def compute_step(cls):
""" Computes next trial step length
"""
unix.cd(cls.path)
m0 = loadnpy('m_new')
p = loadnpy('p_new')
f0 = loadtxt('f_new')
g0 = loadtxt('s_new')
x = cls.step_lens()
f = cls.func_vals()
# compute trial step length
if PAR.SRCHTYPE == 'Backtrack':
alpha = lib.backtrack2(f0, g0, x[1], f[1], b1=0.1, b2=0.5)
elif PAR.SRCHTYPE == 'Bracket':
FACTOR = 2.
if any(f[1:] < f[0]) and (f[-2] < f[-1]):
alpha = lib.polyfit2(x, f)
elif any(f[1:] < f[0]):
alpha = loadtxt('alpha') * FACTOR
else:
alpha = loadtxt('alpha') * FACTOR**-1
elif PAR.SRCHTYPE == 'Fixed':
alpha = cls.step_ratio * (step + 1) * PAR.STEPLEN
else:
raise ValueError
# write trial model
savetxt('alpha', alpha)
savenpy('m_try', m0 + p * alpha)
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 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 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 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_direction(cls):
""" Computes model update direction from stored function and gradient
values
"""
unix.cd(cls.path)
m_new = loadnpy('m_new')
f_new = loadtxt('f_new')
g_new = loadnpy('g_new')
if PAR.SCHEME == 'GradientDescent':
p_new = -g_new
elif PAR.SCHEME == 'ConjugateGradient':
# compute NLCG udpate
p_new = cls.NLCG.compute()
elif PAR.SCHEME == 'QuasiNewton':
# compute L-BFGS update
if cls.iter == 1:
p_new = -g_new
else:
cls.LBFGS.update()
p_new = -cls.LBFGS.solve()
# save results
unix.cd(cls.path)
savenpy('p_new', p_new)
savetxt('s_new', np.dot(g_new, p_new))
def test_saveloadtxt(self):
tmp_file = NamedTemporaryFile(mode='wb', delete=False)
tmp_file.close()
x = 3.14159265359
tools.savetxt(tmp_file.name, x)
self.assertAlmostEqual(x, tools.loadtxt(tmp_file.name), 6)
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 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 search_status(cls):
""" Determines status of line search
"""
unix.cd(cls.path)
f0 = loadtxt('f_new')
g0 = loadtxt('s_new')
x_ = loadtxt('alpha')
f_ = loadtxt('f_try')
if np.isnan(f_):
raise ValueError
cls.search_history += [[x_, f_]]
x = cls.step_lens()
f = cls.func_vals()
# is current step length the best so far?
vals = cls.func_vals(sort=False)
if np.all(vals[-1] < vals[:-1]):
cls.isbest = 1
# are stopping criteria satisfied?
if PAR.SRCHTYPE == 'Backtrack':
if any(f[1:] < f[0]):
cls.isdone = 1
elif PAR.SRCHTYPE == 'Bracket':
if cls.isbrak:
cls.isbest = 1
cls.isdone = 1
elif any(f[1:] < f[0]) and (f[-2] < f[-1]):
cls.isbrak = 1
elif PAR.SRCHTYPE == 'Fixed':
if any(f[1:] < f[0]) and (f[-2] < f[-1]):
cls.isdone = 1
cls.writer([], x_, f_)
return cls.isdone, cls.isbest
def __init__(self, path='.', load=loadnpy, save=savenpy, thresh=1., maxiter=np.inf, precond=None):
self.path = path
self.load = load
self.save = save
self.maxiter = maxiter
self.thresh = thresh
self.precond = precond
try:
self.iter = loadtxt(self.path+'/'+'NLCG/iter')
except IOError:
unix.mkdir(self.path+'/'+'NLCG')
self.iter = 0
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 initialize_search(cls):
""" Determines initial step length for line search
"""
unix.cd(cls.path)
if cls.iter == 1:
s_new = loadtxt('s_new')
f_new = loadtxt('f_new')
else:
s_old = loadtxt('s_old')
s_new = loadtxt('s_new')
f_old = loadtxt('f_old')
f_new = loadtxt('f_new')
alpha = loadtxt('alpha')
m = loadnpy('m_new')
p = loadnpy('p_new')
# reset search history
cls.search_history = [[0., f_new]]
cls.isdone = 0
cls.isbest = 0
cls.isbrak = 0
# determine initial step length
len_m = max(abs(m))
len_d = max(abs(p))
cls.step_ratio = float(len_m / len_d)
if cls.iter == 1:
assert PAR.STEPLEN != 0.
alpha = PAR.STEPLEN * cls.step_ratio
elif PAR.SRCHTYPE in ['Bracket']:
alpha *= 2. * s_old / s_new
elif PAR.SCHEME in ['GradientDescent', 'ConjugateGradient']:
alpha *= 2. * s_old / s_new
else:
alpha = 1.
# ad hoc scaling
if PAR.ADHOCSCALING:
alpha *= PAR.ADHOCSCALING
# limit maximum step length
if PAR.STEPMAX > 0.:
if alpha / cls.step_ratio > PAR.STEPMAX:
alpha = PAR.STEPMAX * cls.step_ratio
# write trial model
savenpy('m_try', m + p * alpha)
savetxt('alpha', alpha)
cls.writer(cls.iter, 0., f_new)
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 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()
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 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(self, ap):
unix.cd(self.path)
self.ilcg += 1
x = self.load('LCG/x')
r = self.load('LCG/r')
y = self.load('LCG/y')
p = self.load('LCG/p')
ry = loadtxt('LCG/ry')
pap = np.dot(p, ap)
if pap < 0:
print ' Stopping LCG [negative curvature]'
isdone = True
return isdone
alpha = ry/pap
x += alpha*p
r += alpha*ap
self.save('LCG/x', x)
self.save('LCG/r', r)
# check status
if self.check_status(ap) == 0:
isdone = True
elif self.ilcg >= self.maxiter:
isdone = True
else:
isdone = False
if not isdone:
y = self.apply_precond(r)
ry_old = ry
ry = np.dot(r, y)
beta = ry/ry_old
p = -y + beta*p
self.save('LCG/y', y)
self.save('LCG/p', p)
savetxt('LCG/ry', np.dot(r, y))
return isdone
def update(self, ap):
unix.cd(self.path)
self.ilcg += 1
x = self.load('LCG/x')
r = self.load('LCG/r')
y = self.load('LCG/y')
p = self.load('LCG/p')
ry = loadtxt('LCG/ry')
pap = np.dot(p, ap)
if pap < 0:
print ' Stopping LCG [negative curvature]'
isdone = True
return isdone
alpha = ry / pap
x += alpha * p
r += alpha * ap
self.save('LCG/x', x)
self.save('LCG/r', r)
# check status
if self.check_status(ap) == 0:
isdone = True
elif self.ilcg >= self.maxiter:
isdone = True
else:
isdone = False
if not isdone:
y = self.apply_precond(r)
ry_old = ry
ry = np.dot(r, y)
beta = ry / ry_old
p = -y + beta * p
self.save('LCG/y', y)
self.save('LCG/p', p)
savetxt('LCG/ry', np.dot(r, y))
return isdone
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.*s_ratio*alpha
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