def prayer(configfile, nprays=0, savefile=None):
"""
Implement a Prayer-bead method to estimate parameter uncertainties.
Parameters
----------
configfile: String
Configuration file name
nprays: Integer
Number of prayer-bead shifts. If nprays==0, set to the number
of data points.
savefile: String
Name of file where to store the prayer-bead results.
Notes
-----
Believing in a prayer bead is a mere act of faith, we are scientists
for god's sake!
"""
config = ConfigParser.SafeConfigParser()
config.read([configfile])
cfgsec = "MCMC"
data = mu.parray(config.get(cfgsec, 'data'))
if isinstance(data[0], str):
array = mu.loadbin(data[0])
data = array[0]
if len(array) == 2:
uncert = array[1]
else:
uncert = mu.parray(config.get(cfgsec, 'uncert'))
params = mu.parray(config.get(cfgsec, 'params'))
if isinstance(params[0], str):
array = mu.loadascii(params[0])
ninfo, nparams = np.shape(array)
if ninfo == 7: # The priors
prior = array[4]
priorlow = array[5]
priorup = array[6]
else:
try:
prior = mu.parray(config.get(cfgsec, 'prior'))
priorlow = mu.parray(config.get(cfgsec, 'priorlow'))
priorup = mu.parray(config.get(cfgsec, 'priorup'))
except:
prior = np.zeros(nparams) # Empty arrays
priorup = priorlow = np.array([])
iprior = np.array([], int)
if ninfo >= 4: # The stepsize
stepsize = array[3]
else:
stepsize = mu.parray(config.get(cfgsec, 'stepsize'))
if ninfo >= 2: # The boundaries
pmin = array[1]
pmax = array[2]
else:
pmin = mu.parray(config.get(cfgsec, 'pmin'))
pmax = mu.parray(config.get(cfgsec, 'pmax'))
params = array[0] # The initial guess
indparams = mu.parray(config.get(cfgsec, 'indparams'))
if indparams != [] and isinstance(indparams[0], str):
indparams = mu.loadbin(indparams[0])
# Number of fitting parameters:
nfree = np.sum(stepsize > 0)
ifree = np.where(stepsize > 0)[0]
iprior = np.where(priorlow > 0)[0]
# Get modeling function:
func = mu.parray(config.get(cfgsec, 'func'))
if type(func) in [list, tuple, np.ndarray]:
if len(func) == 3:
sys.path.append(func[2])
exec('from %s import %s as func'%(func[1], func[0]))
elif not callable(func):
return
# Number of iterations:
if nprays == 0:
nprays = ndata
shifts = np.arange(1, ndata)
else:
shifts = np.random.randint(0, ndata, nprays-1)
# Allocate space for results:
allfits = np.zeros((nprays, nfree))
# Fit model:
fitargs = (params, func, data, uncert, indparams, stepsize, pmin, pmax,
(prior-params)[iprior], priorlow[iprior], priorup[iprior])
chisq, dummy = mf.modelfit(params[ifree], args=fitargs)
# Evaluate best model:
fargs = [params] + indparams
bestmodel = func(*fargs)
chifactor = np.sqrt(chisq/(ndata-nfree))
# Get residuals:
residuals = data - bestmodel
sigma = np.copy(uncert*chifactor)
allfits[0] = params[ifree]
for i in np.arange(nprays-1):
# Permuted data:
pbdata = np.copy(bestmodel + np.roll(residuals, shifts[i]))
# Permuted weights:
pbunc = np.roll(sigma, shifts[i])
# Fitting parameters:
pbfit = np.copy(params)[ifree]
# Fit model:
fitargs = (params, func, pbdata, pbunc, indparams, stepsize, pmin, pmax,
(prior-params)[iprior], priorlow[iprior], priorup[iprior])
chisq, dummy = mf.modelfit(pbfit, args=fitargs)
allfits[i+1] = pbfit
if savefile is not None:
pbfile = open(savefile, "w")
pbfile.write("Prayer-bead uncertainties:\n")
pbunc = np.std(allfits, 0)
for j in np.arange(nfree):
pbfile.write("%s "%str(pbunc[j]))
pbfile.close()
return allfits, residuals
def main():
"""
Multi-Core Markov-Chain Monte Carlo (MC cubed)
This code calls MCMC to work under an MPI multiprocessor protocol or
single-thread mode. When using MPI it will launch one CPU per MCMC chain
to work in parallel.
Parameters:
-----------
cfile: String
Filename of a configuration file.
"""
# Parse the config file from the command line:
cparser = argparse.ArgumentParser(description=__doc__, add_help=False,
formatter_class=argparse.RawDescriptionHelpFormatter)
# Add config file option:
cparser.add_argument("-c", "--config_file",
help="Configuration file", metavar="FILE")
# Remaining_argv contains all other command-line-arguments:
args, remaining_argv = cparser.parse_known_args()
# Take configuration file from command-line:
cfile = args.config_file
# Incorrect configuration file name:
if cfile is not None and not os.path.isfile(cfile):
mu.error("Configuration file: '{:s}' not found.".format(cfile))
if cfile:
config = ConfigParser.SafeConfigParser()
config.read([cfile])
defaults = dict(config.items("MCMC"))
else:
defaults = {}
# Parser for the MCMC arguments:
parser = argparse.ArgumentParser(parents=[cparser])
# MCMC Options:
group = parser.add_argument_group("MCMC General Options")
group.add_argument("-n", "--numit",
dest="numit",
help="Number of MCMC samples [default: %(default)s]",
type=eval, action="store", default=100)
group.add_argument("-x", "--nchains",
dest="nchains",
help="Number of chains [default: %(default)s]",
type=int, action="store", default=10)
group.add_argument("-w", "--walk",
dest="walk",
help="Random walk algorithm [default: %(default)s]",
type=str, action="store", default="demc",
choices=('demc', 'mrw'))
group.add_argument( "--wlikelihood",
dest="wlike",
help="Calculate the likelihood in a wavelet base "
"[default: %(default)s]",
type=eval, action="store", default=False)
group.add_argument( "--leastsq",
dest="leastsq",
help="Perform a least-square minimization before the "
"MCMC run [default: %(default)s]",
type=eval, action="store", default=False)
group.add_argument( "--chisq_scale",
dest="chisqscale",
help="Scale the data uncertainties such that the reduced "
"chi-squared = 1. [default: %(default)s]",
type=eval, action="store", default=False)
group.add_argument("-g", "--gelman_rubin",
dest="grtest",
help="Run Gelman-Rubin test [default: %(default)s]",
type=eval, action="store", default=False)
group.add_argument( "--grexit",
dest="grexit",
help="Exit the MCMC loop if the MCMC satisfies the GR "
"test two consecutive times [default: %(default)s]",
type=eval, action="store", default=False)
group.add_argument("-b", "--burnin",
help="Number of burn-in iterations (per chain) "
"[default: %(default)s]",
dest="burnin",
type=eval, action="store", default=0)
group.add_argument("-t", "--thinning",
dest="thinning",
help="Chains thinning factor (use every thinning-th "
"iteration) for GR test and plots [default: %(default)s]",
type=int, action="store", default=1)
group.add_argument( "--plots",
dest="plots",
help="If True plot parameter traces, pairwise posteriors, "
"and marginal posterior histograms [default: %(default)s]",
type=eval, action="store", default=False)
group.add_argument("-o", "--save_file",
dest="savefile",
help="Output filename to store the parameter posterior "
"distributions [default: %(default)s]",
type=str, action="store", default="output.npy")
group.add_argument( "--savemodel",
dest="savemodel",
help="Output filename to store the evaluated models "
"[default: %(default)s]",
type=str, action="store", default=None)
group.add_argument( "--mpi",
dest="mpi",
help="Run under MPI multiprocessing [default: "
"%(default)s]",
type=eval, action="store", default=False)
group.add_argument( "--resume",
dest="resume",
help="If True, resume a previous run (load output) "
"[default: %(default)s]",
type=eval, action="store", default=False)
group.add_argument( "--rms",
dest="rms",
help="If True, calculate the RMS of (data-bestmodel) "
"[default: %(default)s]",
type=eval, action="store", default=False)
group.add_argument( "--logfile",
dest="logfile",
help="Log file.",
action="store", default=None)
group.add_argument("-T", "--tracktime", dest="tractime", action="store_true")
# Fitting-parameter Options:
group = parser.add_argument_group("Fitting-function Options")
group.add_argument("-f", "--func",
dest="func",
help="List of strings with the function name, module "
"name, and path-to-module [required]",
type=mu.parray, action="store", default=None)
group.add_argument("-p", "--params",
dest="params",
help="Filename or list of initial-guess model-fitting "
"parameter [required]",
type=mu.parray, action="store", default=None)
group.add_argument("-m", "--pmin",
dest="pmin",
help="Filename or list of parameter lower boundaries "
"[default: -inf]",
type=mu.parray, action="store", default=None)
group.add_argument("-M", "--pmax",
dest="pmax",
help="Filename or list of parameter upper boundaries "
"[default: +inf]",
type=mu.parray, action="store", default=None)
group.add_argument("-s", "--stepsize",
dest="stepsize",
help="Filename or list with proposal jump scale "
"[default: 0.1*params]",
type=mu.parray, action="store", default=None)
group.add_argument("-i", "--indparams",
dest="indparams",
help="Filename or list with independent parameters for "
"func [default: None]",
type=mu.parray, action="store", default=[])
# Data Options:
group = parser.add_argument_group("Data Options")
group.add_argument("-d", "--data",
dest="data",
help="Filename or list of the data being fitted "
"[required]",
type=mu.parray, action="store", default=None)
group.add_argument("-u", "--uncertainties",
dest="uncert",
help="Filemane or list with the data uncertainties "
"[default: ones]",
type=mu.parray, action="store", default=None)
group.add_argument( "--prior",
dest="prior",
help="Filename or list with parameter prior estimates "
"[default: %(default)s]",
type=mu.parray, action="store", default=None)
group.add_argument( "--priorlow",
dest="priorlow",
help="Filename or list with prior lower uncertainties "
"[default: %(default)s]",
type=mu.parray, action="store", default=None)
group.add_argument( "--priorup",
dest="priorup",
help="Filename or list with prior upper uncertainties "
"[default: %(default)s]",
type=mu.parray, action="store", default=None)
# Set the defaults from the configuration file:
parser.set_defaults(**defaults)
# Set values from command line:
args2, unknown = parser.parse_known_args(remaining_argv)
# Unpack configuration-file/command-line arguments:
numit = args2.numit
nchains = args2.nchains
walk = args2.walk
wlike = args2.wlike
leastsq = args2.leastsq
chisqscale = args2.chisqscale
grtest = args2.grtest
grexit = args2.grexit
burnin = args2.burnin
thinning = args2.thinning
plots = args2.plots
savefile = args2.savefile
savemodel = args2.savemodel
mpi = args2.mpi
resume = args2.resume
tracktime = args2.tractime
logfile = args2.logfile
rms = args2.rms
func = args2.func
params = args2.params
pmin = args2.pmin
pmax = args2.pmax
stepsize = args2.stepsize
indparams = args2.indparams
data = args2.data
uncert = args2.uncert
prior = args2.prior
priorup = args2.priorup
priorlow = args2.priorlow
nprocs = nchains
# Open a log FILE if requested:
if logfile is not None:
log = open(logfile, "w")
else:
log = None
# Handle arguments:
if params is None:
mu.error("'params' is a required argument.", log)
elif isinstance(params[0], str):
# If params is a filename, unpack:
if not os.path.isfile(params[0]):
mu.error("params file '{:s}' not found.".format(params[0]), log)
array = mu.loadascii(params[0])
# Array size:
ninfo, ndata = np.shape(array)
if ninfo == 7: # The priors
prior = array[4]
priorlow = array[5]
priorup = array[6]
if ninfo >= 4: # The stepsize
stepsize = array[3]
if ninfo >= 2: # The boundaries
pmin = array[1]
pmax = array[2]
params = array[0] # The initial guess
# Check for pmin and pmax files if not read before:
if pmin is not None and isinstance(pmin[0], str):
if not os.path.isfile(pmin[0]):
mu.error("pmin file '{:s}' not found.".format(pmin[0]), log)
pmin = mu.loadascii(pmin[0])[0]
if pmax is not None and isinstance(pmax[0], str):
if not os.path.isfile(pmax[0]):
mu.error("pmax file '{:s}' not found.".format(pmax[0]), log)
pmax = mu.loadascii(pmax[0])[0]
# Stepsize:
if stepsize is not None and isinstance(stepsize[0], str):
if not os.path.isfile(stepsize[0]):
mu.error("stepsize file '{:s}' not found.".format(stepsize[0]), log)
stepsize = mu.loadascii(stepsize[0])[0]
# Priors:
if prior is not None and isinstance(prior[0], str):
if not os.path.isfile(prior[0]):
mu.error("prior file '{:s}' not found.".format(prior[0]), log)
prior = mu.loadascii(prior [0])[0]
if priorlow is not None and isinstance(priorlow[0], str):
if not os.path.isfile(priorlow[0]):
mu.error("priorlow file '{:s}' not found.".format(priorlow[0]), log)
priorlow = mu.loadascii(priorlow[0])[0]
if priorup is not None and isinstance(priorup[0], str):
if not os.path.isfile(priorup[0]):
mu.error("priorup file '{:s}' not found.".format(priorup[0]), log)
priorup = mu.loadascii(priorup [0])[0]
# Process the data and uncertainties:
if data is None:
mu.error("'data' is a required argument.", log)
# If params is a filename, unpack:
elif isinstance(data[0], str):
if not os.path.isfile(data[0]):
mu.error("data file '{:s}' not found.".format(data[0]), log)
array = mu.loadbin(data[0])
data = array[0]
if len(array) == 2:
uncert = array[1]
if uncert is None:
mu.error("'uncert' is a required argument.", log)
elif isinstance(uncert[0], str):
if not os.path.isfile(uncert[0]):
mu.error("uncert file '{:s}' not found.".format(uncert[0]), log)
uncert = mu.loadbin(uncert[0])[0]
# Process the independent parameters:
if indparams != [] and isinstance(indparams[0], str):
if not os.path.isfile(indparams[0]):
mu.error("indparams file '{:s}' not found.".format(indparams[0]), log)
indparams = mu.loadbin(indparams[0])
if tracktime:
start_mpi = timeit.default_timer()
if mpi:
# Checks for mpi4py:
try:
from mpi4py import MPI
except:
mu.error("Attempted to use MPI, but mpi4py is not installed.", log)
# Get source dir:
mcfile = mc.__file__
iright = mcfile.rfind('/')
if iright == -1:
sdir = "."
else:
sdir = mcfile[:iright]
# Hack func here:
funccall = sdir + "/func.py"
if func[0] == 'hack':
funccall = func[2] + "/" + func[1] + ".py"
# Call wrapper of model function:
args = [funccall, "-c" + cfile] + remaining_argv
comm = MPI.COMM_SELF.Spawn(sys.executable, args=args, maxprocs=nprocs)
else:
comm = None
# Use a copy of uncert to avoid overwrite on it.
if uncert is not None:
unc = np.copy(uncert)
else:
unc = None
if tracktime:
start_loop = timeit.default_timer()
# Run the MCMC:
allp, bp = mc.mcmc(data, unc, func, indparams,
params, pmin, pmax, stepsize,
prior, priorlow, priorup,
numit, nchains, walk, wlike,
leastsq, chisqscale, grtest, grexit, burnin,
thinning, plots, savefile, savemodel,
comm, resume, log, rms)
if tracktime:
stop = timeit.default_timer()
# Close communications and disconnect:
if mpi:
mu.comm_disconnect(comm)
#if bench == True:
if tracktime:
mu.msg(1, "Total execution time: %10.6f s"%(stop - start), log)
if log is not None:
log.close()
