def contours(
self,
param_1,
param_1_minimum,
param_1_maximum,
param_1_n_steps,
param_2=None,
param_2_minimum=None,
param_2_maximum=None,
param_2_n_steps=None,
progress=True,
**options
):
"""
Generate confidence contours for the given parameters by stepping for the given number of steps between
the given boundaries. Call it specifying only source_1, param_1, param_1_minimum and param_1_maximum to
generate the profile of the likelihood for parameter 1. Specify all parameters to obtain instead a 2d
contour of param_1 vs param_2
:param param_1: name of the first parameter
:param param_1_minimum: lower bound for the range for the first parameter
:param param_1_maximum: upper bound for the range for the first parameter
:param param_1_n_steps: number of steps for the first parameter
:param param_2: name of the second parameter
:param param_2_minimum: lower bound for the range for the second parameter
:param param_2_maximum: upper bound for the range for the second parameter
:param param_2_n_steps: number of steps for the second parameter
:param progress: (True or False) whether to display progress or not
:param log: by default the steps are taken linearly. With this optional parameter you can provide a tuple of
booleans which specify whether the steps are to be taken logarithmically. For example,
'log=(True,False)' specify that the steps for the first parameter are to be taken logarithmically, while they
are linear for the second parameter. If you are generating the profile for only one parameter, you can specify
'log=(True,)' or 'log=(False,)' (optional)
:param: parallel: whether to use or not parallel computation (default:False)
:return: a : an array corresponding to the steps for the first parameter
b : an array corresponding to the steps for the second parameter (or None if stepping only in one
direction)
contour : a matrix of size param_1_steps x param_2_steps containing the value of the function at the
corresponding points in the grid. If param_2_steps is None (only one parameter), then this reduces to
an array of size param_1_steps.
"""
# Figure out if we are making a 1d or a 2d contour
if param_2 is None:
n_dimensions = 1
else:
n_dimensions = 2
# Check the options
p1log = False
p2log = False
parallel = False
if "log" in options.keys():
assert len(options["log"]) == n_dimensions, (
"When specifying the 'log' option you have to provide a "
+ "boolean for each dimension you are stepping on."
)
p1log = bool(options["log"][0])
if param_2 is not None:
p2log = bool(options["log"][1])
if "parallel" in options.keys():
parallel = bool(options["parallel"])
# Generate the steps
if p1log:
param_1_steps = numpy.logspace(math.log10(param_1_minimum), math.log10(param_1_maximum), param_1_n_steps)
else:
param_1_steps = numpy.linspace(param_1_minimum, param_1_maximum, param_1_n_steps)
if n_dimensions == 2:
if p2log:
param_2_steps = numpy.logspace(
math.log10(param_2_minimum), math.log10(param_2_maximum), param_2_n_steps
)
else:
param_2_steps = numpy.linspace(param_2_minimum, param_2_maximum, param_2_n_steps)
else:
# Only one parameter to step through
# Put param_2_steps as nan so that the worker can realize that it does not have
# to step through it
param_2_steps = numpy.array([numpy.nan])
# Generate the grid
grid = cartesian([param_1_steps, param_2_steps])
# Define the worker which will compute the value of the function at a given point in the grid
# Restore best fit
self._restore_best_fit()
# Duplicate the options used for the original minimizer
new_args = dict(self.minuit.fitarg)
# Get the minuit names for the parameters
minuit_param_1 = self._parameter_name_to_minuit_name(param_1)
if param_2 is None:
minuit_param_2 = None
else:
minuit_param_2 = self._parameter_name_to_minuit_name(param_2)
# Instance the worker
contour_worker = ContourWorker(
self._f, self.minuit.values, new_args, minuit_param_1, minuit_param_2, self.name_to_position
)
# We are finally ready to do the computation
# Serial and parallel computation are slightly different, so check whether we are in one case
# or the other
if not parallel:
# Serial computation
if progress:
# Computation with progress bar
progress_bar = ProgressBar(grid.shape[0])
# Define a wrapper which will increase the progress before as well as run the actual computation
def wrap(args):
results = contour_worker(args)
progress_bar.increase()
return results
# Do the computation
results = map(wrap, grid)
else:
# Computation without the progress bar
results = map(contour_worker, grid)
else:
# Parallel computation
# Connect to the engines
client = ParallelClient(**options)
# Get a balanced view of the engines
load_balance_view = client.load_balanced_view()
# Distribute the work among the engines and start it, but return immediately the control
# to the main thread
amr = load_balance_view.map_async(contour_worker, grid)
# print progress
n_points = grid.flatten().shape[0]
progress = ProgressBar(n_points)
# This loop will check from time to time the status of the computation, which is happening on
# different threads, and update the progress bar
while not amr.ready():
# Check and report the status of the computation every second
time.sleep(1)
# if (debug):
# stdouts = amr.stdout
#
# # clear_output doesn't do much in terminal environments
# for stdout, stderr in zip(amr.stdout, amr.stderr):
# if stdout:
# print "%s" % (stdout[-1000:])
# if stderr:
# print "%s" % (stderr[-1000:])
# sys.stdout.flush()
progress.animate(amr.progress - 1)
# If there have been problems, here is where they will be raised
results = amr.get()
# Always display 100% at the end
progress.animate(n_points)
# Add a new line after the progress bar
print("\n")
# Return results
return (
param_1_steps,
param_2_steps,
numpy.array(results).reshape((param_1_steps.shape[0], param_2_steps.shape[0])),
)
def get_contours(
self,
param_1,
param_1_minimum,
param_1_maximum,
param_1_n_steps,
param_2=None,
param_2_minimum=None,
param_2_maximum=None,
param_2_n_steps=None,
progress=True,
**options
):
"""
Generate confidence contours for the given parameters by stepping for the given number of steps between
the given boundaries. Call it specifying only source_1, param_1, param_1_minimum and param_1_maximum to
generate the profile of the likelihood for parameter 1. Specify all parameters to obtain instead a 2d
contour of param_1 vs param_2.
NOTE: if using parallel computation, param_1_n_steps must be an integer multiple of the number of running
engines. If that is not the case, the code will reduce the number of steps to match that requirement, and
issue a warning
:param param_1: fully qualified name of the first parameter or parameter instance
:param param_1_minimum: lower bound for the range for the first parameter
:param param_1_maximum: upper bound for the range for the first parameter
:param param_1_n_steps: number of steps for the first parameter
:param param_2: fully qualified name of the second parameter or parameter instance
:param param_2_minimum: lower bound for the range for the second parameter
:param param_2_maximum: upper bound for the range for the second parameter
:param param_2_n_steps: number of steps for the second parameter
:param progress: (True or False) whether to display progress or not
:param log: by default the steps are taken linearly. With this optional parameter you can provide a tuple of
booleans which specify whether the steps are to be taken logarithmically. For example,
'log=(True,False)' specify that the steps for the first parameter are to be taken logarithmically,
while they are linear for the second parameter. If you are generating the profile for only one
parameter, you can specify 'log=(True,)' or 'log=(False,)' (optional)
:return: a tuple containing an array corresponding to the steps for the first parameter, an array corresponding
to the steps for the second parameter (or None if stepping only in one direction), a matrix of size
param_1_steps x param_2_steps containing the value of the function at the corresponding points in the
grid. If param_2_steps is None (only one parameter), then this reduces to an array of
size param_1_steps.
"""
if hasattr(param_1, "value"):
# Substitute with the name
param_1 = param_1.path
if hasattr(param_2, "value"):
param_2 = param_2.path
# Check that the parameters exist
assert param_1 in self._likelihood_model.free_parameters, (
"Parameter %s is not a free parameters of the " "current model" % param_1
)
if param_2 is not None:
assert param_2 in self._likelihood_model.free_parameters, (
"Parameter %s is not a free parameters of the " "current model" % param_2
)
# Check that we have a valid fit
assert self._current_minimum is not None, "You have to run the .fit method before calling get_contours."
# Then restore the best fit
self._minimizer._restore_best_fit()
# Check minimal assumptions about the procedure
assert not (param_1 == param_2), "You have to specify two different parameters"
assert param_1_minimum < param_1_maximum, "Minimum larger than maximum for parameter 1"
if param_2 is not None:
assert param_2_minimum < param_2_maximum, "Minimum larger than maximum for parameter 2"
# Check whether we are parallelizing or not
if not threeML_config["parallel"]["use-parallel"]:
a, b, cc = self.minimizer.contours(
param_1,
param_1_minimum,
param_1_maximum,
param_1_n_steps,
param_2,
param_2_minimum,
param_2_maximum,
param_2_n_steps,
progress,
**options
)
# Collapse the second dimension of the results if we are doing a 1d contour
if param_2 is None:
cc = cc[:, 0]
else:
# With parallel computation
# In order to distribute fairly the computation, the strategy is to parallelize the computation
# by assigning to the engines one "line" of the grid at the time
# Connect to the engines
client = ParallelClient(**options)
# Get the number of engines
n_engines = client.get_number_of_engines()
# Check whether the number of threads is larger than the number of steps in the first direction
if n_engines > param_1_n_steps:
n_engines = int(param_1_n_steps)
custom_warnings.warn(
"The number of engines is larger than the number of steps. Using only %s engines." % n_engines,
ReducingNumberOfThreads,
)
# Check if the number of steps is divisible by the number
# of threads, otherwise issue a warning and make it so
if float(param_1_n_steps) % n_engines != 0:
# Set the number of steps to an integer multiple of the engines
# (note that // is the floor division, also called integer division)
param_1_n_steps = (param_1_n_steps // n_engines) * n_engines
custom_warnings.warn(
"Number of steps is not a multiple of the number of threads. Reducing steps to %s"
% param_1_n_steps,
ReducingNumberOfSteps,
)
# Compute the number of splits, i.e., how many lines in the grid for each engine.
# (note that this is guaranteed to be an integer number after the previous checks)
p1_split_steps = param_1_n_steps // n_engines
# Prepare arrays for results
if param_2 is None:
# One array
pcc = numpy.zeros(param_1_n_steps)
pa = numpy.linspace(param_1_minimum, param_1_maximum, param_1_n_steps)
pb = None
else:
pcc = numpy.zeros((param_1_n_steps, param_2_n_steps))
# Prepare the two axes of the parameter space
pa = numpy.linspace(param_1_minimum, param_1_maximum, param_1_n_steps)
pb = numpy.linspace(param_2_minimum, param_2_maximum, param_2_n_steps)
# Define the parallel worker which will go through the computation
# NOTE: I only divide
# on the first parameter axis so that the different
# threads are more or less well mixed for points close and
# far from the best fit
def worker(start_index):
# Re-create the minimizer
# backup_freeParameters = copy.deepcopy(self.freeParameters)
this_minimizer = self.Minimizer(self.minus_log_like_profile, self._free_parameters)
this_p1min = pa[start_index * p1_split_steps]
this_p1max = pa[(start_index + 1) * p1_split_steps - 1]
# print("From %s to %s" % (this_p1min, this_p1max))
aa, bb, ccc = this_minimizer.contours(
param_1,
this_p1min,
this_p1max,
p1_split_steps,
param_2,
param_2_minimum,
param_2_maximum,
param_2_n_steps,
False,
**options
)
# self.freeParameters = backup_freeParameters
return ccc
# Get a balanced view of the engines
lview = client.load_balanced_view()
# lview.block = True
# Distribute the work among the engines and start it, but return immediately the control
# to the main thread
amr = lview.map_async(worker, range(n_engines))
# print progress
progress = ProgressBar(n_engines)
# This loop will check from time to time the status of the computation, which is happening on
# different threads, and update the progress bar
while not amr.ready():
# Check and report the status of the computation every second
time.sleep(1 + np.random.uniform(0, 1))
# if (debug):
# stdouts = amr.stdout
#
# # clear_output doesn't do much in terminal environments
# for stdout, stderr in zip(amr.stdout, amr.stderr):
# if stdout:
# print "%s" % (stdout[-1000:])
# if stderr:
# print "%s" % (stderr[-1000:])
# sys.stdout.flush()
progress.animate(amr.progress - 1)
# Always display 100% at the end
progress.animate(n_engines - 1)
# Add a new line after the progress bar
print("\n")
# print("Serial time: %1.f (speed-up: %.1f)" %(amr.serial_time, float(amr.serial_time) / amr.wall_time))
# Get the results. This will raise exceptions if something wrong happened during the computation.
# We don't catch it so that the user will be aware of that
res = amr.get()
# Now re-assemble the vector of results taking the different parts from the engines
for i in range(n_engines):
if param_2 is None:
pcc[i * p1_split_steps : (i + 1) * p1_split_steps] = res[i][:, 0]
else:
pcc[i * p1_split_steps : (i + 1) * p1_split_steps, :] = res[i]
# Give the results the names that the following code expect. These are kept separate for debugging
# purposes
cc = pcc
a = pa
b = pb
# Here we have done the computation, in parallel computation or not. Let's make the plot
# with the contour
if param_2 is not None:
# 2d contour
fig = self._plot_contours("%s" % (param_1), a, "%s" % (param_2,), b, cc)
else:
# 1d contour (i.e., a profile)
fig = self._plot_profile("%s" % (param_1), a, cc)
# Check if we found a better minimum. This shouldn't happen, but in case of very difficult fit
# it might.
if self._current_minimum - cc.min() > 0.1:
if param_2 is not None:
idx = cc.argmin()
aidx, bidx = numpy.unravel_index(idx, cc.shape)
print(
"\nFound a better minimum: %s with %s = %s and %s = %s. Run again your fit starting from here."
% (cc.min(), param_1, a[aidx], param_2, b[bidx])
)
else:
idx = cc.argmin()
print(
"Found a better minimum: %s with %s = %s. Run again your fit starting from here."
% (cc.min(), param_1, a[idx])
)
return a, b, cc, fig