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
# 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 = get_covariance_matrix(data, command_line)
if data.jumping_factor == 0:
io_mp.message(
"The jumping factor has been set to 0. The above covariance \
matrix will not be used.",
"info")
# 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:
io_mp.message(
"You are running with no varying parameters... I will compute \
only one point and exit",
"info")
data.update_cosmo_arguments() # this fills in the fixed parameters
loglike = compute_lkl(cosmo, data)
io_mp.print_vector([data.out, sys.stdout], 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:
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:
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:
io_mp.message(
"You should probably check your prior boundaries... because \
no valid starting position was found after 100 tries",
"error")
# Compute the starting Likelihood
loglike = compute_lkl(cosmo, data)
# Choose this step as the last accepted value
# (accept_step), and modify accordingly the max_loglike
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([data.out, sys.stdout], 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 = 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([data.out, sys.stdout], N, loglike, data)
# Report the 'current' point to the 'last_accepted'
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)
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([data.out, sys.stdout], 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))
# 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 get_new_position(data, eigv, U, k, Cholesky, Inverse_Cholesky, Rotation):
"""
Obtain a new position in the parameter space from the eigen values of the
inverse covariance matrix, or from the Cholesky decomposition (original
idea by Anthony Lewis, in a yet unpublished paper, Efficient sampling of
fast and slow cosmological parameters).
.. note::
U, eigv are not used anymore in v1.2.0, but might come back in v1.2.1.
:Parameters:
* **eigv** (`numpy array`) - eigenvalues previously computed *obsolete
in v1.2.0*
* **U** (`numpy_array`) - *obsolete in v1.2.0*, was the covariance
matrix.
* **k** (`int`) - Number of points so far in the chain, is used to
rotate through parameters
* **Cholesky** (`numpy_array`) - Cholesky decomposition of the
covariance matrix, and its inverse
* **Rotation** (`numpy_array`) - Not used yet
"""
parameter_names = data.get_mcmc_parameters(['varying'])
vector_new = np.zeros(len(parameter_names), 'float64')
sigmas = np.zeros(len(parameter_names), 'float64')
# Write the vector of last accepted points, or if it does not exist
# (initialization routine), take the mean value
vector = np.zeros(len(parameter_names), 'float64')
try:
for elem in parameter_names:
vector[parameter_names.index(elem)] = \
data.mcmc_parameters[elem]['last_accepted']
except KeyError:
for elem in parameter_names:
vector[parameter_names.index(elem)] = \
data.mcmc_parameters[elem]['initial'][0]
# Initialize random seed
rd.seed()
# Choice here between sequential and global change of direction
if data.jumping == 'global':
for i in range(len(vector)):
sigmas[i] = (math.sqrt(1/eigv[i]/len(vector))) * \
rd.gauss(0, 1)*data.jumping_factor
elif data.jumping == 'sequential':
i = k % len(vector)
sigmas[i] = (math.sqrt(1/eigv[i]))*rd.gauss(0, 1)*data.jumping_factor
elif data.jumping == 'fast':
i = k % len(vector)
###############
# method fast+global
for elem in data.blocks_parameters:
if i < elem:
index = data.blocks_parameters.index(elem)
if index == 0:
Range = elem
Previous = 0
else:
Range = elem-data.blocks_parameters[index-1]
Previous = data.blocks_parameters[index-1]
for j in range(Range):
sigmas[j+Previous] = (math.sqrt(1./Range)) * \
rd.gauss(0, 1)*data.jumping_factor
break
else:
continue
####################
# method fast+sequential
#sigmas[i] = rd.gauss(0,1)*data.jumping_factor
else:
print('\n\n Jumping method unknown (accepted : ')
print('global (default), sequential, fast)')
# Fill in the new vector
if data.jumping in ['global', 'sequential']:
vector_new = vector + np.dot(U, sigmas)
else:
vector_new = vector + np.dot(Cholesky, sigmas)
# Check for boundaries problems
flag = 0
for elem in parameter_names:
i = parameter_names.index(elem)
value = data.mcmc_parameters[elem]['initial']
if((str(value[1]) != str(-1) and value[1] is not None) and
(vector_new[i] < value[1])):
flag += 1 # if a boundary value is reached, increment
elif((str(value[2]) != str(-1) and value[1] is not None) and
vector_new[i] > value[2]):
flag += 1 # same
# At this point, if a boundary condition is not fullfilled, ie, if flag is
# different from zero, return False
if flag != 0:
return False
# Check for a slow step (only after the first time, so we put the test in a
# try: statement: the first time, the exception KeyError will be raised)
try:
data.check_for_slow_step(vector_new)
except KeyError:
pass
# If it is not the case, proceed with normal computation. The value of
# new_vector is then put into the 'current' point in parameter space.
for elem in parameter_names:
i = parameter_names.index(elem)
data.mcmc_parameters[elem]['current'] = vector_new[i]
# Propagate the information towards the cosmo arguments
data.update_cosmo_arguments()
return True
