def optimize_openopt(self, omega_min, lower_bounds, upper_bounds, max_power, fluid_type):
def optimize_force_resolution(x):
c = cantilever_divingboard(self.freq_min, self.freq_max, *x)
return c.force_resolution()*1e12
# We always want power dissipation to be less than max_power
def enforce_max_power(x):
c = cantilever_divingboard(self.freq_min, self.freq_max, *x)
return c.power_dissipation() - max_power
# We always want the natural frequency to be greater than the minimum allowed
def enforce_minimum_natural_frequency(x):
c = cantilever_divingboard(self.freq_min, self.freq_max, *x)
if fluid_type == 'vacuum':
return omega_min - c.omega_vacuum_hz()
elif fluid_type == 'water':
return omega_min - c.omega_damped_hz()
else:
return -c.omega_vacuum_hz()
# Our initial guess is based upon the existing cantilever dimensions
initial_guess = (self.l, self.w, self.t,
self.l_pr_ratio, self.w_pr_ratio, self.w_gap_ratio, self.t_pr_ratio,
self.V_bias, self.N)
# Setup the solver
p = NLP(optimize_force_resolution, initial_guess)
p.lb = lower_bounds
p.ub = upper_bounds
p.scale=(1e-6, 1e-6, 1e-9, 1, 1, 1, 1, 1e2, 1e19)
# c(x) <= 0 constraints (use these if the solver supports NL constraints)
# p.c = (enforce_minimum_natural_frequency,
# enforce_max_power)
# Solving parameters
p.ftol = 1e-12 # one of stop criteria, default 1e-6
p.xtol = 1e-12 # one of stop criteria, default 1e-6
p.gradtol = 1e-7
p.contol = 1e-7
# Set limits of how long to solve for
p.maxIter = 1e4
p.maxFunEvals = 1e8
p.maxTime = 1e4
# p.plot = 1
# p.debug=1
r = p.solve('algencan')
(self.l, self.w, self.t,
self.l_pr_ratio, self.w_pr_ratio, self.w_gap_ratio, self.t_pr_ratio,
self.V_bias, self.N) = r.xf
def max_log_marginal_likelihood(self, hyp_initial_guess, maxiter=1,
optimization_algorithm="scipy_cg", ftol=1.0e-3, fixedHypers=None,
use_gradient=False, logscale=False):
"""
Set up the optimization problem in order to maximize
the log_marginal_likelihood.
:Parameters:
parametric_model : Classifier
the actual parameteric model to be optimized.
hyp_initial_guess : numpy.ndarray
set of hyperparameters' initial values where to start
optimization.
optimization_algorithm : string
actual name of the optimization algorithm. See
http://scipy.org/scipy/scikits/wiki/NLP
for a comprehensive/updated list of available NLP solvers.
(Defaults to 'ralg')
ftol : float
threshold for the stopping criterion of the solver,
which is mapped in OpenOpt NLP.ftol
(Defaults to 1.0e-3)
fixedHypers : numpy.ndarray (boolean array)
boolean vector of the same size of hyp_initial_guess;
'False' means that the corresponding hyperparameter must
be kept fixed (so not optimized).
(Defaults to None, which during means all True)
NOTE: the maximization of log_marginal_likelihood is a non-linear
optimization problem (NLP). This fact is confirmed by Dmitrey,
author of OpenOpt.
"""
self.problem = None
self.use_gradient = use_gradient
self.logscale = logscale # use log-scale on hyperparameters to enhance numerical stability
self.optimization_algorithm = optimization_algorithm
self.hyp_initial_guess = N.array(hyp_initial_guess)
self.hyp_initial_guess_log = N.log(self.hyp_initial_guess)
if fixedHypers is None:
fixedHypers = N.zeros(self.hyp_initial_guess.shape[0],dtype=bool)
pass
self.freeHypers = -fixedHypers
if self.logscale:
self.hyp_running_guess = self.hyp_initial_guess_log.copy()
else:
self.hyp_running_guess = self.hyp_initial_guess.copy()
pass
self.f_last_x = None
def f(x):
"""
Wrapper to the log_marginal_likelihood to be
maximized.
"""
# XXX EO: since some OpenOpt NLP solvers does not
# implement lower bounds the hyperparameters bounds are
# implemented inside PyMVPA: (see dmitrey's post on
# [SciPy-user] 20080628).
#
# XXX EO: OpenOpt does not implement optimization of a
# subset of the hyperparameters so it is implemented here.
#
# XXX EO: OpenOpt does not implement logrithmic scale of
# the hyperparameters (to enhance numerical stability), so
# it is implemented here.
self.f_last_x = x.copy()
self.hyp_running_guess[self.freeHypers] = x
# REMOVE print "guess:",self.hyp_running_guess,x
try:
if self.logscale:
self.parametric_model.set_hyperparameters(N.exp(self.hyp_running_guess))
else:
self.parametric_model.set_hyperparameters(self.hyp_running_guess)
pass
except InvalidHyperparameterError:
if __debug__: debug("MOD_SEL","WARNING: invalid hyperparameters!")
return -N.inf
try:
self.parametric_model.train(self.dataset)
except (N.linalg.linalg.LinAlgError, SL.basic.LinAlgError, ValueError):
# Note that ValueError could be raised when Cholesky gets Inf or Nan.
if __debug__: debug("MOD_SEL", "WARNING: Cholesky failed! Invalid hyperparameters!")
return -N.inf
log_marginal_likelihood = self.parametric_model.compute_log_marginal_likelihood()
# REMOVE print log_marginal_likelihood
return log_marginal_likelihood
def df(x):
"""
Proxy to the log_marginal_likelihood first
derivative. Necessary for OpenOpt when using derivatives.
"""
self.hyp_running_guess[self.freeHypers] = x
# REMOVE print "df guess:",self.hyp_running_guess,x
# XXX EO: Most of the following lines can be skipped if
# df() is computed just after f() with the same
# hyperparameters. The partial results obtained during f()
# are what is needed for df(). For now, in order to avoid
# bugs difficult to trace, we keep this redunundancy. A
# deep check with how OpenOpt works or using memoization
# should solve this issue.
try:
if self.logscale:
self.parametric_model.set_hyperparameters(N.exp(self.hyp_running_guess))
else:
self.parametric_model.set_hyperparameters(self.hyp_running_guess)
pass
except InvalidHyperparameterError:
if __debug__: debug("MOD_SEL", "WARNING: invalid hyperparameters!")
return -N.inf
# Check if it is possible to avoid useless computations
# already done in f(). According to tests and information
# collected from OpenOpt people, it is sufficiently
# unexpected that the following test succeed:
if N.any(x!=self.f_last_x):
if __debug__: debug("MOD_SEL","UNEXPECTED: recomputing train+log_marginal_likelihood.")
try:
self.parametric_model.train(self.dataset)
except (N.linalg.linalg.LinAlgError, SL.basic.LinAlgError, ValueError):
if __debug__: debug("MOD_SEL", "WARNING: Cholesky failed! Invalid hyperparameters!")
# XXX EO: which value for the gradient to return to
# OpenOpt when hyperparameters are wrong?
return N.zeros(x.size)
log_marginal_likelihood = self.parametric_model.compute_log_marginal_likelihood() # recompute what's needed (to be safe) REMOVE IN FUTURE!
pass
if self.logscale:
gradient_log_marginal_likelihood = self.parametric_model.compute_gradient_log_marginal_likelihood_logscale()
else:
gradient_log_marginal_likelihood = self.parametric_model.compute_gradient_log_marginal_likelihood()
pass
# REMOVE print "grad:",gradient_log_marginal_likelihood
return gradient_log_marginal_likelihood[self.freeHypers]
if self.logscale:
# vector of hyperparameters' values where to start the search
x0 = self.hyp_initial_guess_log[self.freeHypers]
else:
x0 = self.hyp_initial_guess[self.freeHypers]
pass
self.contol = 1.0e-20 # Constraint tolerance level
# XXX EO: is it necessary to use contol when self.logscale is
# True and there is no lb? Ask dmitrey.
if self.use_gradient:
# actual instance of the OpenOpt non-linear problem
self.problem = NLP(f, x0, df=df, contol=self.contol, goal='maximum')
else:
self.problem = NLP(f, x0, contol=self.contol, goal='maximum')
pass
self.problem.name = "Max LogMargLikelihood"
if not self.logscale:
# set lower bound for hyperparameters: avoid negative
# hyperparameters. Note: problem.n is the size of
# hyperparameters' vector
self.problem.lb = N.zeros(self.problem.n)+self.contol
pass
# max number of iterations for the optimizer.
self.problem.maxiter = maxiter
# check whether the derivative of log_marginal_likelihood converged to
# zero before ending optimization
self.problem.checkdf = True
# set increment of log_marginal_likelihood under which the optimizer stops
self.problem.ftol = ftol
self.problem.iprint = _openopt_debug()
return self.problem
