/usr/share/pyshared/ase/utils/linesearch.py is in python-ase 3.6.0.2515-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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import __builtin__
pymin = __builtin__.min
pymax = __builtin__.max
class LineSearch:
def __init__(self, xtol=1e-14):
self.xtol = xtol
self.task = 'START'
self.isave = np.zeros((2,), np.intc)
self.dsave = np.zeros((13,), float)
self.fc = 0
self.gc = 0
self.case = 0
self.old_stp = 0
def _line_search(self, func, myfprime, xk, pk, gfk, old_fval, old_old_fval,
maxstep=.2, c1=.23, c2=0.46, xtrapl=1.1, xtrapu=4.,
stpmax=50., stpmin=1e-8, args=()):
self.stpmin = stpmin
self.pk = pk
p_size = np.sqrt((pk **2).sum())
self.stpmax = stpmax
self.xtrapl = xtrapl
self.xtrapu = xtrapu
self.maxstep = maxstep
phi0 = old_fval
derphi0 = np.dot(gfk,pk)
self.dim = len(pk)
self.gms = np.sqrt(self.dim) * maxstep
#alpha1 = pymin(maxstep,1.01*2*(phi0-old_old_fval)/derphi0)
alpha1 = 1.
self.no_update = False
if isinstance(myfprime,type(())):
eps = myfprime[1]
fprime = myfprime[0]
newargs = (f,eps) + args
gradient = False
else:
fprime = myfprime
newargs = args
gradient = True
fval = old_fval
gval = gfk
self.steps=[]
while 1:
stp = self.step(alpha1, phi0, derphi0, c1, c2,
self.xtol,
self.isave, self.dsave)
if self.task[:2] == 'FG':
alpha1 = stp
fval = func(xk + stp * pk, *args)
self.fc += 1
gval = fprime(xk + stp * pk, *newargs)
if gradient: self.gc += 1
else: self.fc += len(xk) + 1
phi0 = fval
derphi0 = np.dot(gval,pk)
self.old_stp = alpha1
if self.no_update == True:
break
else:
break
if self.task[:5] == 'ERROR' or self.task[1:4] == 'WARN':
stp = None # failed
return stp, fval, old_fval, self.no_update
def step(self, stp, f, g, c1, c2, xtol, isave, dsave):
if self.task[:5] == 'START':
# Check the input arguments for errors.
if stp < self.stpmin:
self.task = 'ERROR: STP .LT. minstep'
if stp > self.stpmax:
self.task = 'ERROR: STP .GT. maxstep'
if g >= 0:
self.task = 'ERROR: INITIAL G >= 0'
if c1 < 0:
self.task = 'ERROR: c1 .LT. 0'
if c2 < 0:
self.task = 'ERROR: c2 .LT. 0'
if xtol < 0:
self.task = 'ERROR: XTOL .LT. 0'
if self.stpmin < 0:
self.task = 'ERROR: minstep .LT. 0'
if self.stpmax < self.stpmin:
self.task = 'ERROR: maxstep .LT. minstep'
if self.task[:5] == 'ERROR':
return stp
# Initialize local variables.
self.bracket = False
stage = 1
finit = f
ginit = g
gtest = c1 * ginit
width = self.stpmax - self.stpmin
width1 = width / .5
# The variables stx, fx, gx contain the values of the step,
# function, and derivative at the best step.
# The variables sty, fy, gy contain the values of the step,
# function, and derivative at sty.
# The variables stp, f, g contain the values of the step,
# function, and derivative at stp.
stx = 0
fx = finit
gx = ginit
sty = 0
fy = finit
gy = ginit
stmin = 0
stmax = stp + self.xtrapu * stp
self.task = 'FG'
self.save((stage, ginit, gtest, gx,
gy, finit, fx, fy, stx, sty,
stmin, stmax, width, width1))
stp = self.determine_step(stp)
#return stp, f, g
return stp
else:
if self.isave[0] == 1:
self.bracket = True
else:
self.bracket = False
stage = self.isave[1]
(ginit, gtest, gx, gy, finit, fx, fy, stx, sty, stmin, stmax, \
width, width1) =self.dsave
# If psi(stp) <= 0 and f'(stp) >= 0 for some step, then the
# algorithm enters the second stage.
ftest = finit + stp * gtest
if stage == 1 and f < ftest and g >= 0.:
stage = 2
# Test for warnings.
if self.bracket and (stp <= stmin or stp >= stmax):
self.task = 'WARNING: ROUNDING ERRORS PREVENT PROGRESS'
if self.bracket and stmax - stmin <= self.xtol * stmax:
self.task = 'WARNING: XTOL TEST SATISFIED'
if stp == self.stpmax and f <= ftest and g <= gtest:
self.task = 'WARNING: STP = maxstep'
if stp == self.stpmin and (f > ftest or g >= gtest):
self.task = 'WARNING: STP = minstep'
# Test for convergence.
if f <= ftest and abs(g) <= c2 * (- ginit):
self.task = 'CONVERGENCE'
# Test for termination.
if self.task[:4] == 'WARN' or self.task[:4] == 'CONV':
self.save((stage, ginit, gtest, gx,
gy, finit, fx, fy, stx, sty,
stmin, stmax, width, width1))
#return stp, f, g
return stp
# A modified function is used to predict the step during the
# first stage if a lower function value has been obtained but
# the decrease is not sufficient.
#if stage == 1 and f <= fx and f > ftest:
# # Define the modified function and derivative values.
# fm =f - stp * gtest
# fxm = fx - stx * gtest
# fym = fy - sty * gtest
# gm = g - gtest
# gxm = gx - gtest
# gym = gy - gtest
# Call step to update stx, sty, and to compute the new step.
# stx, sty, stp, gxm, fxm, gym, fym = self.update (stx, fxm, gxm, sty,
# fym, gym, stp, fm, gm,
# stmin, stmax)
# # Reset the function and derivative values for f.
# fx = fxm + stx * gtest
# fy = fym + sty * gtest
# gx = gxm + gtest
# gy = gym + gtest
#else:
# Call step to update stx, sty, and to compute the new step.
stx, sty, stp, gx, fx, gy, fy= self.update(stx, fx, gx, sty,
fy, gy, stp, f, g,
stmin, stmax)
# Decide if a bisection step is needed.
if self.bracket:
if abs(sty-stx) >= .66 * width1:
stp = stx + .5 * (sty - stx)
width1 = width
width = abs(sty - stx)
# Set the minimum and maximum steps allowed for stp.
if self.bracket:
stmin = min(stx, sty)
stmax = max(stx, sty)
else:
stmin = stp + self.xtrapl * (stp - stx)
stmax = stp + self.xtrapu * (stp - stx)
# Force the step to be within the bounds maxstep and minstep.
stp = max(stp, self.stpmin)
stp = min(stp, self.stpmax)
if (stx == stp and stp == self.stpmax and stmin > self.stpmax):
self.no_update = True
# If further progress is not possible, let stp be the best
# point obtained during the search.
if (self.bracket and stp < stmin or stp >= stmax) \
or (self.bracket and stmax - stmin < self.xtol * stmax):
stp = stx
# Obtain another function and derivative.
self.task = 'FG'
self.save((stage, ginit, gtest, gx,
gy, finit, fx, fy, stx, sty,
stmin, stmax, width, width1))
return stp
def update(self, stx, fx, gx, sty, fy, gy, stp, fp, gp,
stpmin, stpmax):
sign = gp * (gx / abs(gx))
# First case: A higher function value. The minimum is bracketed.
# If the cubic step is closer to stx than the quadratic step, the
# cubic step is taken, otherwise the average of the cubic and
# quadratic steps is taken.
if fp > fx: #case1
self.case = 1
theta = 3. * (fx - fp) / (stp - stx) + gx + gp
s = max(abs(theta), abs(gx), abs(gp))
gamma = s * np.sqrt((theta / s) ** 2. - (gx / s) * (gp / s))
if stp < stx:
gamma = -gamma
p = (gamma - gx) + theta
q = ((gamma - gx) + gamma) + gp
r = p / q
stpc = stx + r * (stp - stx)
stpq = stx + ((gx / ((fx - fp) / (stp-stx) + gx)) / 2.) \
* (stp - stx)
if (abs(stpc - stx) < abs(stpq - stx)):
stpf = stpc
else:
stpf = stpc + (stpq - stpc) / 2.
self.bracket = True
# Second case: A lower function value and derivatives of opposite
# sign. The minimum is bracketed. If the cubic step is farther from
# stp than the secant step, the cubic step is taken, otherwise the
# secant step is taken.
elif sign < 0: #case2
self.case = 2
theta = 3. * (fx - fp) / (stp - stx) + gx + gp
s = max(abs(theta), abs(gx), abs(gp))
gamma = s * np.sqrt((theta / s) ** 2 - (gx / s) * (gp / s))
if stp > stx:
gamma = -gamma
p = (gamma - gp) + theta
q = ((gamma - gp) + gamma) + gx
r = p / q
stpc = stp + r * (stx - stp)
stpq = stp + (gp / (gp - gx)) * (stx - stp)
if (abs(stpc - stp) > abs(stpq - stp)):
stpf = stpc
else:
stpf = stpq
self.bracket = True
# Third case: A lower function value, derivatives of the same sign,
# and the magnitude of the derivative decreases.
elif abs(gp) < abs(gx): #case3
self.case = 3
# The cubic step is computed only if the cubic tends to infinity
# in the direction of the step or if the minimum of the cubic
# is beyond stp. Otherwise the cubic step is defined to be the
# secant step.
theta = 3. * (fx - fp) / (stp - stx) + gx + gp
s = max(abs(theta), abs(gx), abs(gp))
# The case gamma = 0 only arises if the cubic does not tend
# to infinity in the direction of the step.
gamma = s * np.sqrt(max(0.,(theta / s) ** 2-(gx / s) * (gp / s)))
if stp > stx:
gamma = -gamma
p = (gamma - gp) + theta
q = (gamma + (gx - gp)) + gamma
r = p / q
if r < 0. and gamma != 0:
stpc = stp + r * (stx - stp)
elif stp > stx:
stpc = stpmax
else:
stpc = stpmin
stpq = stp + (gp / (gp - gx)) * (stx - stp)
if self.bracket:
# A minimizer has been bracketed. If the cubic step is
# closer to stp than the secant step, the cubic step is
# taken, otherwise the secant step is taken.
if abs(stpc - stp) < abs(stpq - stp):
stpf = stpc
else:
stpf = stpq
if stp > stx:
stpf = min(stp + .66 * (sty - stp), stpf)
else:
stpf = max(stp + .66 * (sty - stp), stpf)
else:
# A minimizer has not been bracketed. If the cubic step is
# farther from stp than the secant step, the cubic step is
# taken, otherwise the secant step is taken.
if abs(stpc - stp) > abs(stpq - stp):
stpf = stpc
else:
stpf = stpq
stpf = min(stpmax, stpf)
stpf = max(stpmin, stpf)
# Fourth case: A lower function value, derivatives of the same sign,
# and the magnitude of the derivative does not decrease. If the
# minimum is not bracketed, the step is either minstep or maxstep,
# otherwise the cubic step is taken.
else: #case4
self.case = 4
if self.bracket:
theta = 3. * (fp - fy) / (sty - stp) + gy + gp
s = max(abs(theta), abs(gy), abs(gp))
gamma = s * np.sqrt((theta / s) ** 2 - (gy / s) * (gp / s))
if stp > sty:
gamma = -gamma
p = (gamma - gp) + theta
q = ((gamma - gp) + gamma) + gy
r = p / q
stpc = stp + r * (sty - stp)
stpf = stpc
elif stp > stx:
stpf = stpmax
else:
stpf = stpmin
# Update the interval which contains a minimizer.
if fp > fx:
sty = stp
fy = fp
gy = gp
else:
if sign < 0:
sty = stx
fy = fx
gy = gx
stx = stp
fx = fp
gx = gp
# Compute the new step.
stp = self.determine_step(stpf)
return stx, sty, stp, gx, fx, gy, fy
def determine_step(self, stp):
dr = stp - self.old_stp
if abs(pymax(self.pk) * dr) > self.maxstep:
dr /= abs((pymax(self.pk) * dr) / self.maxstep)
stp = self.old_stp + dr
return stp
def save(self, data):
if self.bracket:
self.isave[0] = 1
else:
self.isave[0] = 0
self.isave[1] = data[0]
self.dsave = data[1:]
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