def find_opt_bfgs(fmap, template_maker, params, bfgs_settings,
save_steps=False, normal_hierarchy=None,
check_octant=False, metric_name='llh'):
"""
Finds the template (and free systematic params) that maximize
likelihood that the data came from the chosen template of
true params (or minimize chisquare), using the limited memory BFGS
algorithm subject to bounds (l_bfgs_b).
returns a dictionary of llh/chisquare data and best fit params, in the format:
{'llh/chisquare': [...],
'param1': [...],
'param2': [...],
...}
where 'param1', 'param2', ... are the free params varied by
optimizer, and they hold a list of all the values tested in
optimizer algorithm, unless save_steps is False, in which case
they are one element in length-the best fit params and best fit llh/chi2.
"""
# Get params dict which will be optimized (free_params) and which
# won't be (fixed_params) but are still needed for get_template()
fixed_params = get_fixed_params(select_hierarchy(params, normal_hierarchy))
free_params = get_free_params(select_hierarchy(params, normal_hierarchy))
if len(free_params) == 0:
logging.warn("NO FREE PARAMS, returning %s"%metric_name)
true_template = template_maker.get_template(get_values(fixed_params))
channel = params['channel']['value']
true_fmap = flatten_map(template=true_template, channel=channel)
if metric_name=='chisquare':
return {'chisquare': [get_binwise_chisquare(fmap, true_fmap)]}
elif metric_name=='llh':
return {'llh': [-get_binwise_llh(fmap, true_fmap)]}
init_vals = get_param_values(free_params)
scales = get_param_scales(free_params)
bounds = get_param_bounds(free_params)
priors = get_param_priors(free_params)
names = sorted(free_params.keys())
# Scale init-vals and bounds to work with bfgs opt:
init_vals = np.array(init_vals)*np.array(scales)
bounds = [bounds[i]*scales[i] for i in range(len(bounds))]
opt_steps_dict = {key:[] for key in names}
opt_steps_dict[metric_name] = []
const_args = (names, scales, fmap, fixed_params, template_maker,
opt_steps_dict, priors, metric_name)
display_optimizer_settings(free_params, names, init_vals, bounds, priors,
bfgs_settings)
best_fit_vals,metric_val,dict_flags = opt.fmin_l_bfgs_b(
func=bfgs_metric, x0=init_vals, args=const_args, approx_grad=True,
iprint=0, bounds=bounds, **get_values(bfgs_settings))
# If needed, run optimizer again, checking for second octant solution:
if check_octant and ('theta23' in free_params.keys()):
physics.info("Checking alternative octant solution")
old_th23_val = free_params['theta23']['value']
# Reflect across pi/4.0:
delta = (np.pi/4.0) - old_th23_val
free_params['theta23']['value'] = (np.pi/4.0) + delta
init_vals = get_param_values(free_params)
alt_opt_steps_dict = {key:[] for key in names}
alt_opt_steps_dict[metric_name] = []
const_args = (names, scales, fmap, fixed_params, template_maker,
alt_opt_steps_dict, priors, metric_name)
display_optimizer_settings(free_params=free_params,
names=names,
init_vals=init_vals,
bounds=bounds,
priors=priors,
bfgs_settings=bfgs_settings)
alt_fit_vals, alt_metric_val, alt_dict_flags = opt.fmin_l_bfgs_b(
func=bfgs_metric, x0=init_vals, args=const_args, approx_grad=True,
iprint=0, bounds=bounds, **get_values(bfgs_settings))
# Alternative octant solution is optimal:
if alt_llh < llh:
best_fit_vals = alt_fit_vals
metric_val = alt_metric_val
dict_flags = alt_dict_flags
opt_steps_dict = alt_opt_steps_dict
best_fit_params = { name: value for name, value in zip(names, best_fit_vals) }
# Report best fit
physics.info('Found best %s = %.2f in %d calls at:'
%(metric_name, metric_val, dict_flags['funcalls']))
for name, val in best_fit_params.items():
physics.info(' %20s = %6.4f'%(name,val))
# Report any warnings if there are
lvl = logging.WARN if (dict_flags['warnflag'] != 0) else logging.DEBUG
for name, val in dict_flags.items():
physics.log(lvl," %s : %s"%(name,val))
if not save_steps:
# Do not store the extra history of opt steps:
for key in opt_steps_dict.keys():
opt_steps_dict[key] = [opt_steps_dict[key][-1]]
return opt_steps_dict
def find_opt_bfgs(fmap,
template_maker,
params,
bfgs_settings,
save_steps=False,
normal_hierarchy=None,
check_octant=False,
metric_name='llh'):
"""
Finds the template (and free systematic params) that maximize
likelihood that the data came from the chosen template of
true params (or minimize chisquare), using the limited memory BFGS
algorithm subject to bounds (l_bfgs_b).
returns a dictionary of llh/chisquare data and best fit params, in the format:
{'llh/chisquare': [...],
'param1': [...],
'param2': [...],
...}
where 'param1', 'param2', ... are the free params varied by
optimizer, and they hold a list of all the values tested in
optimizer algorithm, unless save_steps is False, in which case
they are one element in length-the best fit params and best fit llh/chi2.
"""
# Get params dict which will be optimized (free_params) and which
# won't be (fixed_params) but are still needed for get_template()
fixed_params = get_fixed_params(select_hierarchy(params, normal_hierarchy))
free_params = get_free_params(select_hierarchy(params, normal_hierarchy))
if len(free_params) == 0:
logging.warn("NO FREE PARAMS, returning %s" % metric_name)
true_template = template_maker.get_template(get_values(fixed_params))
channel = params['channel']['value']
true_fmap = flatten_map(template=true_template, channel=channel)
if metric_name == 'chisquare':
return {'chisquare': [get_binwise_chisquare(fmap, true_fmap)]}
elif metric_name == 'llh':
return {'llh': [-get_binwise_llh(fmap, true_fmap)]}
init_vals = get_param_values(free_params)
scales = get_param_scales(free_params)
bounds = get_param_bounds(free_params)
priors = get_param_priors(free_params)
names = sorted(free_params.keys())
# Scale init-vals and bounds to work with bfgs opt:
init_vals = np.array(init_vals) * np.array(scales)
bounds = [bounds[i] * scales[i] for i in range(len(bounds))]
opt_steps_dict = {key: [] for key in names}
opt_steps_dict[metric_name] = []
const_args = (names, scales, fmap, fixed_params, template_maker,
opt_steps_dict, priors, metric_name)
display_optimizer_settings(free_params, names, init_vals, bounds, priors,
bfgs_settings)
best_fit_vals, metric_val, dict_flags = opt.fmin_l_bfgs_b(
func=bfgs_metric,
x0=init_vals,
args=const_args,
approx_grad=True,
iprint=0,
bounds=bounds,
**get_values(bfgs_settings))
# If needed, run optimizer again, checking for second octant solution:
if check_octant and ('theta23' in free_params.keys()):
physics.info("Checking alternative octant solution")
old_th23_val = free_params['theta23']['value']
# Reflect across pi/4.0:
delta = (np.pi / 4.0) - old_th23_val
free_params['theta23']['value'] = (np.pi / 4.0) + delta
init_vals = get_param_values(free_params)
alt_opt_steps_dict = {key: [] for key in names}
alt_opt_steps_dict[metric_name] = []
const_args = (names, scales, fmap, fixed_params, template_maker,
alt_opt_steps_dict, priors, metric_name)
display_optimizer_settings(free_params=free_params,
names=names,
init_vals=init_vals,
bounds=bounds,
priors=priors,
bfgs_settings=bfgs_settings)
alt_fit_vals, alt_metric_val, alt_dict_flags = opt.fmin_l_bfgs_b(
func=bfgs_metric,
x0=init_vals,
args=const_args,
approx_grad=True,
iprint=0,
bounds=bounds,
**get_values(bfgs_settings))
# Alternative octant solution is optimal:
# Note: can use "<" for both metrics since neg. llh returned
print "ALT %s: " % metric_name, alt_metric_val
print "%s: " % metric_name, metric_val
if alt_metric_val < metric_val:
print " >>TRUE..."
best_fit_vals = alt_fit_vals
metric_val = alt_metric_val
dict_flags = alt_dict_flags
opt_steps_dict = alt_opt_steps_dict
best_fit_params = {
name: value
for name, value in zip(names, best_fit_vals)
}
# Report best fit
physics.info('Found best %s = %.2f in %d calls at:' %
(metric_name, metric_val, dict_flags['funcalls']))
for name, val in best_fit_params.items():
physics.info(' %20s = %6.4f' % (name, val))
# Report any warnings if there are
lvl = logging.WARN if (dict_flags['warnflag'] != 0) else logging.DEBUG
for name, val in dict_flags.items():
physics.log(lvl, " %s : %s" % (name, val))
if not save_steps:
# Do not store the extra history of opt steps:
for key in opt_steps_dict.keys():
opt_steps_dict[key] = [opt_steps_dict[key][-1]]
return opt_steps_dict
def bfgs_metric(opt_vals, names, scales, fmap, fixed_params, template_maker,
opt_steps_dict, priors, metric_name='llh'):
"""
Function that the bfgs algorithm tries to minimize: wraps get_template()
and get_binwise_llh() (or get_binwise_chisquare()), and returns
the negative log likelihood (the chisquare).
This function is set up this way because the fmin_l_bfgs_b algorithm must
take a function with two inputs: params & *args, where 'params' are the
actual VALUES to be varied, and must correspond to the limits in 'bounds',
and 'args' are arguments which are not varied and optimized, but needed by
the get_template() function here.
Parameters
----------
opt_vals : sequence of scalars
Systematics varied in the optimization.
Format: [param1, param2, ... , paramN]
names : sequence of str
Dictionary keys corresponding to param1, param2, ...
scales : sequence of float
Scales to be applied before passing to get_template
[IMPORTANT! In the optimizer, all parameters must be ~ the same order.
Here, we keep them between 0.1,1 so the "epsilon" step size will vary
the parameters with roughly the same precision.]
fmap : sequence of float
Pseudo data flattened map
fixed_params : dict
Other paramters needed by the get_template() function.
template_maker : template maker object
opt_steps_dict: dict
Dictionary recording information regarding the steps taken for each
trial of the optimization process.
priors : sequence of pisa.utils.params.Prior objects
Priors corresponding to opt_vals list.
metric_name : string
Returns chisquare instead of negative llh if metric_name is 'chisquare'.
Note: this string has to be present as a key in opt_steps_dict
Returns
-------
metric_val : float
either minimum negative llh or chisquare found by BFGS minimizer
"""
# free parameters being "optimized" by minimizer re-scaled to their true
# values.
unscaled_opt_vals = [opt_vals[i]/scales[i] for i in xrange(len(opt_vals))]
unscaled_free_params = { names[i]: val for i,val in enumerate(unscaled_opt_vals) }
template_params = dict(unscaled_free_params.items() +
get_values(fixed_params).items())
# Now get true template, and compute metric
with Timer() as t:
if template_params['theta23'] == 0.0:
logging.info("Zero theta23, so generating no oscillations template...")
true_template = template_maker.get_template_no_osc(template_params)
else:
true_template = template_maker.get_template(template_params)
tprofile.info("==> elapsed time for template maker: %s sec"%t.secs)
true_fmap = flatten_map(template=true_template,
channel=template_params['channel'])
# NOTE: The minus sign is present on both of these next two lines
# because the optimizer finds a minimum rather than maximum, so we
# have to minimize the negative of the log likelhood.
if metric_name=='chisquare':
metric_val = get_binwise_chisquare(fmap, true_fmap)
metric_val += sum([prior.chi2(opt_val)
for (opt_val, prior) in zip(unscaled_opt_vals, priors)])
elif metric_name=='llh':
metric_val = -get_binwise_llh(fmap, true_fmap)
metric_val -= sum([prior.llh(opt_val)
for (opt_val, prior) in zip(unscaled_opt_vals, priors)])
#prior_list = [prior.llh(opt_val)
# for (opt_val, prior) in zip(unscaled_opt_vals, priors)]
#print(" prior sum: ",sum(prior_list))
#neg_llh -= sum(prior_list)
# Save all optimizer-tested values to opt_steps_dict, to see
# optimizer history later
for key in names:
opt_steps_dict[key].append(template_params[key])
opt_steps_dict[metric_name].append(metric_val)
physics.debug("%s is %.2f at: "%(metric_name, metric_val))
for name, val in zip(names, opt_vals):
physics.debug(" %20s = %6.4f" %(name,val))
return metric_val
def bfgs_metric(opt_vals,
names,
scales,
fmap,
fixed_params,
template_maker,
opt_steps_dict,
priors,
metric_name='llh'):
"""
Function that the bfgs algorithm tries to minimize: wraps get_template()
and get_binwise_llh() (or get_binwise_chisquare()), and returns
the negative log likelihood (the chisquare).
This function is set up this way because the fmin_l_bfgs_b algorithm must
take a function with two inputs: params & *args, where 'params' are the
actual VALUES to be varied, and must correspond to the limits in 'bounds',
and 'args' are arguments which are not varied and optimized, but needed by
the get_template() function here.
Parameters
----------
opt_vals : sequence of scalars
Systematics varied in the optimization.
Format: [param1, param2, ... , paramN]
names : sequence of str
Dictionary keys corresponding to param1, param2, ...
scales : sequence of float
Scales to be applied before passing to get_template
[IMPORTANT! In the optimizer, all parameters must be ~ the same order.
Here, we keep them between 0.1,1 so the "epsilon" step size will vary
the parameters with roughly the same precision.]
fmap : sequence of float
Pseudo data flattened map
fixed_params : dict
Other paramters needed by the get_template() function.
template_maker : template maker object
opt_steps_dict: dict
Dictionary recording information regarding the steps taken for each
trial of the optimization process.
priors : sequence of pisa.utils.params.Prior objects
Priors corresponding to opt_vals list.
metric_name : string
Returns chisquare instead of negative llh if metric_name is 'chisquare'.
Note: this string has to be present as a key in opt_steps_dict
Returns
-------
metric_val : float
either minimum negative llh or chisquare found by BFGS minimizer
"""
# free parameters being "optimized" by minimizer re-scaled to their true
# values.
unscaled_opt_vals = [
opt_vals[i] / scales[i] for i in xrange(len(opt_vals))
]
unscaled_free_params = {
names[i]: val
for i, val in enumerate(unscaled_opt_vals)
}
template_params = dict(unscaled_free_params.items() +
get_values(fixed_params).items())
# Now get true template, and compute metric
with Timer() as t:
if template_params['theta23'] == 0.0:
logging.info(
"Zero theta23, so generating no oscillations template...")
true_template = template_maker.get_template_no_osc(template_params)
else:
true_template = template_maker.get_template(template_params)
tprofile.info("==> elapsed time for template maker: %s sec" % t.secs)
true_fmap = flatten_map(template=true_template,
channel=template_params['channel'])
# NOTE: The minus sign is present on both of these next two lines
# because the optimizer finds a minimum rather than maximum, so we
# have to minimize the negative of the log likelhood.
if metric_name == 'chisquare':
metric_val = get_binwise_chisquare(fmap, true_fmap)
metric_val += sum([
prior.chi2(opt_val)
for (opt_val, prior) in zip(unscaled_opt_vals, priors)
])
elif metric_name == 'llh':
metric_val = -get_binwise_llh(fmap, true_fmap)
metric_val -= sum([
prior.llh(opt_val)
for (opt_val, prior) in zip(unscaled_opt_vals, priors)
])
# Save all optimizer-tested values to opt_steps_dict, to see
# optimizer history later
for key in names:
opt_steps_dict[key].append(template_params[key])
opt_steps_dict[metric_name].append(metric_val)
physics.debug("%s is %.2f at: " % (metric_name, metric_val))
for name, val in zip(names, opt_vals):
physics.debug(" %20s = %6.4f" % (name, val))
return metric_val
