def setup(self):
""" Sets up nonlinear optimization machinery
"""
unix.mkdir(PATH.OPTIMIZE)
# prepare output writers
self.writer = Writer(path=PATH.OUTPUT)
self.stepwriter = StepWriter(path=PATH.SUBMIT)
# prepare algorithm machinery
if PAR.SCHEME in ['NLCG']:
self.NLCG = NLCG(path=PATH.OPTIMIZE,
maxiter=PAR.NLCGMAX,
thresh=PAR.NLCGTHRESH,
precond=self.precond())
elif PAR.SCHEME in ['LBFGS']:
self.LBFGS = LBFGS(path=PATH.OPTIMIZE,
memory=PAR.LBFGSMEM,
maxiter=PAR.LBFGSMAX,
thresh=PAR.LBFGSTHRESH,
precond=self.precond())
# write initial model
if exists(PATH.MODEL_INIT):
import solver
src = PATH.MODEL_INIT
dst = join(PATH.OPTIMIZE, 'm_new')
savenpy(dst, solver.merge(solver.load(src)))
def setup(self):
""" Sets up nonlinear optimization machinery
"""
unix.mkdir(PATH.OPTIMIZE)
# prepare output writers
self.writer = Writer(path=PATH.OUTPUT)
self.stepwriter = StepWriter(path=PATH.SUBMIT)
# prepare algorithm machinery
if PAR.SCHEME in ["NLCG"]:
self.NLCG = NLCG(path=PATH.OPTIMIZE, maxiter=PAR.NLCGMAX, thresh=PAR.NLCGTHRESH, precond=self.precond)
elif PAR.SCHEME in ["LBFGS"]:
self.LBFGS = LBFGS(
path=PATH.OPTIMIZE,
memory=PAR.LBFGSMEM,
maxiter=PAR.LBFGSMAX,
thresh=PAR.LBFGSTHRESH,
precond=self.precond,
)
# write initial model
if exists(PATH.MODEL_INIT):
src = PATH.MODEL_INIT
dst = join(PATH.OPTIMIZE, "m_new")
savenpy(dst, solver.merge(solver.load(src)))
class base(object):
""" Nonlinear optimization base class.
Available nonlinear optimization algorithms include steepest descent,
nonlinear conjugate gradient (NLCG), and limited-memory BFGS (LBFGS).
Available step control algorithms include a backtracking line search and a
bracketing line search.
Though NLCG (a Krylov method) and LBFGS (a quasi-Newton metod) are both
widely used for geophysical inversion, LBFGS is more efficient and more
robust. NLCG requires occasional restarts to avoid numerical stagnation,
while LBFGS generally requires few restarts. Restarts are controlled by
numerical parameters. Default values provided below should work well
for a wide range inversions without the need for manual tuning.
To reduce memory overhead, vectors are read from disk rather than passed
from a calling routine. At the start of each search direction computation
the current model and gradient are read from files 'm_new' and 'g_new';
the resulting search direction is written to 'p_new'. As the inversion
progresses, other information is stored to disk as well.
"""
def check(self):
""" Checks parameters, paths, and dependencies
"""
if 'BEGIN' not in PAR:
raise ParameterError
if 'END' not in PAR:
raise ParameterError
if 'SUBMIT' not in PATH:
raise ParameterError
if 'OPTIMIZE' not in PATH:
setattr(PATH, 'OPTIMIZE', join(PATH.SCRATCH, 'optimize'))
if 'MODEL_INIT' not in PATH:
setattr(PATH, 'MODEL_INIT', None)
# search direction algorithm
if 'SCHEME' not in PAR:
setattr(PAR, 'SCHEME', 'LBFGS')
if 'PRECOND' not in PAR:
setattr(PAR, 'PRECOND', None)
# line search algorithm
if 'LINESEARCH' not in PAR:
if PAR.SCHEME in ['LBFGS']:
setattr(PAR, 'LINESEARCH', 'Backtrack')
else:
setattr(PAR, 'LINESEARCH', 'Bracket')
# search direction tuning parameters
if 'NLCGMAX' not in PAR:
setattr(PAR, 'NLCGMAX', np.inf)
if 'NLCGTHRESH' not in PAR:
setattr(PAR, 'NLCGTHRESH', np.inf)
if 'LBFGSMEM' not in PAR:
setattr(PAR, 'LBFGSMEM', 3)
if 'LBFGSMAX' not in PAR:
setattr(PAR, 'LBFGSMAX', np.inf)
if 'LBFGSTHRESH' not in PAR:
setattr(PAR, 'LBFGSTHRESH', 0.)
# line search tuning paraemters
if 'STEPMAX' not in PAR:
setattr(PAR, 'STEPMAX', 10)
if 'STEPTHRESH' not in PAR:
setattr(PAR, 'STEPTHRESH', None)
if 'STEPINIT' not in PAR:
setattr(PAR, 'STEPINIT', 0.05)
if 'STEPFACTOR' not in PAR:
setattr(PAR, 'STEPFACTOR', 0.5)
if 'STEPOVERSHOOT' not in PAR:
setattr(PAR, 'STEPOVERSHOOT', 0.)
if 'ADHOCFACTOR' not in PAR:
setattr(PAR, 'ADHOCFACTOR', 1.)
def setup(self):
""" Sets up nonlinear optimization machinery
"""
unix.mkdir(PATH.OPTIMIZE)
# prepare output writers
self.writer = Writer(path=PATH.OUTPUT)
self.stepwriter = StepWriter(path=PATH.SUBMIT)
# prepare algorithm machinery
if PAR.SCHEME in ['NLCG']:
self.NLCG = NLCG(path=PATH.OPTIMIZE,
maxiter=PAR.NLCGMAX,
thresh=PAR.NLCGTHRESH,
precond=self.precond())
elif PAR.SCHEME in ['LBFGS']:
self.LBFGS = LBFGS(path=PATH.OPTIMIZE,
memory=PAR.LBFGSMEM,
maxiter=PAR.LBFGSMAX,
thresh=PAR.LBFGSTHRESH,
precond=self.precond())
# write initial model
if exists(PATH.MODEL_INIT):
import solver
src = PATH.MODEL_INIT
dst = join(PATH.OPTIMIZE, 'm_new')
savenpy(dst, solver.merge(solver.load(src)))
def precond(self):
""" Loads preconditioner machinery
"""
from seisflows.seistools import preconds
if PAR.PRECOND in dir(preconds):
return getattr(preconds, PAR.PRECOND)()
elif PAR.PRECOND:
return getattr(preconds, 'diagonal')()
else:
return None
# The following names are used in the 'compute_direction' method and for
# writing information to disk:
# m_new - current model
# m_old - previous model
# m_try - trial model
# f_new - current objective function value
# f_old - previous objective function value
# f_try - trial objective function value
# g_new - current gradient direction
# g_old - previous gradient direction
# p_new - current search direction
# p_old - previous search direction
# s_new - current slope along search direction
# s_old - previous slope along search direction
# alpha - trial step length
def compute_direction(self):
""" Computes model update direction from stored gradient
"""
unix.cd(PATH.OPTIMIZE)
g_new = self.load('g_new')
if PAR.SCHEME in ['GradientDescent', 'SteepestDescent']:
p_new, self.restarted = -g_new, False
elif PAR.SCHEME in ['NLCG']:
p_new, self.restarted = self.NLCG()
elif PAR.SCHEME in ['LBFGS']:
p_new, self.restarted = self.LBFGS()
self.save('p_new', p_new)
savetxt('s_new', self.dot(g_new, p_new))
return p_new
# The following names are used exclusively for the line search:
# m - model vector
# p - search direction vector
# s - slope along search direction
# f - value of objective function, evaluated at m
# x - step length along search direction
# p_ratio - ratio of model norm to search direction norm
# s_ratio - ratio of current slope to previous slope
def initialize_search(self):
""" Determines initial step length for line search
"""
unix.cd(PATH.OPTIMIZE)
m = self.load('m_new')
p = self.load('p_new')
f = loadtxt('f_new')
norm_m = max(abs(m))
norm_p = max(abs(p))
p_ratio = float(norm_m / norm_p)
# reset search history
self.search_history = [[0., f]]
self.step_count = 0
self.isdone = 0
self.isbest = 0
self.isbrak = 0
# determine initial step length
if self.iter == 1:
alpha = p_ratio * PAR.STEPINIT
elif self.restarted:
alpha = p_ratio * PAR.STEPINIT
elif PAR.SCHEME in ['LBFGS']:
alpha = 1.
else:
alpha = self.initial_step()
# optional ad hoc scaling
if PAR.STEPOVERSHOOT:
alpha *= PAR.STEPOVERSHOOT
# optional maximum step length safegaurd
if PAR.STEPTHRESH:
if alpha > p_ratio * PAR.STEPTHRESH and \
self.iter > 1:
alpha = p_ratio * PAR.STEPTHRESH
# write trial model corresponding to chosen step length
savetxt('alpha', alpha)
self.save('m_try', m + alpha * p)
# upate log
self.stepwriter(steplen=0., funcval=f)
def update_status(self):
""" Updates line search status
Maintains line search history by keeping track of step length and
function value from each trial model evaluation. From line search
history, determines whether stopping criteria have been satisfied.
"""
unix.cd(PATH.OPTIMIZE)
x_ = loadtxt('alpha')
f_ = loadtxt('f_try')
if np.isnan(f_):
raise ValueError
# update search history
self.search_history += [[x_, f_]]
self.step_count += 1
x = self.step_lens()
f = self.func_vals()
fmin = f.min()
imin = f.argmin()
# is current step length the best so far?
vals = self.func_vals(sort=False)
if np.all(vals[-1] < vals[:-1]):
self.isbest = 1
# are stopping criteria satisfied?
if PAR.LINESEARCH == 'Fixed':
if (fmin < f[0]) and any(fmin < f[imin:]):
self.isdone = 1
#elif PAR.LINESEARCH == 'Bracket' or \
# self.iter == 1 or self.restarted:
elif PAR.LINESEARCH == 'Bracket':
if self.isbrak:
self.isdone = 1
elif (fmin < f[0]) and any(fmin < f[imin:]):
self.isbrak = 1
elif PAR.LINESEARCH == 'Backtrack':
if fmin < f[0]:
self.isdone = 1
# update log
self.stepwriter(steplen=x_, funcval=f_)
return self.isdone
def compute_step(self):
""" Computes next trial step length
"""
unix.cd(PATH.OPTIMIZE)
m = self.load('m_new')
g = self.load('g_new')
p = self.load('p_new')
s = loadtxt('s_new')
norm_m = max(abs(m))
norm_p = max(abs(p))
p_ratio = float(norm_m / norm_p)
x = self.step_lens()
f = self.func_vals()
# compute trial step length
if PAR.LINESEARCH == 'Fixed':
alpha = p_ratio * (self.step_count + 1) * PAR.STEPINIT
#elif PAR.LINESEARCH == 'Bracket' or \
# self.iter == 1 or self.restarted:
elif PAR.LINESEARCH == 'Bracket':
if any(f[1:] < f[0]) and (f[-2] < f[-1]):
alpha = polyfit2(x, f)
elif any(f[1:] <= f[0]):
alpha = loadtxt('alpha') * PAR.STEPFACTOR**-1
else:
alpha = loadtxt('alpha') * PAR.STEPFACTOR
elif PAR.LINESEARCH == 'Backtrack':
# calculate slope along 1D profile
slope = s / self.dot(g, g)**0.5
if PAR.ADHOCFACTOR:
slope *= PAR.ADHOCFACTOR
alpha = backtrack2(f[0], slope, x[1], f[1], b1=0.1, b2=0.5)
# write trial model corresponding to chosen step length
savetxt('alpha', alpha)
self.save('m_try', m + alpha * p)
def finalize_search(self):
""" Cleans working directory and writes updated model
"""
unix.cd(PATH.OPTIMIZE)
m = self.load('m_new')
g = self.load('g_new')
p = self.load('p_new')
s = loadtxt('s_new')
x = self.step_lens()
f = self.func_vals()
# clean working directory
unix.rm('alpha')
unix.rm('m_try')
unix.rm('f_try')
if self.iter > 1:
unix.rm('m_old')
unix.rm('f_old')
unix.rm('g_old')
unix.rm('p_old')
unix.rm('s_old')
unix.mv('m_new', 'm_old')
unix.mv('f_new', 'f_old')
unix.mv('g_new', 'g_old')
unix.mv('p_new', 'p_old')
unix.mv('s_new', 's_old')
# write updated model
alpha = x[f.argmin()]
savetxt('alpha', alpha)
self.save('m_new', m + alpha * p)
savetxt('f_new', f.min())
# append latest statistics
self.writer('factor',
-self.dot(g, g)**-0.5 * (f[1] - f[0]) / (x[1] - x[0]))
self.writer('gradient_norm_L1', np.linalg.norm(g, 1))
self.writer('gradient_norm_L2', np.linalg.norm(g, 2))
self.writer('misfit', f[0])
self.writer('restarted', self.restarted)
self.writer('slope', (f[1] - f[0]) / (x[1] - x[0]))
self.writer('step_count', self.step_count)
self.writer('step_length', x[f.argmin()])
self.writer('theta', 180. * np.pi**-1 * angle(p, -g))
self.stepwriter.newline()
def retry_status(self):
""" Returns false if search direction was the same as gradient
direction; returns true otherwise
"""
unix.cd(PATH.OPTIMIZE)
g = self.load('g_new')
p = self.load('p_new')
thresh = 1.e-3
theta = angle(p, -g)
if PAR.VERBOSE >= 2:
print ' theta: %6.3f' % theta
if abs(theta) < thresh:
return 0
else:
return 1
def restart(self):
""" Discards history of algorithm; prepares to start again from
gradient direction
"""
unix.cd(PATH.OPTIMIZE)
g = self.load('g_new')
self.save('p_new', -g)
savetxt('s_new', self.dot(g, g))
if PAR.SCHEME in ['NLCG']:
self.NLCG.restart()
elif PAR.SCHEME in ['LBFGS']:
self.LBFGS.restart()
self.restarted = 1
self.stepwriter.iter -= 1
self.stepwriter.newline()
### line search utilities
def initial_step(self):
""" Determines first trial step in line search; see eg Nocedal and
Wright 2e section 3.5
"""
alpha = loadtxt('alpha')
s_new = loadtxt('s_new')
s_old = loadtxt('s_old')
s_ratio = s_new / s_old
return 2. * s_ratio * alpha
def step_lens(self, sort=True):
""" Returns previous step lengths from search history
"""
x, f = zip(*self.search_history)
x = np.array(x)
f = np.array(f)
f_sorted = f[abs(x).argsort()]
x_sorted = x[abs(x).argsort()]
if sort:
return x_sorted
else:
return x
def func_vals(self, sort=True):
""" Returns previous function values from search history
"""
x, f = zip(*self.search_history)
x = np.array(x)
f = np.array(f)
f_sorted = f[abs(x).argsort()]
x_sorted = x[abs(x).argsort()]
if sort:
return f_sorted
else:
return f
### utilities
def dot(self, x, y):
""" Computes inner product between vectors
"""
return np.dot(np.squeeze(x), np.squeeze(y))
load = staticmethod(loadnpy)
save = staticmethod(savenpy)
class base(object):
""" Nonlinear optimization base class.
Available nonlinear optimization algorithms include steepest descent (SD),
nonlinear conjugate gradient (NLCG), and limited-memory BFGS (LBFGS).
Available step control algorithms include a backtracking line search and a
bracketing line search.
Though NLCG (a Krylov method) and LBFGS (a quasi-Newton metod) are both
widely used for geophysical inversion, LBFGS is more efficient and more
robust. NLCG requires occasional restarts to avoid numerical stagnation,
while LBFGS generally requires few restarts. Restarts are controlled by
numerical parameters. Default values provided below should work well
for a wide range inversions without the need for manual tuning.
To reduce memory overhead, vectors are read from disk rather than passed
from a calling routine. At the start of each search direction computation
the current model and gradient are read from files 'm_new' and 'g_new';
the resulting search direction is written to 'p_new'. As the inversion
progresses, other information is stored to disk as well.
"""
def check(self):
""" Checks parameters, paths, and dependencies
"""
if "BEGIN" not in PAR:
raise ParameterError
if "END" not in PAR:
raise ParameterError
if "SUBMIT" not in PATH:
raise ParameterError
if "OPTIMIZE" not in PATH:
setattr(PATH, "OPTIMIZE", join(PATH.GLOBAL, "optimize"))
if "MODEL_INIT" not in PATH:
setattr(PATH, "MODEL_INIT", None)
# search direction algorithm
if "SCHEME" not in PAR:
setattr(PAR, "SCHEME", "LBFGS")
if "PRECOND" not in PAR:
setattr(PAR, "PRECOND", None)
# line search algorithm
if "LINESEARCH" not in PAR:
if PAR.SCHEME in ["LBFGS"]:
setattr(PAR, "LINESEARCH", "Backtrack")
else:
setattr(PAR, "LINESEARCH", "Bracket")
# search direction tuning parameters
if "NLCGMAX" not in PAR:
setattr(PAR, "NLCGMAX", np.inf)
if "NLCGTHRESH" not in PAR:
setattr(PAR, "NLCGTHRESH", np.inf)
if "LBFGSMEM" not in PAR:
setattr(PAR, "LBFGSMEM", 3)
if "LBFGSMAX" not in PAR:
setattr(PAR, "LBFGSMAX", np.inf)
if "LBFGSTHRESH" not in PAR:
setattr(PAR, "LBFGSTHRESH", 0.0)
# line search tuning paraemters
if "STEPMAX" not in PAR:
setattr(PAR, "STEPMAX", 10)
if "STEPTHRESH" not in PAR:
setattr(PAR, "STEPTHRESH", None)
if "STEPINIT" not in PAR:
setattr(PAR, "STEPINIT", 0.05)
if "STEPFACTOR" not in PAR:
setattr(PAR, "STEPFACTOR", 0.5)
if "STEPOVERSHOOT" not in PAR:
setattr(PAR, "STEPOVERSHOOT", 0.0)
if "ADHOCFACTOR" not in PAR:
setattr(PAR, "ADHOCFACTOR", 1.0)
def setup(self):
""" Sets up nonlinear optimization machinery
"""
unix.mkdir(PATH.OPTIMIZE)
# prepare output writers
self.writer = Writer(path=PATH.OUTPUT)
self.stepwriter = StepWriter(path=PATH.SUBMIT)
# prepare algorithm machinery
if PAR.SCHEME in ["NLCG"]:
self.NLCG = NLCG(path=PATH.OPTIMIZE, maxiter=PAR.NLCGMAX, thresh=PAR.NLCGTHRESH, precond=self.precond)
elif PAR.SCHEME in ["LBFGS"]:
self.LBFGS = LBFGS(
path=PATH.OPTIMIZE,
memory=PAR.LBFGSMEM,
maxiter=PAR.LBFGSMAX,
thresh=PAR.LBFGSTHRESH,
precond=self.precond,
)
# write initial model
if exists(PATH.MODEL_INIT):
src = PATH.MODEL_INIT
dst = join(PATH.OPTIMIZE, "m_new")
savenpy(dst, solver.merge(solver.load(src)))
@property
def precond(self):
""" Loads preconditioner machinery
"""
from seisflows.seistools import preconds
if PAR.PRECOND in dir(preconds):
return getattr(preconds, PAR.PRECOND)()
elif PAR.PRECOND:
return getattr(preconds, "diagonal")()
else:
return None
# The following names are used in the 'compute_direction' method and for
# writing information to disk:
# m_new - current model
# m_old - previous model
# m_try - trial model
# f_new - current objective function value
# f_old - previous objective function value
# f_try - trial objective function value
# g_new - current gradient direction
# g_old - previous gradient direction
# p_new - current search direction
# p_old - previous search direction
# s_new - current slope along search direction
# s_old - previous slope along search direction
# alpha - trial step length
def compute_direction(self):
""" Computes model update direction from stored gradient
"""
unix.cd(PATH.OPTIMIZE)
g_new = self.load("g_new")
if PAR.SCHEME in ["SD"]:
p_new, self.restarted = -g_new, False
elif PAR.SCHEME in ["NLCG"]:
p_new, self.restarted = self.NLCG()
elif PAR.SCHEME in ["LBFGS"]:
p_new, self.restarted = self.LBFGS()
self.save("p_new", p_new)
savetxt("s_new", self.dot(g_new, p_new))
return p_new
# The following names are used exclusively for the line search:
# m - model vector
# p - search direction vector
# s - slope along search direction
# f - value of objective function, evaluated at m
# x - step length along search direction
# p_ratio - ratio of model norm to search direction norm
# s_ratio - ratio of current slope to previous slope
def initialize_search(self):
""" Determines initial step length for line search
"""
unix.cd(PATH.OPTIMIZE)
m = self.load("m_new")
p = self.load("p_new")
f = loadtxt("f_new")
norm_m = max(abs(m))
norm_p = max(abs(p))
p_ratio = float(norm_m / norm_p)
# reset search history
self.search_history = [[0.0, f]]
self.step_count = 0
self.isdone = 0
self.isbest = 0
self.isbrak = 0
# determine initial step length
if self.iter == 1:
alpha = p_ratio * PAR.STEPINIT
elif self.restarted:
alpha = p_ratio * PAR.STEPINIT
elif PAR.SCHEME in ["LBFGS"]:
alpha = 1.0
else:
alpha = self.initial_step()
# optional ad hoc scaling
if PAR.STEPOVERSHOOT:
alpha *= PAR.STEPOVERSHOOT
# optional maximum step length safegaurd
if PAR.STEPTHRESH:
if alpha > p_ratio * PAR.STEPTHRESH and self.iter > 1:
alpha = p_ratio * PAR.STEPTHRESH
# write trial model corresponding to chosen step length
savetxt("alpha", alpha)
self.save("m_try", m + alpha * p)
# upate log
self.stepwriter(steplen=0.0, funcval=f)
def update_status(self):
""" Updates line search status
Maintains line search history by keeping track of step length and
function value from each trial model evaluation. From line search
history, determines whether stopping criteria have been satisfied.
"""
unix.cd(PATH.OPTIMIZE)
x_ = loadtxt("alpha")
f_ = loadtxt("f_try")
if np.isnan(f_):
raise ValueError
# update search history
self.search_history += [[x_, f_]]
self.step_count += 1
x = self.step_lens()
f = self.func_vals()
fmin = f.min()
imin = f.argmin()
# is current step length the best so far?
vals = self.func_vals(sort=False)
if np.all(vals[-1] < vals[:-1]):
self.isbest = 1
# are stopping criteria satisfied?
if PAR.LINESEARCH == "Fixed":
if (fmin < f[0]) and any(fmin < f[imin:]):
self.isdone = 1
elif PAR.LINESEARCH == "Bracket" or self.iter == 1 or self.restarted:
if self.isbrak:
self.isdone = 1
elif (fmin < f[0]) and any(fmin < f[imin:]):
self.isbrak = 1
elif PAR.LINESEARCH == "Backtrack":
if fmin < f[0]:
self.isdone = 1
# update log
self.stepwriter(steplen=x_, funcval=f_)
return self.isdone
def compute_step(self):
""" Computes next trial step length
"""
unix.cd(PATH.OPTIMIZE)
m = self.load("m_new")
g = self.load("g_new")
p = self.load("p_new")
s = loadtxt("s_new")
norm_m = max(abs(m))
norm_p = max(abs(p))
p_ratio = float(norm_m / norm_p)
x = self.step_lens()
f = self.func_vals()
# compute trial step length
if PAR.LINESEARCH == "Fixed":
alpha = p_ratio * (self.step_count + 1) * PAR.STEPINIT
elif PAR.LINESEARCH == "Bracket" or self.iter == 1 or self.restarted:
if any(f[1:] < f[0]) and (f[-2] < f[-1]):
alpha = polyfit2(x, f)
elif any(f[1:] <= f[0]):
alpha = loadtxt("alpha") * PAR.STEPFACTOR ** -1
else:
alpha = loadtxt("alpha") * PAR.STEPFACTOR
elif PAR.LINESEARCH == "Backtrack":
# calculate slope along 1D profile
slope = s / self.dot(g, g) ** 0.5
if PAR.ADHOCFACTOR:
slope *= PAR.ADHOCFACTOR
alpha = backtrack2(f[0], slope, x[1], f[1], b1=0.1, b2=0.5)
# write trial model corresponding to chosen step length
savetxt("alpha", alpha)
self.save("m_try", m + alpha * p)
def finalize_search(self):
""" Cleans working directory and writes updated model
"""
unix.cd(PATH.OPTIMIZE)
m = self.load("m_new")
g = self.load("g_new")
p = self.load("p_new")
s = loadtxt("s_new")
x = self.step_lens()
f = self.func_vals()
# clean working directory
unix.rm("alpha")
unix.rm("m_try")
unix.rm("f_try")
if self.iter > 1:
unix.rm("m_old")
unix.rm("f_old")
unix.rm("g_old")
unix.rm("p_old")
unix.rm("s_old")
unix.mv("m_new", "m_old")
unix.mv("f_new", "f_old")
unix.mv("g_new", "g_old")
unix.mv("p_new", "p_old")
unix.mv("s_new", "s_old")
# write updated model
alpha = x[f.argmin()]
savetxt("alpha", alpha)
self.save("m_new", m + alpha * p)
savetxt("f_new", f.min())
# append latest output
self.writer("factor", -self.dot(g, g) ** -0.5 * (f[1] - f[0]) / (x[1] - x[0]))
self.writer("gradient_norm_L1", np.linalg.norm(g, 1))
self.writer("gradient_norm_L2", np.linalg.norm(g, 2))
self.writer("misfit", f[0])
self.writer("restarted", self.restarted)
self.writer("slope", (f[1] - f[0]) / (x[1] - x[0]))
self.writer("step_count", self.step_count)
self.writer("step_length", x[f.argmin()])
self.writer("theta", 180.0 * np.pi ** -1 * angle(p, -g))
self.stepwriter.newline()
@property
def retry_status(self):
""" Returns false if search direction was the same as gradient
direction. Returns true otherwise.
"""
unix.cd(PATH.OPTIMIZE)
g = self.load("g_new")
p = self.load("p_new")
thresh = 1.0e-3
theta = angle(p, -g)
# print ' theta: %6.3f' % theta
if abs(theta) < thresh:
return 0
else:
return 1
def restart(self):
""" Discards history of algorithm; prepares to start again from
gradient direction
"""
unix.cd(PATH.OPTIMIZE)
g = self.load("g_new")
self.save("p_new", -g)
savetxt("s_new", self.dot(g, g))
if PAR.SCHEME in ["NLCG"]:
self.NLCG.restart()
elif PAR.SCHEME in ["LBFGS"]:
self.LBFGS.restart()
self.restarted = 1
self.stepwriter.iter -= 1
self.stepwriter.newline()
### line search utilities
def initial_step(self):
alpha = loadtxt("alpha")
s_new = loadtxt("s_new")
s_old = loadtxt("s_old")
s_ratio = s_new / s_old
return 2.0 * s_ratio * alpha
def step_lens(self, sort=True):
x, f = zip(*self.search_history)
x = np.array(x)
f = np.array(f)
f_sorted = f[abs(x).argsort()]
x_sorted = x[abs(x).argsort()]
if sort:
return x_sorted
else:
return x
def func_vals(self, sort=True):
x, f = zip(*self.search_history)
x = np.array(x)
f = np.array(f)
f_sorted = f[abs(x).argsort()]
x_sorted = x[abs(x).argsort()]
if sort:
return f_sorted
else:
return f
### utilities
def dot(self, x, y):
return np.dot(np.squeeze(x), np.squeeze(y))
load = staticmethod(loadnpy)
save = staticmethod(savenpy)