""" Backtracking line search using the Armijo-Goldstein condition."""
from math import isnan
import numpy as np
from openmdao.core.system import AnalysisError
from openmdao.solvers.solver_base import LineSearch
from openmdao.util.record_util import update_local_meta, create_local_meta
[docs]class BackTracking(LineSearch):
"""A line search subsolver that implements backracking using the
Armijo-Goldstein condition..
Options
-------
options['err_on_maxiter'] : bool(False)
If True, raise an AnalysisError if not converged at maxiter.
options['iprint'] : int(0)
Set to 0 to print only failures, set to 1 to print iteration totals to
stdout, set to 2 to print the residual each iteration to stdout,
or -1 to suppress all printing.
options['maxiter'] : int(10)
Maximum number of line searches.
options['solve_subsystems'] : bool(True)
Set to True to solve subsystems. You may need this for solvers nested under Newton.
options['rho'] : int(0.5)
Backtracking step.
options['c'] : int(0.5)
Slope check trigger.
"""
def __init__(self):
super(BackTracking, self).__init__()
opt = self.options
opt.add_option('maxiter', 5, lower=0,
desc='Maximum number of line searches.')
opt.add_option('solve_subsystems', True,
desc='Set to True to solve subsystems. You may need this for solvers nested under Newton.')
opt.add_option('rho', 0.5,
desc="Backtracking step.")
opt.add_option('c', 0.5,
desc="Slope check trigger.")
self.print_name = 'BK_TKG'
[docs] def solve(self, params, unknowns, resids, system, solver, alpha_scalar, alpha,
base_u, base_norm, fnorm, fnorm0, metadata=None):
""" Take the gradient calculated by the parent solver and figure out
how far to go.
Args
----
params : `VecWrapper`
`VecWrapper` containing parameters. (p)
unknowns : `VecWrapper`
`VecWrapper` containing outputs and states. (u)
resids : `VecWrapper`
`VecWrapper` containing residuals. (r)
system : `System`
Parent `System` object.
solver : `Solver`
Parent solver instance.
alpha_scalar : float
Initial over-relaxation factor as used in parent solver.
alpha : ndarray
Initial over-relaxation factor as used in parent solver, vector
(so we don't re-allocate).
base_u : ndarray
Initial value of unknowns before the Newton step.
base_norm : float
Norm of the residual prior to taking the Newton step.
fnorm : float
Norm of the residual after taking the Newton step.
fnorm0 : float
Initial norm of the residual for iteration printing.
metadata : dict, optional
Dictionary containing execution metadata (e.g. iteration coordinate).
Returns
--------
float
Norm of the final residual
"""
maxiter = self.options['maxiter']
rho = self.options['rho']
c = self.options['c']
iprint = self.options['iprint']
result = system.dumat[None]
local_meta = create_local_meta(metadata, system.pathname)
itercount = 0
ls_alpha = alpha_scalar
# Further backtacking if needed.
# The Armijo-Goldstein is basically a slope comparison --actual vs predicted.
# We don't have an actual gradient, but we have the Newton vector that should
# take us to zero, and our "runs" are the same, and we can just compare the
# "rise".
while itercount < maxiter and (base_norm - fnorm) < c*ls_alpha*base_norm:
ls_alpha *= rho
# If our step will violate any upper or lower bounds, then reduce
# alpha in just that direction so that we only step to that
# boundary.
unknowns.vec[:] = base_u
alpha[:] = ls_alpha
alpha = unknowns.distance_along_vector_to_limit(alpha, result)
unknowns.vec += alpha*result.vec
itercount += 1
# Metadata update
update_local_meta(local_meta, (solver.iter_count, itercount))
# Just evaluate the model with the new points
if self.options['solve_subsystems']:
system.children_solve_nonlinear(local_meta)
system.apply_nonlinear(params, unknowns, resids, local_meta)
solver.recorders.record_iteration(system, local_meta)
fnorm = resids.norm()
if iprint == 2:
self.print_norm(self.print_name, system, itercount,
fnorm, fnorm0, indent=1, solver='LS')
# Final residual print if you only want the last one
if iprint == 1:
self.print_norm(self.print_name, system, itercount,
fnorm, fnorm0, indent=1, solver='LS')
if itercount >= maxiter or isnan(fnorm):
if self.options['err_on_maxiter']:
msg = "Solve in '{}': BackTracking failed to converge after {} " \
"iterations."
raise AnalysisError(msg.format(system.pathname, maxiter))
msg = 'FAILED to converge after %d iterations' % itercount
fail = True
else:
msg = 'Converged in %d iterations' % itercount
fail = False
if iprint > 0 or (fail and iprint > -1 ):
self.print_norm(self.print_name, system, itercount,
fnorm, fnorm0, msg=msg, indent=1, solver='LS')
return fnorm
