gtol]
warnflag = 0
gnorm = vecnorm(gfk, ord=norm)
while (gnorm > gtol) and (k < maxiter):
pk = -numpy.dot(Hk, gfk)
ls = LineSearch()
alpha_k, fc, gc, old_fval, old_old_fval, gfkp1 = ls._line_search(
f, myfprime, xk, pk, gfk, old_fval, old_old_fval, maxstep=maxstep
)
if alpha_k is None: # line search failed try different one.
alpha_k, fc, gc, old_fval, old_old_fval, gfkp1 = line_search(
f, myfprime, xk, pk, gfk, old_fval, old_old_fval
)
if alpha_k is None:
# This line search also failed to find a better solution.
warnflag = 2
break
xkp1 = xk + alpha_k * pk
if retall:
allvecs.append(xkp1)
sk = xkp1 - xk
xk = xkp1
if gfkp1 is None:
gfkp1 = myfprime(xkp1)
yk = gfkp1 - gfk
gfk = gfkp1
if callback is not None:
callback(xk)
k += 1
gnorm = vecnorm(gfk, ord=norm)
if gnorm <= gtol:
break
try: # this was handled in numeric, let it remaines for more safety
rhok = 1.0 / (numpy.dot(yk, sk))
except ZeroDivisionError:
rhok = 1000.0
print "Divide-by-zero encountered: rhok assumed large"
if isinf(rhok): # this is patch for numpy
rhok = 1000.0
print "Divide-by-zero encountered: rhok assumed large"
A1 = I - sk[:, numpy.newaxis] * yk[numpy.newaxis, :] * rhok
A2 = I - yk[:, numpy.newaxis] * sk[numpy.newaxis, :] * rhok
Hk = numpy.dot(A1, numpy.dot(Hk, A2)) + rhok * sk[:, numpy.newaxis] * sk[numpy.newaxis, :]
if disp or full_output:
fval = old_fval
if warnflag == 2:
if disp:
print "Warning: Desired error not necessarily achieved" "due to precision loss"
print " Current function value: %f" % fval
print " Iterations: %d" % k
print " Function evaluations: %d" % func_calls[0]
print " Gradient evaluations: %d" % grad_calls[0]
elif k >= maxiter:
warnflag = 1
if disp:
print "Warning: Maximum number of iterations has been exceeded"
print " Current function value: %f" % fval
print " Iterations: %d" % k
print " Function evaluations: %d" % func_calls[0]
print " Gradient evaluations: %d" % grad_calls[0]
else:
if disp:
print "Optimization terminated successfully."
print " Current function value: %f" % fval
print " Iterations: %d" % k
print " Function evaluations: %d" % func_calls[0]
print " Gradient evaluations: %d" % grad_calls[0]
if full_output:
retlist = xk, fval, gfk, Hk, func_calls[0], grad_calls[0], warnflag
if retall:
retlist += (allvecs,)
else:
retlist = xk
if retall:
retlist = (xk, allvecs)
return retlist
def fmin_bfgs(f,
x0,
fprime=None,
args=(),
gtol=1e-5,
norm=Inf,
epsilon=_epsilon,
maxiter=None,
full_output=0,
disp=1,
retall=0,
callback=None,
maxstep=0.2):
"""Minimize a function using the BFGS algorithm.
Parameters:
f : callable f(x,*args)
Objective function to be minimized.
x0 : ndarray
Initial guess.
fprime : callable f'(x,*args)
Gradient of f.
args : tuple
Extra arguments passed to f and fprime.
gtol : float
Gradient norm must be less than gtol before successful termination.
norm : float
Order of norm (Inf is max, -Inf is min)
epsilon : int or ndarray
If fprime is approximated, use this value for the step size.
callback : callable
An optional user-supplied function to call after each
iteration. Called as callback(xk), where xk is the
current parameter vector.
Returns: (xopt, {fopt, gopt, Hopt, func_calls, grad_calls, warnflag}, <allvecs>)
xopt : ndarray
Parameters which minimize f, i.e. f(xopt) == fopt.
fopt : float
Minimum value.
gopt : ndarray
Value of gradient at minimum, f'(xopt), which should be near 0.
Bopt : ndarray
Value of 1/f''(xopt), i.e. the inverse hessian matrix.
func_calls : int
Number of function_calls made.
grad_calls : int
Number of gradient calls made.
warnflag : integer
1 : Maximum number of iterations exceeded.
2 : Gradient and/or function calls not changing.
allvecs : list
Results at each iteration. Only returned if retall is True.
*Other Parameters*:
maxiter : int
Maximum number of iterations to perform.
full_output : bool
If True,return fopt, func_calls, grad_calls, and warnflag
in addition to xopt.
disp : bool
Print convergence message if True.
retall : bool
Return a list of results at each iteration if True.
Notes:
Optimize the function, f, whose gradient is given by fprime
using the quasi-Newton method of Broyden, Fletcher, Goldfarb,
and Shanno (BFGS) See Wright, and Nocedal 'Numerical
Optimization', 1999, pg. 198.
*See Also*:
scikits.openopt : SciKit which offers a unified syntax to call
this and other solvers.
"""
x0 = asarray(x0).squeeze()
if x0.ndim == 0:
x0.shape = (1, )
if maxiter is None:
maxiter = len(x0) * 200
func_calls, f = wrap_function(f, args)
if fprime is None:
grad_calls, myfprime = wrap_function(approx_fprime, (f, epsilon))
else:
grad_calls, myfprime = wrap_function(fprime, args)
gfk = myfprime(x0)
k = 0
N = len(x0)
I = numpy.eye(N, dtype=int)
Hk = I
old_fval = f(x0)
old_old_fval = old_fval + 5000
xk = x0
if retall:
allvecs = [x0]
sk = [2 * gtol]
warnflag = 0
gnorm = vecnorm(gfk, ord=norm)
while (gnorm > gtol) and (k < maxiter):
pk = -numpy.dot(Hk, gfk)
ls = LineSearch()
alpha_k, fc, gc, old_fval, old_old_fval, gfkp1 = \
ls._line_search(f,myfprime,xk,pk,gfk,
old_fval,old_old_fval,maxstep=maxstep)
if alpha_k is None: # line search failed try different one.
alpha_k, fc, gc, old_fval, old_old_fval, gfkp1 = \
line_search(f,myfprime,xk,pk,gfk,
old_fval,old_old_fval)
if alpha_k is None:
# This line search also failed to find a better solution.
warnflag = 2
break
xkp1 = xk + alpha_k * pk
if retall:
allvecs.append(xkp1)
sk = xkp1 - xk
xk = xkp1
if gfkp1 is None:
gfkp1 = myfprime(xkp1)
yk = gfkp1 - gfk
gfk = gfkp1
if callback is not None:
callback(xk)
k += 1
gnorm = vecnorm(gfk, ord=norm)
if (gnorm <= gtol):
break
try: # this was handled in numeric, let it remaines for more safety
rhok = 1.0 / (numpy.dot(yk, sk))
except ZeroDivisionError:
rhok = 1000.0
print("Divide-by-zero encountered: rhok assumed large")
if isinf(rhok): # this is patch for numpy
rhok = 1000.0
print("Divide-by-zero encountered: rhok assumed large")
A1 = I - sk[:, numpy.newaxis] * yk[numpy.newaxis, :] * rhok
A2 = I - yk[:, numpy.newaxis] * sk[numpy.newaxis, :] * rhok
Hk = numpy.dot(A1,numpy.dot(Hk,A2)) + rhok * sk[:,numpy.newaxis] \
* sk[numpy.newaxis,:]
if disp or full_output:
fval = old_fval
if warnflag == 2:
if disp:
print("Warning: Desired error not necessarily achieved" \
"due to precision loss")
print(" Current function value: %f" % fval)
print(" Iterations: %d" % k)
print(" Function evaluations: %d" % func_calls[0])
print(" Gradient evaluations: %d" % grad_calls[0])
elif k >= maxiter:
warnflag = 1
if disp:
print("Warning: Maximum number of iterations has been exceeded")
print(" Current function value: %f" % fval)
print(" Iterations: %d" % k)
print(" Function evaluations: %d" % func_calls[0])
print(" Gradient evaluations: %d" % grad_calls[0])
else:
if disp:
print("Optimization terminated successfully.")
print(" Current function value: %f" % fval)
print(" Iterations: %d" % k)
print(" Function evaluations: %d" % func_calls[0])
print(" Gradient evaluations: %d" % grad_calls[0])
if full_output:
retlist = xk, fval, gfk, Hk, func_calls[0], grad_calls[0], warnflag
if retall:
retlist += (allvecs, )
else:
retlist = xk
if retall:
retlist = (xk, allvecs)
return retlist