def calculate_step(self):
""" Determines step length and search status
"""
x, f, gtg, gtp, step_count, update_count = self.search_history()
if step_count == 0 and update_count == 0:
# based on idea from Dennis and Schnabel
alpha = gtg[-1]**-1
status = 0
elif step_count == 0:
# based on the first equation in sec 3.5 of Nocedal and Wright 2ed
idx = np.argmin(self.func_vals[:-1])
alpha = self.step_lens[idx] * gtp[-2] / gtp[-1]
status = 0
elif _check_bracket(x, f) and _good_enough(x, f):
alpha = x[f.argmin()]
status = 1
elif _check_bracket(x, f):
alpha = polyfit2(x, f)
status = 0
elif step_count <= self.step_count_max and all(f <= f[0]):
# we need a larger step length
alpha = 1.618034 * x[-1]
status = 0
elif step_count <= self.step_count_max:
print("we need a smaller step length")
# we need a smaller step length
slope = gtp[-1] / gtg[-1]
alpha = backtrack2(f[0], slope, x[1], f[1], b1=0.1, b2=0.5)
#print("we need a smaller step length")
status = 0
else:
# failed because step_count_max exceeded
alpha = None
status = -1
# apply optional step length safeguard
if alpha > self.step_len_max and \
step_count == 0:
alpha = 0.618034 * self.step_len_max
status = 0
elif alpha > self.step_len_max:
# stop because safeguard prevents us from going further
alpha = self.step_len_max
status = 1
return alpha, status
def _good_enough(step_lens, func_vals, thresh=np.log10(1.2)):
""" Checks if step length is reasonably close to quadratic estimate
"""
x, f = step_lens, func_vals
if not _check_bracket(x,f):
return 0
x0 = polyfit2(x,f)
if any(np.abs(np.log10(x[1:]/x0)) < thresh):
return 1
else:
return 0
def calculate_step(self):
""" Determines step length and search status
"""
x, f, gtg, gtp, step_count, update_count = self.search_history()
if step_count==0 and update_count==0:
# based on idea from Dennis and Schnabel
alpha = gtg[-1]**-1
status = 0
elif step_count==0:
# based on the first equation in sec 3.5 of Nocedal and Wright 2ed
idx = np.argmin(self.func_vals[:-1])
alpha = self.step_lens[idx] * gtp[-2]/gtp[-1]
status = 0
elif _check_bracket(x,f) and _good_enough(x,f):
alpha = x[f.argmin()]
status = 1
elif _check_bracket(x,f):
alpha = polyfit2(x,f)
status = 0
elif step_count <= self.step_count_max and all(f <= f[0]):
# we need a larger step length
alpha = 1.618034*x[-1]
status = 0
elif step_count <= self.step_count_max:
# we need a smaller step length
slope = gtp[-1]/gtg[-1]
alpha = backtrack2(f[0], slope, x[1], f[1], b1=0.1, b2=0.5)
status = 0
else:
# failed because step_count_max exceeded
alpha = None
status = -1
# apply optional step length safeguard
if alpha > self.step_len_max and \
step_count==0:
alpha = 0.618034*self.step_len_max
status = 0
elif alpha > self.step_len_max:
# stop because safeguard prevents us from going further
alpha = self.step_len_max
status = 1
return alpha, status
def _good_enough(step_lens, func_vals, thresh=np.log10(1.2)):
""" Checks if step length is reasonably close to quadratic estimate
"""
x, f = step_lens, func_vals
if not _check_bracket(x, f):
return 0
print("x", x)
print("f", f)
x0 = polyfit2(x, f)
print("x0 " + str(x0))
if any(np.abs(np.log10(x[1:] / x0)) < thresh):
return 1
else:
print("not good ", np.min(np.abs(np.log10(x[1:] / x0))), thresh)
return 0
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 _good_enough(step_lens, func_vals, thresh=np.log10(1.2)):
"""
Checks if step length is reasonably close to quadratic estimate
polyfit2 requires
:type step_lens: np.array
:param step_lens: an array of the step lengths taken during iteration
:type func_vals: np.array
:param func_vals: array of misfit values from eval func function
:type thresh: numpy.float64
:param thresh: threshold value for comparison against quadratic estimate
:rtype: int
:return: status of function as a bool
"""
x, f = step_lens, func_vals
if not _check_bracket(x,f):
return 0
x0 = polyfit2(x,f)
if any(np.abs(np.log10(x[1:]/x0)) < thresh):
return 1
else:
return 0
def calculate_step(self):
""" Determines step length and search status
"""
x, f, gtg, gtp, step_count, update_count = self.search_history()
print '\tBracketing line search'
print '\t\tStep lengths = {}'.format(x)
print '\t\tMisfits = {}'.format(f)
# For the first inversion and initial step, set alpha
if step_count==0 and update_count==0:
# based on idea from Dennis and Schnabel
print "\t\tFirst inversion, initial trial step, continuing..."
alpha = gtg[-1]**-1
status = 0
# For every i'th inversion's initial step, set alpha
elif step_count==0:
# based on the first equation in sec 3.5 of Nocedal and Wright 2ed
print "\t\tInitial trial step, setting scaled step length"
idx = np.argmin(self.func_vals[:-1])
alpha = self.step_lens[idx] * gtp[-2]/gtp[-1]
status = 0
# If misfit is reduced and then increased, we've bracketed. Pass
elif _check_bracket(x,f) and _good_enough(x,f):
print "\t\tBracket okay, step length reasonable, pass"
alpha = x[f.argmin()]
status = 1
# if misfit is reduced but not close, set to quadratic fit
elif _check_bracket(x,f):
print "\t\tBracket okay, step length unreasonable, manual step..."
alpha = polyfit2(x,f)
status = 0
# if misfit continues to step down, increase step length
elif step_count <= self.step_count_max and all(f <= f[0]):
print "\t\tMisfit not bracketed, increasing step length..."
alpha = 1.618034*x[-1]
status = 0
# if misfit increases, reduce step length
elif step_count <= self.step_count_max:
print "\t\tMisfit increasing, reducing step length..."
slope = gtp[-1]/gtg[-1]
alpha = backtrack2(f[0], slope, x[1], f[1], b1=0.1, b2=0.5)
status = 0
# step_count_max exceeded, fail
else:
print "\t\tBracketing failed, step_count_max exceeded"
alpha = None
status = -1
# apply optional step length safeguard
if alpha > self.step_len_max and step_count==0:
print "\tInitial step length safegaurd, setting manual step length"
alpha = 0.618034*self.step_len_max
status = 0
# stop because safeguard prevents us from going further
elif alpha > self.step_len_max:
print "step_len_max exceeded, manual set alpha"
alpha = self.step_len_max
status = 1
return alpha, status