def plot_asimov_line(llh_dict, tkey, max_yval, **kwargs):
"""
llh_dict - dictionary of llh data
tkey - key of the true hierarchy (from asimov or pseudo data set)
max_yval - maximum yvalue for asimov line.
"""
validate_key(tkey)
asimov_data = llh_dict[tkey]['asimov_data']
asimov_data_null = llh_dict[tkey]['asimov_data_null']
llh_asimov = get_binwise_llh(asimov_data,asimov_data)
llh_null = -llh_dict[tkey]['llh_null']['llh'][-1]
logging.info(" >> llh_asimov: %.4f"%llh_asimov)
logging.info(" >> llh null: %.4f"%llh_null)
logging.info("Null hypothesis: ")
for k,v in llh_dict[tkey]['llh_null'].items():
logging.info(" >> %s: %f"%(k,v[-1]))
asimov_llr = (llh_null - llh_asimov if 'true_N' in tkey
else llh_asimov - llh_null)
vline = plt.vlines(
asimov_llr, 0.1, max_yval ,colors='k',**kwargs)
return asimov_llr
def find_max_llh_bfgs(fmap, template_maker, params, bfgs_settings, save_steps=False,
normal_hierarchy=None, check_octant=False):
"""
Finds the template (and free systematic params) that maximize
likelihood that the data came from the chosen template of true
params, using the limited memory BFGS algorithm subject to bounds
(l_bfgs_b).
returns a dictionary of llh data and best fit params, in the format:
{'llh': [...],
'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.
"""
# 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 LLH")
true_template = template_maker.get_template(get_values(fixed_params))
channel = params['channel']['value']
true_fmap = flatten_map(true_template,chan=channel)
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['llh'] = []
const_args = (names,scales,fmap,fixed_params,template_maker,opt_steps_dict,priors)
display_optimizer_settings(free_params, names, init_vals, bounds, priors,
bfgs_settings)
best_fit_vals,llh,dict_flags = opt.fmin_l_bfgs_b(
llh_bfgs, 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']
delta = np.pi - old_th23_val
free_params['theta23']['value'] = np.pi + delta
init_vals = get_param_values(free_params)
const_args = (names,scales,fmap,fixed_params,template_maker,opt_steps_dict,priors)
display_optimizer_settings(free_params, names, init_vals, bounds, priors,
bfgs_settings)
alt_fit_vals,alt_llh,alt_dict_flags = opt.fmin_l_bfgs_b(
llh_bfgs, 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
llh = alt_llh
dict_flags = alt_dict_flags
best_fit_params = { name: value for name, value in zip(names, best_fit_vals) }
#Report best fit
physics.info('Found best LLH = %.2f in %d calls at:'
%(llh,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 llh_bfgs(opt_vals,*args):
"""
Function that the bfgs algorithm tries to minimize. Essentially,
it is a wrapper function around get_template() and
get_binwise_llh().
This fuction 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. Thus, we pass the arguments to this
function as follows:
--opt_vals: [param1,param2,...,paramN] - systematics varied in the optimization.
--args: [names,scales,fmap,fixed_params,template_maker,opt_steps_dict,priors]
where
names: are the dict keys corresponding to param1, param2,...
scales: the 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 in roughly the same precision.]
fmap: pseudo data flattened map
fixed_params: dictionary of other paramters needed by the get_template()
function
template_maker: template maker object
opt_steps_dict: dictionary recording information regarding the steps taken
for each trial of the optimization process.
priors: gaussian priors corresponding to opt_vals list.
Format: [(prior1,best1),(prior2,best2),...,(priorN,bestN)]
"""
names,scales,fmap,fixed_params,template_maker,opt_steps_dict,priors = args
# 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 LLH
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)
profile.info("==> elapsed time for template maker: %s sec"%t.secs)
true_fmap = flatten_map(true_template,chan=template_params['channel'])
# NOTE: The minus sign is present on both of these next two lines
# to reflect the fact that the optimizer finds a minimum rather
# than maximum.
llh = -get_binwise_llh(fmap,true_fmap)
llh -= sum([ get_prior_llh(opt_val,sigma,value)
for (opt_val,(sigma,value)) 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['llh'].append(llh)
physics.debug("LLH is %.2f at: "%llh)
for name, val in zip(names, opt_vals):
physics.debug(" %20s = %6.4f" %(name,val))
return llh
def find_max_llh_bfgs(fmap,template_maker,params,bfgs_settings,save_steps=False,
normal_hierarchy=None):
'''
Finds the template (and free systematic params) that maximize
likelihood that the data came from the chosen template of true
params, using the limited memory BFGS algorithm subject to bounds
(l_bfgs_b).
returns a dictionary of llh data and best fit params, in the format:
{'llh': [...],
'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.
'''
# 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 LLH")
true_template = template_maker.get_template(get_values(fixed_params))
channel = params['channel']['value']
true_fmap = flatten_map(true_template,chan=channel)
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['llh'] = []
const_args = (names,scales,fmap,fixed_params,template_maker,opt_steps_dict,priors)
physics.info('%d parameters to be optimized'%len(free_params))
for name,init,(down,up),(prior, best) in zip(names, init_vals, bounds, priors):
physics.info(('%20s : init = %6.4f, bounds = [%6.4f,%6.4f], '
'best = %6.4f, prior = '+
('%6.4f' if prior else "%s"))%
(name, init, up, down, best, prior))
physics.debug("Optimizer settings:")
for key,item in bfgs_settings.items():
physics.debug(" %s -> `%s` = %.2e"%(item['desc'],key,item['value']))
best_fit_vals,llh,dict_flags = opt.fmin_l_bfgs_b(llh_bfgs,
init_vals,
args=const_args,
approx_grad=True,
iprint=0,
bounds=bounds,
**get_values(bfgs_settings))
best_fit_params = { name: value for name, value in zip(names, best_fit_vals) }
#Report best fit
physics.info('Found best LLH = %.2f in %d calls at:'
%(llh,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_max_grid(fmap,
template_maker,
params,
grid_settings,
save_steps=True,
normal_hierarchy=True):
'''
Finds the template (and free systematic params) that maximize
likelihood that the data came from the chosen template of true
params, using a brute force grid scan over the whole parameter space.
returns a dictionary of llh data and best fit params, in the format:
{'llh': [...],
'param1': [...],
'param2': [...],
...}
where 'param1', 'param2', ... are the free params that are varied in the
scan. If save_steps is False, all lists only contain the best-fit parameters
and llh values.
'''
#print "NOW INSIDE find_max_grid:"
#print "After fixing to their true values, params dict is now: "
#for key in params.keys():
# try: print " >>param: %s value: %s"%(key,str(params[key]['best']))
# except: continue
# 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))
# Obtain just the priors
priors = get_param_priors(free_params)
# Calculate steps [(prior,value),...] for all free parameters
calc_steps(free_params, grid_settings['steps'])
# Build a list from all parameters that holds a list of (name, step) tuples
steplist = [[(name, step) for step in param['steps']]
for name, param in sorted(free_params.items())]
# Prepare to store all the steps
steps = {key: [] for key in free_params.keys()}
steps['llh'] = []
# Iterate over the cartesian product
for pos in product(*steplist):
# Get a dict with all parameter values at this position
# including the fixed parameters
template_params = dict(list(pos) + get_values(fixed_params).items())
#print " >> NOW IN LOOP: "
#for key in template_params.keys():
# try: print " >>param: %s value: %s"%(key,str(template_params[key]['value']))
# except: continue
# Now get true template
tprofile.info('start template calculation')
true_template = template_maker.get_template(template_params)
tprofile.info('stop template calculation')
true_fmap = flatten_map(true_template)
# and calculate the likelihood
llh = -get_binwise_llh(fmap, true_fmap)
# get sorted vals to match with priors
vals = [v for k, v in sorted(pos)]
llh -= sum([prior.llh(val) for val, prior in zip(vals, priors)])
# Save all values to steps and report
steps['llh'].append(llh)
physics.debug("LLH is %.2f at: " % llh)
for key, val in pos:
steps[key].append(val)
physics.debug(" %20s = %6.4f" % (key, val))
# Find best fit value
maxllh = min(steps['llh'])
maxpos = steps['llh'].index(maxllh)
# Report best fit
physics.info('Found best LLH = %.2f in %d calls at:' %
(maxllh, len(steps['llh'])))
for name, vals in steps.items():
physics.info(' %20s = %6.4f' % (name, vals[maxpos]))
# only save this maximum if asked for
if not save_steps:
steps[name] = vals[maxpos]
return steps
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 find_max_llh_bfgs(fmap,
template_maker,
params,
bfgs_settings,
save_steps=False,
normal_hierarchy=None,
check_octant=False):
"""
Finds the template (and free systematic params) that maximize
likelihood that the data came from the chosen template of true
params, using the limited memory BFGS algorithm subject to bounds
(l_bfgs_b).
returns a dictionary of llh data and best fit params, in the format:
{'llh': [...],
'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.
"""
# 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 LLH")
true_template = template_maker.get_template(get_values(fixed_params))
channel = params['channel']['value']
true_fmap = flatten_map(true_template, chan=channel)
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['llh'] = []
const_args = (names, scales, fmap, fixed_params, template_maker,
opt_steps_dict, priors)
display_optimizer_settings(free_params, names, init_vals, bounds, priors,
bfgs_settings)
best_fit_vals, llh, dict_flags = opt.fmin_l_bfgs_b(
llh_bfgs,
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']
delta = np.pi - old_th23_val
free_params['theta23']['value'] = np.pi + delta
init_vals = get_param_values(free_params)
const_args = (names, scales, fmap, fixed_params, template_maker,
opt_steps_dict, priors)
display_optimizer_settings(free_params, names, init_vals, bounds,
priors, bfgs_settings)
alt_fit_vals, alt_llh, alt_dict_flags = opt.fmin_l_bfgs_b(
llh_bfgs,
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
llh = alt_llh
dict_flags = alt_dict_flags
best_fit_params = {
name: value
for name, value in zip(names, best_fit_vals)
}
#Report best fit
physics.info('Found best LLH = %.2f in %d calls at:' %
(llh, 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 llh_bfgs(opt_vals, *args):
"""
Function that the bfgs algorithm tries to minimize. Essentially,
it is a wrapper function around get_template() and
get_binwise_llh().
This fuction 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. Thus, we pass the arguments to this
function as follows:
--opt_vals: [param1,param2,...,paramN] - systematics varied in the optimization.
--args: [names,scales,fmap,fixed_params,template_maker,opt_steps_dict,priors]
where
names: are the dict keys corresponding to param1, param2,...
scales: the 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 in roughly the same precision.]
fmap: pseudo data flattened map
fixed_params: dictionary of other paramters needed by the get_template()
function
template_maker: template maker object
opt_steps_dict: dictionary recording information regarding the steps taken
for each trial of the optimization process.
priors: gaussian priors corresponding to opt_vals list.
Format: [(prior1,best1),(prior2,best2),...,(priorN,bestN)]
"""
names, scales, fmap, fixed_params, template_maker, opt_steps_dict, priors = args
# 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 LLH
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)
profile.info("==> elapsed time for template maker: %s sec" % t.secs)
true_fmap = flatten_map(true_template, chan=template_params['channel'])
# NOTE: The minus sign is present on both of these next two lines
# to reflect the fact that the optimizer finds a minimum rather
# than maximum.
llh = -get_binwise_llh(fmap, true_fmap)
llh -= sum([
get_prior_llh(opt_val, sigma, value)
for (opt_val, (sigma, value)) 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['llh'].append(llh)
physics.debug("LLH is %.2f at: " % llh)
for name, val in zip(names, opt_vals):
physics.debug(" %20s = %6.4f" % (name, val))
return llh
def find_max_grid(fmap,template_maker,params,grid_settings,save_steps=True,
normal_hierarchy=True):
'''
Finds the template (and free systematic params) that maximize
likelihood that the data came from the chosen template of true
params, using a brute force grid scan over the whole parameter space.
returns a dictionary of llh data and best fit params, in the format:
{'llh': [...],
'param1': [...],
'param2': [...],
...}
where 'param1', 'param2', ... are the free params that are varied in the
scan. If save_steps is False, all lists only contain the best-fit parameters
and llh values.
'''
#print "NOW INSIDE find_max_grid:"
#print "After fixing to their true values, params dict is now: "
#for key in params.keys():
# try: print " >>param: %s value: %s"%(key,str(params[key]['best']))
# except: continue
# 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))
#Obtain just the priors
priors = get_param_priors(free_params)
#Calculate steps for all free parameters
calc_steps(free_params, grid_settings['steps'])
#Build a list from all parameters that holds a list of (name, step) tuples
steplist = [ [(name,step) for step in param['steps']] for name, param in sorted(free_params.items())]
#Prepare to store all the steps
steps = {key:[] for key in free_params.keys()}
steps['llh'] = []
#Iterate over the cartesian product
for pos in product(*steplist):
#Get a dict with all parameter values at this position
#including the fixed parameters
template_params = dict(list(pos) + get_values(fixed_params).items())
#print " >> NOW IN LOOP: "
#for key in template_params.keys():
# try: print " >>param: %s value: %s"%(key,str(template_params[key]['value']))
# except: continue
# Now get true template
profile.info('start template calculation')
true_template = template_maker.get_template(template_params)
profile.info('stop template calculation')
true_fmap = flatten_map(true_template)
#and calculate the likelihood
llh = -get_binwise_llh(fmap,true_fmap)
#get sorted vals to match with priors
vals = [ v for k,v in sorted(pos) ]
llh -= sum([ get_prior_llh(vals,sigma,value) for (vals,(sigma,value)) in zip(vals,priors)])
# Save all values to steps and report
steps['llh'].append(llh)
physics.debug("LLH is %.2f at: "%llh)
for key, val in pos:
steps[key].append(val)
physics.debug(" %20s = %6.4f" %(key, val))
#Find best fit value
maxllh = min(steps['llh'])
maxpos = steps['llh'].index(maxllh)
#Report best fit
physics.info('Found best LLH = %.2f in %d calls at:'
%(maxllh,len(steps['llh'])))
for name, vals in steps.items():
physics.info(' %20s = %6.4f'%(name,vals[maxpos]))
#only save this maximum if asked for
if not save_steps:
steps[name]=vals[maxpos]
return steps
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