def loglike(theta):
"""
Please see the encompassing function docstring
"""
# Updates values: theta --> data
try:
data.check_for_slow_step(theta)
except KeyError:
pass
for i, name in enumerate(data.PC_param_names):
data.mcmc_parameters[name]['current'] = theta[i]
data.update_cosmo_arguments()
# Compute likelihood
#logl = sampler.compute_lkl(cosmo, data)[0,0]
# FK: index to scalar variable error...
logl = sampler.compute_lkl(cosmo, data)
# Compute derived parameters and pass them back
phi = [0.0] * nDerived
for i, name in enumerate(derived_param_names):
phi[i] = float(data.mcmc_parameters[name]['current'])
return logl, phi
def loglike(thetas):
logls = []
for theta in thetas:
try:
data.check_for_slow_step(theta)
except KeyError:
pass
flag = 0
for i, name in enumerate(data.NN_param_names):
value = data.mcmc_parameters[name]['initial']
if ((str(value[1]) != str(-1) and value[1] is not None)
and (theta[i] < value[1])):
flag += 1 # if a boundary value is reached, increment
elif ((str(value[2]) != str(-1) and value[2] is not None)
and theta[i] > value[2]):
flag += 1 # same
if flag == 0:
for i, name in enumerate(data.NN_param_names):
data.mcmc_parameters[name]['current'] = theta[i]
data.update_cosmo_arguments()
# Compute likelihood
logl = sampler.compute_lkl(cosmo, data)
if not np.isfinite(logl):
print('Nan encountered in likelihood')
print(data.mcmc_parameters)
else:
logl = data.boundary_loglike
logls.append(logl)
logls = np.array(logls)
return logls
def loglike(cube, ndim, *args):
"""
Please see the encompassing function docstring
"""
# Updates values: cube --> data
for i, name in zip(range(ndim), NS_param_names):
data.mcmc_parameters[name]['current'] = cube[i]
# Propagate the information towards the cosmo arguments
data.update_cosmo_arguments()
lkl = sampler.compute_lkl(cosmo, data)
for i, name in enumerate(derived_param_names):
cube[ndim+i] = data.mcmc_parameters[name]['current']
return lkl
def loglike(cube, ndim, *args):
"""
Please see the encompassing function docstring
"""
# Updates values: cube --> data
for i, name in zip(list(range(ndim)), NS_param_names):
data.mcmc_parameters[name]['current'] = cube[i]
# Propagate the information towards the cosmo arguments
data.update_cosmo_arguments()
lkl = sampler.compute_lkl(cosmo, data)
for i, name in enumerate(derived_param_names):
cube[ndim + i] = data.mcmc_parameters[name]['current']
return lkl
def loglike(thetas):
logls = []
for theta in thetas:
try:
data.check_for_slow_step(theta)
except KeyError:
pass
for i, name in enumerate(data.NN_param_names):
data.mcmc_parameters[name]['current'] = theta[i]
data.update_cosmo_arguments()
# Compute likelihood
logl = sampler.compute_lkl(cosmo, data)
if not np.isfinite(logl):
print('Nan encountered in likelihood')
print(data.mcmc_parameters)
logls.append(logl)
logls = np.array(logls)
return logls
def translate_chain(data,
cosmo,
command_line,
starting_folder,
chain_name,
ignore_likelihood=False):
"""Translate the input to the output
.. note::
If the keyword argument `ignore_likelihood` is set to true, the
previous value of the likelihood is discarded.
"""
input_path = os.path.join(starting_folder, chain_name)
output_path = os.path.join(command_line.folder, chain_name)
print ' -> reading ', input_path
parameter_names = data.get_mcmc_parameters(['varying'])
with open(input_path, 'r') as input_chain:
with open(output_path, 'w') as output_chain:
for line in input_chain:
params = line.split()
# recover the likelihood of this point
if not ignore_likelihood:
loglike = -float(params[1])
else:
loglike = 0
N = float(params[0])
# Assign all the recovered values to the data structure
for index, param in enumerate(parameter_names):
data.mcmc_parameters[param]['current'] = \
float(params[2+index])
data.update_cosmo_arguments()
newloglike = sampler.compute_lkl(cosmo, data)
weight = math.exp(newloglike)
newloglike += loglike
# Accept the point
sampler.accept_step(data)
io_mp.print_vector([output_chain], N * weight, newloglike,
data)
print output_path, 'written'
def translate_chain(data, cosmo, command_line,
starting_folder, chain_name, ignore_likelihood=False):
"""Translate the input to the output
.. note::
If the keyword argument `ignore_likelihood` is set to true, the
previous value of the likelihood is discarded.
"""
input_path = os.path.join(starting_folder, chain_name)
output_path = os.path.join(command_line.folder, chain_name)
print ' -> reading ', input_path
parameter_names = data.get_mcmc_parameters(['varying'])
with open(input_path, 'r') as input_chain:
with open(output_path, 'w') as output_chain:
for line in input_chain:
params = line.split()
# recover the likelihood of this point
if not ignore_likelihood:
loglike = -float(params[1])
else:
loglike = 0
N = float(params[0])
# Assign all the recovered values to the data structure
for index, param in enumerate(parameter_names):
data.mcmc_parameters[param]['current'] = \
float(params[2+index])
data.update_cosmo_arguments()
newloglike = sampler.compute_lkl(cosmo, data)
weight = math.exp(newloglike)
newloglike += loglike
# Accept the point
sampler.accept_step(data)
io_mp.print_vector([output_chain], N*weight, newloglike, data)
print output_path, 'written'
def chain(cosmo, data, command_line):
"""
Run a Markov chain of fixed length.
Main function of this module, this is the actual Markov chain procedure.
After having selected a starting point in parameter space defining the
first **last accepted** one, it will, for a given amount of steps :
+ choose randomnly a new point following the *proposal density*,
+ compute the cosmological *observables* through the cosmological module,
+ compute the value of the *likelihoods* of the desired experiments at this point,
+ *accept/reject* this point given its likelihood compared to the one of
the last accepted one.
Every time the code accepts :code:`data.write_step` number of points
(quantity defined in the input parameter file), it will write the result to
disk (flushing the buffer by forcing to exit the output file, and reopen it
again.
.. note::
to use the code to set a fiducial file for certain fixed parameters,
you can use two solutions. The first one is to put all input 1-sigma
proposal density to zero (this method still works, but is not
recommended anymore). The second one consist in using the flag "-f 0",
to force a step of zero amplitude.
"""
## Initialisation
loglike = 0
# In case command_line.silent has been asked, outputs should only contain
# data.out. Otherwise, it will also contain sys.stdout
outputs = [data.out]
if not command_line.silent:
outputs.append(sys.stdout)
# Recover the covariance matrix according to the input, if the varying set
# of parameters is non-zero
if (data.get_mcmc_parameters(['varying']) != []):
sigma_eig, U, C = sampler.get_covariance_matrix(data, command_line)
if data.jumping_factor == 0:
warnings.warn(
"The jumping factor has been set to 0. The above covariance " +
"matrix will not be used.")
# In case of a fiducial run (all parameters fixed), simply run once and
# print out the likelihood. This should not be used any more (one has to
# modify the log.param, which is never a good idea. Instead, force the code
# to use a jumping factor of 0 with the option "-f 0".
else:
warnings.warn(
"You are running with no varying parameters... I will compute " +
"only one point and exit")
data.update_cosmo_arguments() # this fills in the fixed parameters
loglike = sampler.compute_lkl(cosmo, data)
io_mp.print_vector(outputs, 1, loglike, data)
return 1, loglike
# In the fast-slow method, one need the Cholesky decomposition of the
# covariance matrix. Return the Cholesky decomposition as a lower
# triangular matrix
Cholesky = None
Inverse_Cholesky = None
Rotation = None
if command_line.jumping == 'fast':
Cholesky = la.cholesky(C).T
Inverse_Cholesky = np.linalg.inv(Cholesky)
Rotation = np.identity(len(sigma_eig))
# If restart wanted, pick initial value for arguments
if command_line.restart is not None:
sampler.read_args_from_chain(data, command_line.restart)
# If restart from best fit file, read first point (overwrite settings of
# read_args_from_chain)
if command_line.bf is not None:
sampler.read_args_from_bestfit(data, command_line.bf)
# Pick a position (from last accepted point if restart, from the mean value
# else), with a 100 tries.
for i in range(100):
if get_new_position(data, sigma_eig, U, i, Cholesky, Inverse_Cholesky,
Rotation) is True:
break
if i == 99:
raise io_mp.ConfigurationError(
"You should probably check your prior boundaries... because " +
"no valid starting position was found after 100 tries")
# Compute the starting Likelihood
loglike = sampler.compute_lkl(cosmo, data)
# Choose this step as the last accepted value
# (accept_step), and modify accordingly the max_loglike
sampler.accept_step(data)
max_loglike = loglike
# If the jumping factor is 0, the likelihood associated with this point is
# displayed, and the code exits.
if data.jumping_factor == 0:
io_mp.print_vector(outputs, 1, loglike, data)
return 1, loglike
acc, rej = 0.0, 0.0 # acceptance and rejection number count
N = 1 # number of time the system stayed in the current position
# Print on screen the computed parameters
io_mp.print_parameters(sys.stdout, data)
k = 1
# Main loop, that goes on while the maximum number of failure is not
# reached, and while the expected amount of steps (N) is not taken.
while k <= command_line.N:
# Pick a new position ('current' flag in mcmc_parameters), and compute
# its likelihood. If get_new_position returns True, it means it did not
# encounter any boundary problem. Otherwise, just increase the
# multiplicity of the point and start the loop again
if get_new_position(data, sigma_eig, U, k, Cholesky, Inverse_Cholesky,
Rotation) is True:
newloglike = sampler.compute_lkl(cosmo, data)
else: # reject step
rej += 1
N += 1
k += 1
continue
# Harmless trick to avoid exponentiating large numbers. This decides
# whether or not the system should move.
if (newloglike != data.boundary_loglike):
if (newloglike >= loglike):
alpha = 1.
else:
alpha = np.exp(newloglike - loglike)
else:
alpha = -1
if ((alpha == 1.) or (rd.uniform(0, 1) < alpha)): # accept step
# Print out the last accepted step (WARNING: this is NOT the one we
# just computed ('current' flag), but really the previous one.)
# with its proper multiplicity (number of times the system stayed
# there).
io_mp.print_vector(outputs, N, loglike, data)
# Report the 'current' point to the 'last_accepted'
sampler.accept_step(data)
loglike = newloglike
if loglike > max_loglike:
max_loglike = loglike
acc += 1.0
N = 1 # Reset the multiplicity
else: # reject step
rej += 1.0
N += 1 # Increase multiplicity of last accepted point
# Regularly (option to set in parameter file), close and reopen the
# buffer to force to write on file.
if acc % data.write_step == 0:
io_mp.refresh_file(data)
# Update the outputs list
outputs[0] = data.out
k += 1 # One iteration done
# END OF WHILE LOOP
# If at this moment, the multiplicity is higher than 1, it means the
# current point is not yet accepted, but it also mean that we did not print
# out the last_accepted one yet. So we do.
if N > 1:
io_mp.print_vector(outputs, N - 1, loglike, data)
# Print out some information on the finished chain
rate = acc / (acc + rej)
sys.stdout.write('\n# {0} steps done, acceptance rate: {1}\n'.format(
command_line.N, rate))
# In case the acceptance rate is too low, or too high, print a warning
if rate < 0.05:
warnings.warn("The acceptance rate is below 0.05. You might want to "
"set the jumping factor to a lower value than the "
"default (2.4), with the option `-f 1.5` for instance.")
elif rate > 0.6:
warnings.warn("The acceptance rate is above 0.6, which means you might"
" have difficulties exploring the entire parameter space"
". Try analysing these chains, and use the output "
"covariance matrix to decrease the acceptance rate to a "
"value between 0.2 and 0.4 (roughly).")
# For a restart, erase the starting point to keep only the new, longer
# chain.
if command_line.restart is not None:
os.remove(command_line.restart)
sys.stdout.write(
' deleting starting point of the chain {0}\n'.format(
command_line.restart))
return
def chain(cosmo, data, command_line):
"""
Run a Markov chain of fixed length with a Metropolis Hastings algorithm.
Main function of this module, this is the actual Markov chain procedure.
After having selected a starting point in parameter space defining the
first **last accepted** one, it will, for a given amount of steps :
+ choose randomly a new point following the *proposal density*,
+ compute the cosmological *observables* through the cosmological module,
+ compute the value of the *likelihoods* of the desired experiments at this
point,
+ *accept/reject* this point given its likelihood compared to the one of
the last accepted one.
Every time the code accepts :code:`data.write_step` number of points
(quantity defined in the input parameter file), it will write the result to
disk (flushing the buffer by forcing to exit the output file, and reopen it
again.
.. note::
to use the code to set a fiducial file for certain fixed parameters,
you can use two solutions. The first one is to put all input 1-sigma
proposal density to zero (this method still works, but is not
recommended anymore). The second one consist in using the flag "-f 0",
to force a step of zero amplitude.
"""
## Initialisation
loglike = 0
# In case command_line.silent has been asked, outputs should only contain
# data.out. Otherwise, it will also contain sys.stdout
outputs = [data.out]
if not command_line.silent:
outputs.append(sys.stdout)
use_mpi = False
# check for MPI
try:
from mpi4py import MPI
comm = MPI.COMM_WORLD
rank = comm.Get_rank()
# suppress duplicate output from slaves
if rank:
command_line.quiet = True
use_mpi = True
except ImportError:
# set all chains to master if no MPI
rank = 0
# Initialise master and slave chains for superupdate.
# Workaround in order to have one master chain and several slave chains even when
# communication fails between MPI chains. It could malfunction on some hardware.
# TODO: Would like to merge with MPI initialization above and make robust and logical
# TODO: Or if keeping current scheme, store value and delete jumping_factor.txt
# TODO: automatically if --parallel-chains is enabled
if command_line.superupdate and data.jumping_factor:
try:
jump_file = open(command_line.folder + '/jumping_factor.txt', 'r')
#if command_line.restart is None:
if not use_mpi and command_line.parallel_chains:
rank = 1
warnings.warn(
'MPI not in use, flag --parallel-chains enabled, '
'superupdate enabled, and a jumping_factor.txt file detected. '
'If relaunching in the same folder or restarting a run this '
'will cause all chains to be assigned as slaves. In this case '
'instead note the value in jumping_factor.txt, delete the '
'file, and pass the value with flag -f <value>. This warning '
'may then appear again, but you can safely disregard it.')
else:
# For restart runs we want to save the input jumping factor
# as starting jumping factor, but continue from the jumping
# factor stored in the file.
starting_jumping_factor = data.jumping_factor
# This will load the value irrespective of whether it starts
# with # (i.e. the jumping factor adaptation was started) or not.
jump_value = jump_file.read().replace('# ', '')
data.jumping_factor = float(jump_value)
jump_file.close()
print 'rank = ', rank
except:
jump_file = open(command_line.folder + '/jumping_factor.txt', 'w')
jump_file.write(str(data.jumping_factor))
jump_file.close()
rank = 0
print 'rank = ', rank
starting_jumping_factor = data.jumping_factor
# Recover the covariance matrix according to the input, if the varying set
# of parameters is non-zero
if (data.get_mcmc_parameters(['varying']) != []):
# Read input covariance matrix
sigma_eig, U, C = sampler.get_covariance_matrix(
cosmo, data, command_line)
# if we want to compute the starting point by minimising lnL (instead of taking it from input file or bestfit file)
minimum = 0
if command_line.minimize:
minimum = sampler.get_minimum(cosmo, data, command_line, C)
parameter_names = data.get_mcmc_parameters(['last_accepted'])
for index, elem in parameter_names:
data.mcmc_parameters[elem]['last_accepted'] = minimum[index]
# if we want to compute Fisher matrix and then stop
if command_line.fisher:
sampler.get_fisher_matrix(cosmo, data, command_line, C, minimum)
return
# warning if no jumps are requested
if data.jumping_factor == 0:
warnings.warn(
"The jumping factor has been set to 0. The above covariance " +
"matrix will not be used.")
# In case of a fiducial run (all parameters fixed), simply run once and
# print out the likelihood. This should not be used any more (one has to
# modify the log.param, which is never a good idea. Instead, force the code
# to use a jumping factor of 0 with the option "-f 0".
else:
warnings.warn(
"You are running with no varying parameters... I will compute " +
"only one point and exit")
data.update_cosmo_arguments() # this fills in the fixed parameters
loglike = sampler.compute_lkl(cosmo, data)
io_mp.print_vector(outputs, 1, loglike, data)
return 1, loglike
# In the fast-slow method, one need the Cholesky decomposition of the
# covariance matrix. Return the Cholesky decomposition as a lower
# triangular matrix
Cholesky = None
Rotation = None
if command_line.jumping == 'fast':
Cholesky = la.cholesky(C).T
Rotation = np.identity(len(sigma_eig))
# define path and covmat
input_covmat = command_line.cov
base = os.path.basename(command_line.folder)
# the previous line fails when "folder" is a string ending with a slash. This issue is cured by the next lines:
if base == '':
base = os.path.basename(command_line.folder[:-1])
command_line.cov = os.path.join(command_line.folder, base + '.covmat')
# Fast Parameter Multiplier (fpm) for adjusting update and superupdate numbers.
# This is equal to N_slow + f_fast N_fast, where N_slow is the number of slow
# parameters, f_fast is the over sampling number for each fast block and f_fast
# is the number of parameters in each fast block.
for i in range(len(data.block_parameters)):
if i == 0:
fpm = data.over_sampling[i] * data.block_parameters[i]
else:
fpm += data.over_sampling[i] * (data.block_parameters[i] -
data.block_parameters[i - 1])
# If the update mode was selected, the previous (or original) matrix should be stored
if command_line.update:
if not rank and not command_line.silent:
print 'Update routine is enabled with value %d (recommended: 50)' % command_line.update
print 'This number is rescaled by cycle length %d (N_slow + f_fast * N_fast) to %d' % (
fpm, fpm * command_line.update)
# Rescale update number by cycle length N_slow + f_fast * N_fast to account for fast parameters
command_line.update *= fpm
previous = (sigma_eig, U, C, Cholesky)
# Initialise adaptive
if command_line.adaptive:
if not command_line.silent:
print 'Adaptive routine is enabled with value %d (recommended: 10*dimension)' % command_line.adaptive
print 'and adaptive_ts = %d (recommended: 100*dimension)' % command_line.adaptive_ts
print 'Please note: current implementation not suitable for multiple chains'
if rank > 0:
raise io_mp.ConfigurationError(
'Adaptive routine not compatible with MPI')
if command_line.update:
warnings.warn(
'Adaptive routine not compatible with update, overwriting input update value'
)
if command_line.superupdate:
warnings.warn(
'Adaptive routine not compatible with superupdate, deactivating superupdate'
)
command_line.superupdate = 0
# Define needed parameters
parameter_names = data.get_mcmc_parameters(['varying'])
mean = np.zeros(len(parameter_names))
last_accepted = np.zeros(len(parameter_names), 'float64')
ar = np.zeros(100)
if command_line.cov == None:
# If no input covmat was given, the starting jumping factor
# should be very small until a covmat is obtained and the
# original start jumping factor should be saved
start_jumping_factor = command_line.jumping_factor
data.jumping_factor = command_line.jumping_factor / 100.
# Analyze module will be forced to compute one covmat,
# after which update flag will be set to False.
command_line.update = command_line.adaptive
else:
# If an input covmat was provided, take mean values from param file
# Question: is it better to always do this, rather than setting mean
# to last accepted after the initial update run?
for elem in parameter_names:
mean[parameter_names.index(
elem)] = data.mcmc_parameters[elem]['initial'][0]
# Initialize superupdate
if command_line.superupdate:
if not rank and not command_line.silent:
print 'Superupdate routine is enabled with value %d (recommended: 20)' % command_line.superupdate
if command_line.superupdate < 20:
warnings.warn(
'Superupdate value lower than the recommended value. This '
'may increase the risk of poorly converged acceptance rate'
)
print 'This number is rescaled by cycle length %d (N_slow + f_fast * N_fast) to %d' % (
fpm, fpm * command_line.superupdate)
# Rescale superupdate number by cycle length N_slow + f_fast * N_fast to account for fast parameters
command_line.superupdate *= fpm
# Define needed parameters
parameter_names = data.get_mcmc_parameters(['varying'])
updated_steps = 0
stop_c = False
jumping_factor_rescale = 0
if command_line.restart:
try:
jump_file = open(command_line.cov, 'r')
jumping_factor_rescale = 1
except:
jumping_factor_rescale = 0
c_array = np.zeros(command_line.superupdate
) # Allows computation of mean of jumping factor
R_minus_one = np.array([
100., 100.
]) # 100 to make sure max(R-1) value is high if computation failed
# Local acceptance rate of last SU*(N_slow + f_fast * N_fast) steps
ar = np.zeros(command_line.superupdate)
# Store acceptance rate of last 5*SU*(N_slow + f_fast * N_fast) steps
backup_ar = np.zeros(5 * command_line.superupdate)
# Make sure update is enabled
if command_line.update == 0:
if not rank and not command_line.silent:
print 'Update routine required by superupdate. Setting --update 50'
print 'This number is then rescaled by cycle length: %d (N_slow + f_fast * N_fast)' % fpm
command_line.update = 50 * fpm
previous = (sigma_eig, U, C, Cholesky)
# If restart wanted, pick initial value for arguments
if command_line.restart is not None:
sampler.read_args_from_chain(data, command_line.restart)
# If restart from best fit file, read first point (overwrite settings of
# read_args_from_chain)
if command_line.bf is not None and not command_line.minimize:
sampler.read_args_from_bestfit(data, command_line.bf)
# Pick a position (from last accepted point if restart, from the mean value
# else), with a 100 tries.
for i in range(100):
if get_new_position(data, sigma_eig, U, i, Cholesky, Rotation) is True:
break
if i == 99:
raise io_mp.ConfigurationError(
"You should probably check your prior boundaries... because " +
"no valid starting position was found after 100 tries")
# Compute the starting Likelihood
loglike = sampler.compute_lkl(cosmo, data)
# Choose this step as the last accepted value
# (accept_step), and modify accordingly the max_loglike
sampler.accept_step(data)
max_loglike = loglike
# If the jumping factor is 0, the likelihood associated with this point is
# displayed, and the code exits.
if data.jumping_factor == 0:
io_mp.print_vector(outputs, 1, loglike, data)
return 1, loglike
acc, rej = 0.0, 0.0 # acceptance and rejection number count
N = 1 # number of time the system stayed in the current position
# Print on screen the computed parameters
if not command_line.silent and not command_line.quiet:
io_mp.print_parameters(sys.stdout, data)
# Suppress non-informative output after initializing
command_line.quiet = True
k = 1
# Main loop, that goes on while the maximum number of failure is not
# reached, and while the expected amount of steps (N) is not taken.
while k <= command_line.N:
# If the number of steps reaches the number set in the adaptive method plus one,
# then the proposal distribution should be gradually adapted.
# If the number of steps also exceeds the number set in adaptive_ts,
# the jumping factor should be gradually adapted.
if command_line.adaptive and k > command_line.adaptive + 1:
# Start of adaptive routine
# By B. Schroer and T. Brinckmann
# Modified version of the method outlined in the PhD thesis of Marta Spinelli
# Store last accepted step
for elem in parameter_names:
last_accepted[parameter_names.index(
elem)] = data.mcmc_parameters[elem]['last_accepted']
# Recursion formula for mean and covmat (and jumping factor after ts steps)
# mean(k) = mean(k-1) + (last_accepted - mean(k-1))/k
mean += 1. / k * (last_accepted - mean)
# C(k) = C(k-1) + [(last_accepted - mean(k))^T * (last_accepted - mean(k)) - C(k-1)]/k
C += 1. / k * (
np.dot(np.transpose(np.asmatrix(last_accepted - mean)),
np.asmatrix(last_accepted - mean)) - C)
sigma_eig, U = np.linalg.eig(np.linalg.inv(C))
if command_line.jumping == 'fast':
Cholesky = la.cholesky(C).T
if k > command_line.adaptive_ts:
# c = j^2/d
c = data.jumping_factor**2 / len(parameter_names)
# c(k) = c(k-1) + [acceptance_rate(last 100 steps) - 0.25]/k
c += (np.mean(ar) - 0.25) / k
data.jumping_factor = np.sqrt(len(parameter_names) * c)
# Save the covariance matrix and the jumping factor in a file
# For a possible MPI implementation
#if not (k-command_line.adaptive) % 5:
# io_mp.write_covariance_matrix(C,parameter_names,str(command_line.cov))
# jump_file = open(command_line.folder + '/jumping_factor.txt','w')
# jump_file.write(str(data.jumping_factor))
# jump_file.close()
# End of adaptive routine
# If the number of steps reaches the number set in the update method,
# then the proposal distribution should be adapted.
if command_line.update:
# Start of update routine
# By M. Ballardini and T. Brinckmann
# Also used by superupdate and adaptive
# master chain behavior
if not rank:
# Add the folder to the list of files to analyze, and switch on the
# options for computing only the covmat
from parser_mp import parse
info_command_line = parse(
'info %s --minimal --noplot --keep-fraction 0.5 --keep-non-markovian --want-covmat'
% command_line.folder)
info_command_line.update = command_line.update
if command_line.adaptive:
# Keep all points for covmat guess in adaptive
info_command_line = parse(
'info %s --minimal --noplot --keep-non-markovian --want-covmat'
% command_line.folder)
# Tell the analysis to update the covmat after t0 steps if it is adaptive
info_command_line.adaptive = command_line.adaptive
# Only compute covmat if no input covmat was provided
if input_covmat != None:
info_command_line.want_covmat = False
# This is in order to allow for more frequent R-1 computation with superupdate
compute_R_minus_one = False
if command_line.superupdate:
if not (k + 10) % command_line.superupdate:
compute_R_minus_one = True
# the +10 below is here to ensure that the first master update will take place before the first slave updates,
# but this is a detail, the code is robust against situations where updating is not possible, so +10 could be omitted
if (not (k + 10) % command_line.update
or compute_R_minus_one) and k > 10:
# Try to launch an analyze (computing a new covmat if successful)
try:
if not (k + 10) % command_line.update:
from analyze import analyze
R_minus_one = analyze(info_command_line)
elif command_line.superupdate:
# Compute (only, i.e. no covmat) R-1 more often when using superupdate
info_command_line = parse(
'info %s --minimal --noplot --keep-fraction 0.5 --keep-non-markovian'
% command_line.folder)
info_command_line.update = command_line.update
R_minus_one = analyze(info_command_line)
except:
if not command_line.silent:
print 'Step ', k, ' chain ', rank, ': Failed to calculate covariance matrix'
if command_line.superupdate:
# Start of superupdate routine
# By B. Schroer and T. Brinckmann
c_array[(k - 1) %
(command_line.superupdate)] = data.jumping_factor
# If acceptance rate deviates too much from the target acceptance
# rate we want to resume adapting the jumping factor
# T. Brinckmann 02/2019: use mean a.r. over the last 5*len(ar) steps
# instead or the over last len(ar), which is more stable
if abs(np.mean(backup_ar) - command_line.superupdate_ar
) > 5. * command_line.superupdate_ar_tol:
stop_c = False
# Start adapting the jumping factor after command_line.superupdate steps if R-1 < 10
# The lower R-1 criterium is an arbitrary choice to keep from updating when the R-1
# calculation fails (i.e. returns only zeros).
if (k > updated_steps + command_line.superupdate
) and 0.01 < (max(R_minus_one) < 10.) and not stop_c:
c = data.jumping_factor**2 / len(parameter_names)
# To avoid getting trapped in local minima, the jumping factor should
# not go below 0.1 (arbitrary) times the starting jumping factor.
if (c + (np.mean(ar) - command_line.superupdate_ar) /
(k - updated_steps)) > (
0.1 * starting_jumping_factor
)**2. / len(parameter_names) or (
(np.mean(ar) - command_line.superupdate_ar) /
(k - updated_steps) > 0):
c += (np.mean(ar) - command_line.superupdate_ar
) / (k - updated_steps)
data.jumping_factor = np.sqrt(
len(parameter_names) * c)
if not (k - 1) % 5:
# Check if the jumping factor adaptation should stop.
# An acceptance rate of 25% balances the wish for more accepted
# points, while ensuring the parameter space is properly sampled.
# The convergence criterium is by default (26+/-1)%, so the adaptation
# will stop when the code reaches an acceptance rate of at least 25%.
# T. Brinckmann 02/2019: use mean a.r. over the last 5*len(ar) steps
# instead or the over last len(ar), which is more stable
if (max(R_minus_one) < 0.4) and (
abs(
np.mean(backup_ar) -
command_line.superupdate_ar) <
command_line.superupdate_ar_tol) and (abs(
np.mean(c_array) / c_array[
(k - 1) %
(command_line.superupdate)] -
1) < 0.01):
stop_c = True
data.out.write(
'# After %d accepted steps: stop adapting the jumping factor at a value of %f with a local acceptance rate %f \n'
% (int(acc), data.jumping_factor,
np.mean(backup_ar)))
if not command_line.silent:
print 'After %d accepted steps: stop adapting the jumping factor at a value of %f with a local acceptance rate of %f \n' % (
int(acc), data.jumping_factor,
np.mean(backup_ar))
jump_file = open(
command_line.folder +
'/jumping_factor.txt', 'w')
jump_file.write('# ' +
str(data.jumping_factor))
jump_file.close()
else:
jump_file = open(
command_line.folder +
'/jumping_factor.txt', 'w')
jump_file.write(str(data.jumping_factor))
jump_file.close()
# Write the evolution of the jumping factor to a file
if not k % (command_line.superupdate):
jump_file = open(
command_line.folder + '/jumping_factors.txt', 'a')
for i in xrange(command_line.superupdate):
jump_file.write(str(c_array[i]) + '\n')
jump_file.close()
# End of main part of superupdate routine
if not (k - 1) % (command_line.update / 3):
try:
# Read the covmat
sigma_eig, U, C = sampler.get_covariance_matrix(
cosmo, data, command_line)
if command_line.jumping == 'fast':
Cholesky = la.cholesky(C).T
# Test here whether the covariance matrix has really changed
# We should in principle test all terms, but testing the first one should suffice
if not C[0, 0] == previous[2][0, 0]:
if k == 1:
if not command_line.silent:
if not input_covmat == None:
warnings.warn(
'Appending to an existing folder: using %s instead of %s. '
'If new input covmat is desired, please delete previous covmat.'
% (command_line.cov, input_covmat))
else:
warnings.warn(
'Appending to an existing folder: using %s. '
'If no starting covmat is desired, please delete previous covmat.'
% command_line.cov)
else:
# Start of second part of superupdate routine
if command_line.superupdate:
# Adaptation of jumping factor should start again after the covmat is updated
# Save the step number after it updated for superupdate and start adaption of c again
updated_steps = k
stop_c = False
cov_det = np.linalg.det(C)
prev_cov_det = np.linalg.det(previous[2])
# Rescale jumping factor in order to keep the magnitude of the jumps the same.
# Skip this update the first time the covmat is updated in order to prevent
# problems due to a poor initial covmat. Rescale the jumping factor after the
# first calculated covmat to the expected optimal one of 2.4.
if jumping_factor_rescale:
new_jumping_factor = data.jumping_factor * (
prev_cov_det / cov_det)**(
1. /
(2 * len(parameter_names)))
data.out.write(
'# After %d accepted steps: rescaled jumping factor from %f to %f, due to updated covariance matrix \n'
% (int(acc), data.jumping_factor,
new_jumping_factor))
if not command_line.silent:
print 'After %d accepted steps: rescaled jumping factor from %f to %f, due to updated covariance matrix \n' % (
int(acc), data.jumping_factor,
new_jumping_factor)
data.jumping_factor = new_jumping_factor
else:
data.jumping_factor = starting_jumping_factor
jumping_factor_rescale += 1
# End of second part of superupdate routine
# Write to chains file when the covmat was updated
data.out.write(
'# After %d accepted steps: update proposal with max(R-1) = %f and jumping factor = %f \n'
% (int(acc), max(R_minus_one),
data.jumping_factor))
if not command_line.silent:
print 'After %d accepted steps: update proposal with max(R-1) = %f and jumping factor = %f \n' % (
int(acc), max(R_minus_one),
data.jumping_factor)
try:
if stop - after - update:
k = command_line.N
print 'Covariance matrix updated - stopping run'
except:
pass
previous = (sigma_eig, U, C, Cholesky)
except:
pass
command_line.quiet = True
# Start of second part of adaptive routine
# Stop updating the covmat after t0 steps in adaptive
if command_line.adaptive and k > 1:
command_line.update = 0
data.jumping_factor = start_jumping_factor
# Test if there are still enough steps left before the adaption of the jumping factor starts
if k > 0.5 * command_line.adaptive_ts:
command_line.adaptive_ts += k
# Set the mean for the recursion formula to the last accepted point
for elem in parameter_names:
mean[parameter_names.index(
elem
)] = data.mcmc_parameters[elem]['last_accepted']
# End of second part of adaptive routine
# slave chain behavior
else:
# Start of slave superupdate routine
if command_line.superupdate:
# If acceptance rate deviates too much from the target acceptance
# rate we want to resume adapting the jumping factor. This line
# will force the slave chains to check if the jumping factor
# has been updated
if abs(np.mean(backup_ar) - command_line.superupdate_ar
) > 5. * command_line.superupdate_ar_tol:
stop_c = False
# Update the jumping factor every 5 steps in superupdate
if not k % 5 and k > command_line.superupdate and command_line.superupdate and (
not stop_c or
(stop_c and k % command_line.update)):
try:
jump_file = open(
command_line.folder + '/jumping_factor.txt',
'r')
# If there is a # in the file, the master has stopped adapting c
for line in jump_file:
if line.find('#') == -1:
jump_file.seek(0)
jump_value = jump_file.read()
data.jumping_factor = float(jump_value)
else:
jump_file.seek(0)
jump_value = jump_file.read().replace(
'# ', '')
#if not stop_c or (stop_c and not float(jump_value) == data.jumping_factor):
if not float(
jump_value) == data.jumping_factor:
data.jumping_factor = float(jump_value)
stop_c = True
data.out.write(
'# After %d accepted steps: stop adapting the jumping factor at a value of %f with a local acceptance rate %f \n'
% (int(acc), data.jumping_factor,
np.mean(backup_ar)))
if not command_line.silent:
print 'After %d accepted steps: stop adapting the jumping factor at a value of %f with a local acceptance rate of %f \n' % (
int(acc), data.jumping_factor,
np.mean(backup_ar))
jump_file.close()
except:
if not command_line.silent:
print 'Reading jumping_factor file failed'
pass
# End of slave superupdate routine
# Start of slave update routine
if not (k - 1) % (command_line.update / 10):
try:
sigma_eig, U, C = sampler.get_covariance_matrix(
cosmo, data, command_line)
if command_line.jumping == 'fast':
Cholesky = la.cholesky(C).T
# Test here whether the covariance matrix has really changed
# We should in principle test all terms, but testing the first one should suffice
if not C[0, 0] == previous[2][0, 0] and not k == 1:
if command_line.superupdate:
# If the covmat was updated, the master has resumed adapting c
stop_c = False
data.out.write(
'# After %d accepted steps: update proposal \n'
% int(acc))
if not command_line.silent:
print 'After %d accepted steps: update proposal \n' % int(
acc)
try:
if stop_after_update:
k = command_line.N
print 'Covariance matrix updated - stopping run'
except:
pass
previous = (sigma_eig, U, C, Cholesky)
except:
pass
# End of slave update routine
# End of update routine
# Pick a new position ('current' flag in mcmc_parameters), and compute
# its likelihood. If get_new_position returns True, it means it did not
# encounter any boundary problem. Otherwise, just increase the
# multiplicity of the point and start the loop again
if get_new_position(data, sigma_eig, U, k, Cholesky, Rotation) is True:
newloglike = sampler.compute_lkl(cosmo, data)
else: # reject step
rej += 1
if command_line.superupdate:
ar[k % len(
ar
)] = 0 # Local acceptance rate of last SU*(N_slow + f_fast * N_fast) steps
elif command_line.adaptive:
ar[k % len(ar)] = 0 # Local acceptance rate of last 100 steps
N += 1
k += 1
continue
# Harmless trick to avoid exponentiating large numbers. This decides
# whether or not the system should move.
if (newloglike != data.boundary_loglike):
if (newloglike >= loglike):
alpha = 1.
else:
alpha = np.exp(newloglike - loglike)
else:
alpha = -1
if ((alpha == 1.) or (rd.uniform(0, 1) < alpha)): # accept step
# Print out the last accepted step (WARNING: this is NOT the one we
# just computed ('current' flag), but really the previous one.)
# with its proper multiplicity (number of times the system stayed
# there).
io_mp.print_vector(outputs, N, loglike, data)
# Report the 'current' point to the 'last_accepted'
sampler.accept_step(data)
loglike = newloglike
if loglike > max_loglike:
max_loglike = loglike
acc += 1.0
N = 1 # Reset the multiplicity
if command_line.superupdate:
ar[k % len(
ar
)] = 1 # Local acceptance rate of last SU*(N_slow + f_fast * N_fast) steps
elif command_line.adaptive:
ar[k % len(ar)] = 1 # Local acceptance rate of last 100 steps
else: # reject step
rej += 1.0
N += 1 # Increase multiplicity of last accepted point
if command_line.superupdate:
ar[k % len(
ar
)] = 0 # Local acceptance rate of last SU*(N_slow + f_fast * N_fast) steps
elif command_line.adaptive:
ar[k % len(ar)] = 0 # Local acceptance rate of last 100 steps
# Store a.r. for last 5 x SU*(N_slow + f_fast * N_fast) steps
if command_line.superupdate:
backup_ar[k % len(backup_ar)] = ar[k % len(ar)]
# Regularly (option to set in parameter file), close and reopen the
# buffer to force to write on file.
if acc % data.write_step == 0:
io_mp.refresh_file(data)
# Update the outputs list
outputs[0] = data.out
k += 1 # One iteration done
# END OF WHILE LOOP
# If at this moment, the multiplicity is higher than 1, it means the
# current point is not yet accepted, but it also mean that we did not print
# out the last_accepted one yet. So we do.
if N > 1:
io_mp.print_vector(outputs, N - 1, loglike, data)
# Print out some information on the finished chain
rate = acc / (acc + rej)
sys.stdout.write('\n# {0} steps done, acceptance rate: {1}\n'.format(
command_line.N, rate))
# In case the acceptance rate is too low, or too high, print a warning
if rate < 0.05:
warnings.warn("The acceptance rate is below 0.05. You might want to "
"set the jumping factor to a lower value than the "
"default (2.4), with the option `-f 1.5` for instance.")
elif rate > 0.6:
warnings.warn("The acceptance rate is above 0.6, which means you might"
" have difficulties exploring the entire parameter space"
". Try analysing these chains, and use the output "
"covariance matrix to decrease the acceptance rate to a "
"value between 0.2 and 0.4 (roughly).")
# For a restart, erase the starting point to keep only the new, longer
# chain.
if command_line.restart is not None:
os.remove(command_line.restart)
sys.stdout.write(
' deleting starting point of the chain {0}\n'.format(
command_line.restart))
return
def chain(cosmo, data, command_line):
"""
Run a Markov chain of fixed length with a Metropolis Hastings algorithm.
Main function of this module, this is the actual Markov chain procedure.
After having selected a starting point in parameter space defining the
first **last accepted** one, it will, for a given amount of steps :
+ choose randomnly a new point following the *proposal density*,
+ compute the cosmological *observables* through the cosmological module,
+ compute the value of the *likelihoods* of the desired experiments at this
point,
+ *accept/reject* this point given its likelihood compared to the one of
the last accepted one.
Every time the code accepts :code:`data.write_step` number of points
(quantity defined in the input parameter file), it will write the result to
disk (flushing the buffer by forcing to exit the output file, and reopen it
again.
.. note::
to use the code to set a fiducial file for certain fixed parameters,
you can use two solutions. The first one is to put all input 1-sigma
proposal density to zero (this method still works, but is not
recommended anymore). The second one consist in using the flag "-f 0",
to force a step of zero amplitude.
"""
## Initialisation
loglike = 0
# In case command_line.silent has been asked, outputs should only contain
# data.out. Otherwise, it will also contain sys.stdout
outputs = [data.out]
if not command_line.silent:
outputs.append(sys.stdout)
# check for MPI
try:
from mpi4py import MPI
comm = MPI.COMM_WORLD
rank = comm.Get_rank()
# suppress duplicate output from slaves
if rank:
command_line.quiet = True
except ImportError:
# set all chains to master if no MPI
rank = 0
# Recover the covariance matrix according to the input, if the varying set
# of parameters is non-zero
if (data.get_mcmc_parameters(['varying']) != []):
sigma_eig, U, C = sampler.get_covariance_matrix(
cosmo, data, command_line)
if data.jumping_factor == 0:
warnings.warn(
"The jumping factor has been set to 0. The above covariance " +
"matrix will not be used.")
# In case of a fiducial run (all parameters fixed), simply run once and
# print out the likelihood. This should not be used any more (one has to
# modify the log.param, which is never a good idea. Instead, force the code
# to use a jumping factor of 0 with the option "-f 0".
else:
warnings.warn(
"You are running with no varying parameters... I will compute " +
"only one point and exit")
data.update_cosmo_arguments() # this fills in the fixed parameters
loglike = sampler.compute_lkl(cosmo, data)
io_mp.print_vector(outputs, 1, loglike, data)
return 1, loglike
# In the fast-slow method, one need the Cholesky decomposition of the
# covariance matrix. Return the Cholesky decomposition as a lower
# triangular matrix
Cholesky = None
Rotation = None
if command_line.jumping == 'fast':
Cholesky = la.cholesky(C).T
Rotation = np.identity(len(sigma_eig))
# If the update mode was selected, the previous (or original) matrix should be stored
if command_line.update:
previous = (sigma_eig, U, C, Cholesky)
# If restart wanted, pick initial value for arguments
if command_line.restart is not None:
sampler.read_args_from_chain(data, command_line.restart)
# If restart from best fit file, read first point (overwrite settings of
# read_args_from_chain)
if command_line.bf is not None:
sampler.read_args_from_bestfit(data, command_line.bf)
# Pick a position (from last accepted point if restart, from the mean value
# else), with a 100 tries.
for i in range(100):
if get_new_position(data, sigma_eig, U, i, Cholesky, Rotation) is True:
break
if i == 99:
raise io_mp.ConfigurationError(
"You should probably check your prior boundaries... because " +
"no valid starting position was found after 100 tries")
# Compute the starting Likelihood
loglike = sampler.compute_lkl(cosmo, data)
# Choose this step as the last accepted value
# (accept_step), and modify accordingly the max_loglike
sampler.accept_step(data)
max_loglike = loglike
# If the jumping factor is 0, the likelihood associated with this point is
# displayed, and the code exits.
if data.jumping_factor == 0:
io_mp.print_vector(outputs, 1, loglike, data)
return 1, loglike
acc, rej = 0.0, 0.0 # acceptance and rejection number count
N = 1 # number of time the system stayed in the current position
# define path and covmat
input_covmat = command_line.cov
base = os.path.basename(command_line.folder)
# the previous line fails when "folder" is a string ending with a slash. This issue is cured by the next lines:
if base == '':
base = os.path.basename(command_line.folder[:-1])
command_line.cov = os.path.join(command_line.folder, base + '.covmat')
# Print on screen the computed parameters
if not command_line.silent and not command_line.quiet:
io_mp.print_parameters(sys.stdout, data)
# Suppress non-informative output after initializing
command_line.quiet = True
k = 1
# Main loop, that goes on while the maximum number of failure is not
# reached, and while the expected amount of steps (N) is not taken.
while k <= command_line.N:
# If the number of steps reaches the number set in the update method,
# then the proposal distribution should be adapted.
if command_line.update:
# master chain behavior
if not rank:
# Add the folder to the list of files to analyze, and switch on the
# options for computing only the covmat
from parser_mp import parse
info_command_line = parse(
'info %s --minimal --noplot --keep-fraction 0.5 --keep-non-markovian --want-covmat'
% command_line.folder)
info_command_line.update = command_line.update
# the +10 below is here to ensure that the first master update will take place before the first slave updates,
# but this is a detail, the code is robust against situations where updating is not possible, so +10 could be omitted
if not (k + 10) % command_line.update and k > 10:
# Try to launch an analyze
try:
from analyze import analyze
R_minus_one = analyze(info_command_line)
except:
if not command_line.silent:
print 'Step ', k, ' chain ', rank, ': Failed to calculate covariant matrix'
pass
if not (k - 1) % command_line.update:
try:
# Read the covmat
sigma_eig, U, C = sampler.get_covariance_matrix(
cosmo, data, command_line)
if command_line.jumping == 'fast':
Cholesky = la.cholesky(C).T
# Test here whether the covariance matrix has really changed
# We should in principle test all terms, but testing the first one should suffice
if not C[0, 0] == previous[2][0, 0]:
previous = (sigma_eig, U, C, Cholesky)
if k == 1:
if not command_line.silent:
if not input_covmat == None:
warnings.warn(
'Appending to an existing folder: using %s instead of %s. '
'If new input covmat is desired, please delete previous covmat.'
% (command_line.cov, input_covmat))
else:
warnings.warn(
'Appending to an existing folder: using %s. '
'If no starting covmat is desired, please delete previous covmat.'
% command_line.cov)
else:
data.out.write(
'# After %d accepted steps: update proposal with max(R-1) = %f \n'
% (int(acc), max(R_minus_one)))
if not command_line.silent:
print 'After %d accepted steps: update proposal with max(R-1) = %f \n' % (
int(acc), max(R_minus_one))
try:
if stop - after - update:
k = command_line.N
print 'Covariant matrix updated - stopping run'
except:
pass
except:
pass
command_line.quiet = True
# slave chain behavior
else:
if not (k - 1) % command_line.update:
try:
sigma_eig, U, C = sampler.get_covariance_matrix(
cosmo, data, command_line)
if command_line.jumping == 'fast':
Cholesky = la.cholesky(C).T
# Test here whether the covariance matrix has really changed
# We should in principle test all terms, but testing the first one should suffice
if not C[0, 0] == previous[2][0, 0] and not k == 1:
data.out.write(
'# After %d accepted steps: update proposal \n'
% int(acc))
if not command_line.silent:
print 'After %d accepted steps: update proposal \n' % int(
acc)
try:
if stop_after_update:
k = command_line.N
print 'Covariant matrix updated - stopping run'
except:
pass
previous = (sigma_eig, U, C, Cholesky)
except IOError:
pass
# Pick a new position ('current' flag in mcmc_parameters), and compute
# its likelihood. If get_new_position returns True, it means it did not
# encounter any boundary problem. Otherwise, just increase the
# multiplicity of the point and start the loop again
if get_new_position(data, sigma_eig, U, k, Cholesky, Rotation) is True:
newloglike = sampler.compute_lkl(cosmo, data)
else: # reject step
rej += 1
N += 1
k += 1
continue
# Harmless trick to avoid exponentiating large numbers. This decides
# whether or not the system should move.
if (newloglike != data.boundary_loglike):
if (newloglike >= loglike):
alpha = 1.
else:
alpha = np.exp(newloglike - loglike)
else:
alpha = -1
if ((alpha == 1.) or (rd.uniform(0, 1) < alpha)): # accept step
# Print out the last accepted step (WARNING: this is NOT the one we
# just computed ('current' flag), but really the previous one.)
# with its proper multiplicity (number of times the system stayed
# there).
io_mp.print_vector(outputs, N, loglike, data)
# Report the 'current' point to the 'last_accepted'
sampler.accept_step(data)
loglike = newloglike
if loglike > max_loglike:
max_loglike = loglike
acc += 1.0
N = 1 # Reset the multiplicity
else: # reject step
rej += 1.0
N += 1 # Increase multiplicity of last accepted point
# Regularly (option to set in parameter file), close and reopen the
# buffer to force to write on file.
if acc % data.write_step == 0:
io_mp.refresh_file(data)
# Update the outputs list
outputs[0] = data.out
k += 1 # One iteration done
# END OF WHILE LOOP
# If at this moment, the multiplicity is higher than 1, it means the
# current point is not yet accepted, but it also mean that we did not print
# out the last_accepted one yet. So we do.
if N > 1:
io_mp.print_vector(outputs, N - 1, loglike, data)
# Print out some information on the finished chain
rate = acc / (acc + rej)
sys.stdout.write('\n# {0} steps done, acceptance rate: {1}\n'.format(
command_line.N, rate))
# In case the acceptance rate is too low, or too high, print a warning
if rate < 0.05:
warnings.warn("The acceptance rate is below 0.05. You might want to "
"set the jumping factor to a lower value than the "
"default (2.4), with the option `-f 1.5` for instance.")
elif rate > 0.6:
warnings.warn("The acceptance rate is above 0.6, which means you might"
" have difficulties exploring the entire parameter space"
". Try analysing these chains, and use the output "
"covariance matrix to decrease the acceptance rate to a "
"value between 0.2 and 0.4 (roughly).")
# For a restart, erase the starting point to keep only the new, longer
# chain.
if command_line.restart is not None:
os.remove(command_line.restart)
sys.stdout.write(
' deleting starting point of the chain {0}\n'.format(
command_line.restart))
return
def chain(cosmo, data, command_line):
"""
Run a Markov chain of fixed length with a Metropolis Hastings algorithm.
Main function of this module, this is the actual Markov chain procedure.
After having selected a starting point in parameter space defining the
first **last accepted** one, it will, for a given amount of steps :
+ choose randomnly a new point following the *proposal density*,
+ compute the cosmological *observables* through the cosmological module,
+ compute the value of the *likelihoods* of the desired experiments at this
point,
+ *accept/reject* this point given its likelihood compared to the one of
the last accepted one.
Every time the code accepts :code:`data.write_step` number of points
(quantity defined in the input parameter file), it will write the result to
disk (flushing the buffer by forcing to exit the output file, and reopen it
again.
.. note::
to use the code to set a fiducial file for certain fixed parameters,
you can use two solutions. The first one is to put all input 1-sigma
proposal density to zero (this method still works, but is not
recommended anymore). The second one consist in using the flag "-f 0",
to force a step of zero amplitude.
"""
## Initialisation
loglike = 0
# In case command_line.silent has been asked, outputs should only contain
# data.out. Otherwise, it will also contain sys.stdout
outputs = [data.out]
if not command_line.silent:
outputs.append(sys.stdout)
# check for MPI
try:
from mpi4py import MPI
comm = MPI.COMM_WORLD
rank = comm.Get_rank()
# suppress duplicate output from slaves
if rank:
command_line.quiet = True
except ImportError:
# set all chains to master if no MPI
rank = 0
# Recover the covariance matrix according to the input, if the varying set
# of parameters is non-zero
if (data.get_mcmc_parameters(['varying']) != []):
sigma_eig, U, C = sampler.get_covariance_matrix(cosmo, data, command_line)
if data.jumping_factor == 0:
warnings.warn(
"The jumping factor has been set to 0. The above covariance " +
"matrix will not be used.")
# In case of a fiducial run (all parameters fixed), simply run once and
# print out the likelihood. This should not be used any more (one has to
# modify the log.param, which is never a good idea. Instead, force the code
# to use a jumping factor of 0 with the option "-f 0".
else:
warnings.warn(
"You are running with no varying parameters... I will compute " +
"only one point and exit")
data.update_cosmo_arguments() # this fills in the fixed parameters
loglike = sampler.compute_lkl(cosmo, data)
io_mp.print_vector(outputs, 1, loglike, data)
return 1, loglike
# In the fast-slow method, one need the Cholesky decomposition of the
# covariance matrix. Return the Cholesky decomposition as a lower
# triangular matrix
Cholesky = None
Rotation = None
if command_line.jumping == 'fast':
Cholesky = la.cholesky(C).T
Rotation = np.identity(len(sigma_eig))
# If the update mode was selected, the previous (or original) matrix should be stored
if command_line.update:
previous = (sigma_eig, U, C, Cholesky)
# If restart wanted, pick initial value for arguments
if command_line.restart is not None:
sampler.read_args_from_chain(data, command_line.restart)
# If restart from best fit file, read first point (overwrite settings of
# read_args_from_chain)
if command_line.bf is not None:
sampler.read_args_from_bestfit(data, command_line.bf)
# Pick a position (from last accepted point if restart, from the mean value
# else), with a 100 tries.
for i in range(100):
if get_new_position(data, sigma_eig, U, i,
Cholesky, Rotation) is True:
break
if i == 99:
raise io_mp.ConfigurationError(
"You should probably check your prior boundaries... because " +
"no valid starting position was found after 100 tries")
# Compute the starting Likelihood
loglike = sampler.compute_lkl(cosmo, data)
# Choose this step as the last accepted value
# (accept_step), and modify accordingly the max_loglike
sampler.accept_step(data)
max_loglike = loglike
# If the jumping factor is 0, the likelihood associated with this point is
# displayed, and the code exits.
if data.jumping_factor == 0:
io_mp.print_vector(outputs, 1, loglike, data)
return 1, loglike
acc, rej = 0.0, 0.0 # acceptance and rejection number count
N = 1 # number of time the system stayed in the current position
# define path and covmat
input_covmat = command_line.cov
base = os.path.basename(command_line.folder)
# the previous line fails when "folder" is a string ending with a slash. This issue is cured by the next lines:
if base == '':
base = os.path.basename(command_line.folder[:-1])
command_line.cov = os.path.join(
command_line.folder, base+'.covmat')
# Print on screen the computed parameters
if not command_line.silent and not command_line.quiet:
io_mp.print_parameters(sys.stdout, data)
# Suppress non-informative output after initializing
command_line.quiet = True
k = 1
# Main loop, that goes on while the maximum number of failure is not
# reached, and while the expected amount of steps (N) is not taken.
while k <= command_line.N:
# If the number of steps reaches the number set in the update method,
# then the proposal distribution should be adapted.
if command_line.update:
# master chain behavior
if not rank:
# Add the folder to the list of files to analyze, and switch on the
# options for computing only the covmat
from parser_mp import parse
info_command_line = parse(
'info %s --minimal --noplot --keep-fraction 0.5 --keep-non-markovian --want-covmat' % command_line.folder)
info_command_line.update = command_line.update
# the +10 below is here to ensure that the first master update will take place before the first slave updates,
# but this is a detail, the code is robust against situations where updating is not possible, so +10 could be omitted
if not (k+10) % command_line.update and k > 10:
# Try to launch an analyze
try:
from analyze import analyze
R_minus_one = analyze(info_command_line)
except:
if not command_line.silent:
print 'Step ',k,' chain ', rank,': Failed to calculate covariant matrix'
pass
if not (k-1) % command_line.update:
try:
# Read the covmat
sigma_eig, U, C = sampler.get_covariance_matrix(
cosmo, data, command_line)
if command_line.jumping == 'fast':
Cholesky = la.cholesky(C).T
# Test here whether the covariance matrix has really changed
# We should in principle test all terms, but testing the first one should suffice
if not C[0,0] == previous[2][0,0]:
previous = (sigma_eig, U, C, Cholesky)
if k == 1:
if not command_line.silent:
if not input_covmat == None:
warnings.warn(
'Appending to an existing folder: using %s instead of %s. '
'If new input covmat is desired, please delete previous covmat.'
% (command_line.cov, input_covmat))
else:
warnings.warn(
'Appending to an existing folder: using %s. '
'If no starting covmat is desired, please delete previous covmat.'
% command_line.cov)
else:
data.out.write('# After %d accepted steps: update proposal with max(R-1) = %f \n' % (int(acc), max(R_minus_one)))
if not command_line.silent:
print 'After %d accepted steps: update proposal with max(R-1) = %f \n' % (int(acc), max(R_minus_one))
try:
if stop-after-update:
k = command_line.N
print 'Covariant matrix updated - stopping run'
except:
pass
except:
pass
command_line.quiet = True
# slave chain behavior
else:
if not (k-1) % command_line.update:
try:
sigma_eig, U, C = sampler.get_covariance_matrix(
cosmo, data, command_line)
if command_line.jumping == 'fast':
Cholesky = la.cholesky(C).T
# Test here whether the covariance matrix has really changed
# We should in principle test all terms, but testing the first one should suffice
if not C[0,0] == previous[2][0,0] and not k == 1:
data.out.write('# After %d accepted steps: update proposal \n' % int(acc))
if not command_line.silent:
print 'After %d accepted steps: update proposal \n' % int(acc)
try:
if stop_after_update:
k = command_line.N
print 'Covariant matrix updated - stopping run'
except:
pass
previous = (sigma_eig, U, C, Cholesky)
except:
pass
# Pick a new position ('current' flag in mcmc_parameters), and compute
# its likelihood. If get_new_position returns True, it means it did not
# encounter any boundary problem. Otherwise, just increase the
# multiplicity of the point and start the loop again
if get_new_position(
data, sigma_eig, U, k, Cholesky, Rotation) is True:
newloglike = sampler.compute_lkl(cosmo, data)
else: # reject step
rej += 1
N += 1
k += 1
continue
# Harmless trick to avoid exponentiating large numbers. This decides
# whether or not the system should move.
if (newloglike != data.boundary_loglike):
if (newloglike >= loglike):
alpha = 1.
else:
alpha = np.exp(newloglike-loglike)
else:
alpha = -1
if ((alpha == 1.) or (rd.uniform(0, 1) < alpha)): # accept step
# Print out the last accepted step (WARNING: this is NOT the one we
# just computed ('current' flag), but really the previous one.)
# with its proper multiplicity (number of times the system stayed
# there).
io_mp.print_vector(outputs, N, loglike, data)
# Report the 'current' point to the 'last_accepted'
sampler.accept_step(data)
loglike = newloglike
if loglike > max_loglike:
max_loglike = loglike
acc += 1.0
N = 1 # Reset the multiplicity
else: # reject step
rej += 1.0
N += 1 # Increase multiplicity of last accepted point
# Regularly (option to set in parameter file), close and reopen the
# buffer to force to write on file.
if acc % data.write_step == 0:
io_mp.refresh_file(data)
# Update the outputs list
outputs[0] = data.out
k += 1 # One iteration done
# END OF WHILE LOOP
# If at this moment, the multiplicity is higher than 1, it means the
# current point is not yet accepted, but it also mean that we did not print
# out the last_accepted one yet. So we do.
if N > 1:
io_mp.print_vector(outputs, N-1, loglike, data)
# Print out some information on the finished chain
rate = acc / (acc + rej)
sys.stdout.write('\n# {0} steps done, acceptance rate: {1}\n'.
format(command_line.N, rate))
# In case the acceptance rate is too low, or too high, print a warning
if rate < 0.05:
warnings.warn("The acceptance rate is below 0.05. You might want to "
"set the jumping factor to a lower value than the "
"default (2.4), with the option `-f 1.5` for instance.")
elif rate > 0.6:
warnings.warn("The acceptance rate is above 0.6, which means you might"
" have difficulties exploring the entire parameter space"
". Try analysing these chains, and use the output "
"covariance matrix to decrease the acceptance rate to a "
"value between 0.2 and 0.4 (roughly).")
# For a restart, erase the starting point to keep only the new, longer
# chain.
if command_line.restart is not None:
os.remove(command_line.restart)
sys.stdout.write(' deleting starting point of the chain {0}\n'.
format(command_line.restart))
return
def chain(cosmo, data, command_line):
"""
Run a Markov chain of fixed length.
Main function of this module, this is the actual Markov chain procedure.
After having selected a starting point in parameter space defining the
first **last accepted** one, it will, for a given amount of steps :
+ choose randomnly a new point following the *proposal density*,
+ compute the cosmological *observables* through the cosmological module,
+ compute the value of the *likelihoods* of the desired experiments at this point,
+ *accept/reject* this point given its likelihood compared to the one of
the last accepted one.
Every time the code accepts :code:`data.write_step` number of points
(quantity defined in the input parameter file), it will write the result to
disk (flushing the buffer by forcing to exit the output file, and reopen it
again.
.. note::
to use the code to set a fiducial file for certain fixed parameters,
you can use two solutions. The first one is to put all input 1-sigma
proposal density to zero (this method still works, but is not
recommended anymore). The second one consist in using the flag "-f 0",
to force a step of zero amplitude.
"""
## Initialisation
loglike = 0
# In case command_line.silent has been asked, outputs should only contain
# data.out. Otherwise, it will also contain sys.stdout
outputs = [data.out]
if not command_line.silent:
outputs.append(sys.stdout)
# Recover the covariance matrix according to the input, if the varying set
# of parameters is non-zero
if (data.get_mcmc_parameters(['varying']) != []):
sigma_eig, U, C = sampler.get_covariance_matrix(data, command_line)
if data.jumping_factor == 0:
warnings.warn(
"The jumping factor has been set to 0. The above covariance " +
"matrix will not be used.")
# In case of a fiducial run (all parameters fixed), simply run once and
# print out the likelihood. This should not be used any more (one has to
# modify the log.param, which is never a good idea. Instead, force the code
# to use a jumping factor of 0 with the option "-f 0".
else:
warnings.warn(
"You are running with no varying parameters... I will compute " +
"only one point and exit")
data.update_cosmo_arguments() # this fills in the fixed parameters
loglike = sampler.compute_lkl(cosmo, data)
io_mp.print_vector(outputs, 1, loglike, data)
return 1, loglike
# In the fast-slow method, one need the Cholesky decomposition of the
# covariance matrix. Return the Cholesky decomposition as a lower
# triangular matrix
Cholesky = None
Inverse_Cholesky = None
Rotation = None
if command_line.jumping == 'fast':
Cholesky = la.cholesky(C).T
Inverse_Cholesky = np.linalg.inv(Cholesky)
Rotation = np.identity(len(sigma_eig))
# If restart wanted, pick initial value for arguments
if command_line.restart is not None:
sampler.read_args_from_chain(data, command_line.restart)
# If restart from best fit file, read first point (overwrite settings of
# read_args_from_chain)
if command_line.bf is not None:
sampler.read_args_from_bestfit(data, command_line.bf)
# Pick a position (from last accepted point if restart, from the mean value
# else), with a 100 tries.
for i in range(100):
if get_new_position(data, sigma_eig, U, i,
Cholesky, Inverse_Cholesky, Rotation) is True:
break
if i == 99:
raise io_mp.ConfigurationError(
"You should probably check your prior boundaries... because " +
"no valid starting position was found after 100 tries")
# Compute the starting Likelihood
loglike = sampler.compute_lkl(cosmo, data)
# Choose this step as the last accepted value
# (accept_step), and modify accordingly the max_loglike
sampler.accept_step(data)
max_loglike = loglike
# If the jumping factor is 0, the likelihood associated with this point is
# displayed, and the code exits.
if data.jumping_factor == 0:
io_mp.print_vector(outputs, 1, loglike, data)
return 1, loglike
acc, rej = 0.0, 0.0 # acceptance and rejection number count
N = 1 # number of time the system stayed in the current position
# Print on screen the computed parameters
io_mp.print_parameters(sys.stdout, data)
k = 1
# Main loop, that goes on while the maximum number of failure is not
# reached, and while the expected amount of steps (N) is not taken.
while k <= command_line.N:
# Pick a new position ('current' flag in mcmc_parameters), and compute
# its likelihood. If get_new_position returns True, it means it did not
# encounter any boundary problem. Otherwise, just increase the
# multiplicity of the point and start the loop again
if get_new_position(
data, sigma_eig, U, k, Cholesky,
Inverse_Cholesky, Rotation) is True:
newloglike = sampler.compute_lkl(cosmo, data)
else: # reject step
rej += 1
N += 1
k += 1
continue
# Harmless trick to avoid exponentiating large numbers. This decides
# whether or not the system should move.
if (newloglike != data.boundary_loglike):
if (newloglike >= loglike):
alpha = 1.
else:
alpha = np.exp(newloglike-loglike)
else:
alpha = -1
if ((alpha == 1.) or (rd.uniform(0, 1) < alpha)): # accept step
# Print out the last accepted step (WARNING: this is NOT the one we
# just computed ('current' flag), but really the previous one.)
# with its proper multiplicity (number of times the system stayed
# there).
io_mp.print_vector(outputs, N, loglike, data)
# Report the 'current' point to the 'last_accepted'
sampler.accept_step(data)
loglike = newloglike
if loglike > max_loglike:
max_loglike = loglike
acc += 1.0
N = 1 # Reset the multiplicity
else: # reject step
rej += 1.0
N += 1 # Increase multiplicity of last accepted point
# Regularly (option to set in parameter file), close and reopen the
# buffer to force to write on file.
if acc % data.write_step == 0:
io_mp.refresh_file(data)
# Update the outputs list
outputs[0] = data.out
k += 1 # One iteration done
# END OF WHILE LOOP
# If at this moment, the multiplicity is higher than 1, it means the
# current point is not yet accepted, but it also mean that we did not print
# out the last_accepted one yet. So we do.
if N > 1:
io_mp.print_vector(outputs, N-1, loglike, data)
# Print out some information on the finished chain
rate = acc / (acc + rej)
sys.stdout.write('\n# {0} steps done, acceptance rate: {1}\n'.
format(command_line.N, rate))
# In case the acceptance rate is too low, or too high, print a warning
if rate < 0.05:
warnings.warn("The acceptance rate is below 0.05. You might want to "
"set the jumping factor to a lower value than the "
"default (2.4), with the option `-f 1.5` for instance.")
elif rate > 0.6:
warnings.warn("The acceptance rate is above 0.6, which means you might"
" have difficulties exploring the entire parameter space"
". Try analysing these chains, and use the output "
"covariance matrix to decrease the acceptance rate to a "
"value between 0.2 and 0.4 (roughly).")
# For a restart, erase the starting point to keep only the new, longer
# chain.
if command_line.restart is not None:
os.remove(command_line.restart)
sys.stdout.write(' deleting starting point of the chain {0}\n'.
format(command_line.restart))
return