def mcmc(data, uncert=None, func=None, indparams=[],
params=None, pmin=None, pmax=None, stepsize=None,
prior=None, priorlow=None, priorup=None, numit=10,
nchains=10, walk='demc', wlike=False, leastsq=True,
chisqscale=False, grtest=True, grexit=False, burnin=0,
thinning=1, plots=False, savefile=None, savemodel=None,
comm=None, resume=False, log=None, rms=False):
"""
This beautiful piece of code runs a Markov-chain Monte Carlo algoritm.
Parameters
----------
data: 1D ndarray
Dependent data fitted by func.
uncert: 1D ndarray
Uncertainty of data.
func: callable or string-iterable
The callable function that models data as:
model = func(params, *indparams)
Or an iterable (list, tuple, or ndarray) of 3 strings:
(funcname, modulename, path)
that specify the function name, function module, and module path.
If the module is already in the python-path scope, path can be omitted.
indparams: tuple
Additional arguments required by func.
params: 1D or 2D ndarray
Set of initial fitting parameters for func. If 2D, of shape
(nparams, nchains), it is assumed that it is one set for each chain.
pmin: 1D ndarray
Lower boundaries of the posteriors.
pmax: 1D ndarray
Upper boundaries of the posteriors.
stepsize: 1D ndarray
Proposal jump scale. If a values is 0, keep the parameter fixed.
Negative values indicate a shared parameter (See Note 1).
prior: 1D ndarray
Parameter prior distribution means (See Note 2).
priorlow: 1D ndarray
Lower prior uncertainty values (See Note 2).
priorup: 1D ndarray
Upper prior uncertainty values (See Note 2).
numit: Scalar
Total number of iterations.
nchains: Scalar
Number of simultaneous chains to run.
walk: String
Random walk algorithm:
- 'mrw': Metropolis random walk.
- 'demc': Differential Evolution Markov chain.
wlike: Boolean
If True, calculate the likelihood in a wavelet-base. This requires
three additional parameters (See Note 3).
leastsq: Boolean
Perform a least-square minimization before the MCMC run.
chisqscale: Boolean
Scale the data uncertainties such that the reduced chi-squared = 1.
grtest: Boolean
Run Gelman & Rubin test.
grexit: Boolean
Exit the MCMC loop if the MCMC satisfies GR two consecutive times.
burnin: Scalar
Burned-in (discarded) number of iterations at the beginning
of the chains.
thinning: Integer
Thinning factor of the chains (use every thinning-th iteration) used
in the GR test and plots.
plots: Boolean
If True plot parameter traces, pairwise-posteriors, and posterior
histograms.
savefile: String
If not None, filename to store allparams (with np.save).
savemodel: String
If not None, filename to store the values of the evaluated function
(with np.save).
comm: MPI Communicator
A communicator object to transfer data through MPI.
resume: Boolean
If True resume a previous run.
log: FILE pointer
File object to write log into.
Returns
-------
allparams: 2D ndarray
An array of shape (nfree, numit-nchains*burnin) with the MCMC
posterior distribution of the fitting parameters.
bestp: 1D ndarray
Array of the best fitting parameters.
Notes
-----
1.- To set one parameter equal to another, set its stepsize to the
negative index in params (Starting the count from 1); e.g.: to set
the second parameter equal to the first one, do: stepsize[1] = -1.
2.- If any of the fitting parameters has a prior estimate, e.g.,
param[i] = p0 +up/-low,
with up and low the 1sigma uncertainties. This information can be
considered in the MCMC run by setting:
prior[i] = p0
priorup[i] = up
priorlow[i] = low
All three: prior, priorup, and priorlow must be set and, furthermore,
priorup and priorlow must be > 0 to be considered as prior.
3.- FINDME WAVELET LIKELIHOOD
Examples
--------
>>> # See examples: https://github.com/pcubillos/MCcubed/tree/master/examples
Previous (uncredited) developers
--------------------------------
Kevin Stevenson UCF [email protected]
"""
mu.msg(1, "{:s}\n Multi-Core Markov-Chain Monte Carlo (MC3).\n"
" Version {:d}.{:d}.{:d}.\n"
" Copyright (c) 2015-2016 Patricio Cubillos and collaborators.\n"
" MC3 is open-source software under the MIT license "
"(see LICENSE).\n{:s}\n\n".
format(mu.sep, ver.MC3_VER, ver.MC3_MIN, ver.MC3_REV, mu.sep), log)
# Import the model function:
if type(func) in [list, tuple, np.ndarray]:
if func[0] != 'hack':
if len(func) == 3:
sys.path.append(func[2])
exec('from %s import %s as func'%(func[1], func[0]))
elif not callable(func):
mu.error("'func' must be either, a callable, or an iterable (list, "
"tuple, or ndarray) of strings with the model function, file, "
"and path names.", log)
if np.ndim(params) == 1: # Force it to be 2D (one for each chain)
params = np.atleast_2d(params)
nparams = len(params[0]) # Number of model params
ndata = len(data) # Number of data values
# Set default uncertainties:
if uncert is None:
uncert = np.ones(ndata)
# Set default boundaries:
if pmin is None:
pmin = np.zeros(nparams) - np.inf
if pmax is None:
pmax = np.zeros(nparams) + np.inf
# Set default stepsize:
if stepsize is None:
stepsize = 0.1 * np.abs(params[0])
# Set prior parameter indices:
if (prior is None) or (priorup is None) or (priorlow is None):
prior = priorup = priorlow = np.zeros(nparams) # Zero arrays
iprior = np.where(priorlow != 0)[0]
ilog = np.where(priorlow < 0)[0]
# Check that initial values lie within the boundaries:
if np.any(np.asarray(params) < pmin):
mu.error("One or more of the initial-guess values:\n{:s}\n are smaller "
"than their lower boundaries:\n{:s}".format(str(params), str(pmin)), log)
if np.any(np.asarray(params) > pmax):
mu.error("One or more of the initial-guess values:\n{:s}\n are greater "
"than their higher boundaries:\n{:s}".format(str(params), str(pmax)), log)
nfree = np.sum(stepsize > 0) # Number of free parameters
chainsize = int(np.ceil(numit/nchains)) # Number of iterations per chain
ifree = np.where(stepsize > 0)[0] # Free parameter indices
ishare = np.where(stepsize < 0)[0] # Shared parameter indices
# Number of model parameters (excluding wavelet parameters):
if wlike:
mpars = nparams - 3
else:
mpars = nparams
if chainsize < burnin:
mu.error("The number of burned-in samples ({:d}) is greater than "
"the number of iterations per chain ({:d}).".
format(burnin, chainsize), log)
# Intermediate steps to run GR test and print progress report:
intsteps = chainsize / 10
# Allocate arrays with variables:
numaccept = np.zeros(nchains) # Number of accepted proposal jumps
outbounds = np.zeros((nchains, nfree), np.int) # Out of bounds proposals
allparams = np.zeros((nchains, nfree, chainsize)) # Parameter's record
if savemodel is not None:
allmodel = np.zeros((nchains, ndata, chainsize)) # Fit model
if resume:
oldparams = np.load(savefile)
nold = np.shape(oldparams)[2] # Number of old-run iterations
allparams = np.dstack((oldparams, allparams))
if savemodel is not None:
allmodel = np.dstack((np.load(savemodel), allmodel))
# Set params to the last-iteration state of the previous run:
params = np.repeat(params, nchains, 0)
params[:,ifree] = oldparams[:,:,-1]
else:
nold = 0
# Set MPI flag:
mpi = comm is not None
if mpi:
from mpi4py import MPI
# Send sizes info to other processes:
array1 = np.asarray([mpars, chainsize], np.int)
mu.comm_bcast(comm, array1, MPI.INT)
# DEMC parameters:
gamma = 2.4 / np.sqrt(2*nfree)
gamma2 = 0.001 # Jump scale factor of support distribution
# Least-squares minimization:
if leastsq:
fitargs = (params[0], func, data, uncert, indparams, stepsize, pmin, pmax,
prior, priorlow, priorup)
fitchisq, dummy = mf.modelfit(params[0,ifree], args=fitargs)
fitbestp = np.copy(params[0, ifree])
mu.msg(1, "Least-squares best-fitting parameters: \n{:s}\n\n".
format(str(fitbestp)), log)
# Replicate to make one set for each chain: (nchains, nparams):
if np.shape(params)[0] != nchains:
params = np.repeat(params, nchains, 0)
# Start chains with an initial jump:
for p in ifree:
# For each free param, use a normal distribution:
params[1:, p] = np.random.normal(params[0, p], stepsize[p], nchains-1)
# Stay within pmin and pmax boundaries:
params[np.where(params[:, p] < pmin[p]), p] = pmin[p]
params[np.where(params[:, p] > pmax[p]), p] = pmax[p]
# Update shared parameters:
for s in ishare:
params[:, s] = params[:, -int(stepsize[s])-1]
# Calculate chi-squared for model using current params:
models = np.zeros((nchains, ndata))
if mpi:
# Scatter (send) parameters to func:
mu.comm_scatter(comm, params[:,0:mpars].flatten(), MPI.DOUBLE)
# Gather (receive) evaluated models:
mpimodels = np.zeros(nchains*ndata, np.double)
mu.comm_gather(comm, mpimodels)
# Store them in models variable:
models = np.reshape(mpimodels, (nchains, ndata))
else:
for c in np.arange(nchains):
fargs = [params[c, 0:mpars]] + indparams # List of function's arguments
models[c] = func(*fargs)
# Calculate chi-squared for each chain:
currchisq = np.zeros(nchains)
c2 = np.zeros(nchains) # No-Jeffrey's chisq
for c in np.arange(nchains):
if wlike: # Wavelet-based likelihood (chi-squared, actually)
currchisq[c], c2[c] = dwt.wlikelihood(params[c, mpars:], models[c]-data,
(params[c]-prior)[iprior], priorlow[iprior], priorlow[iprior])
else:
currchisq[c], c2[c] = cs.chisq(models[c], data, uncert,
(params[c]-prior)[iprior], priorlow[iprior], priorlow[iprior])
# Scale data-uncertainties such that reduced chisq = 1:
if chisqscale:
chifactor = np.sqrt(np.amin(currchisq)/(ndata-nfree))
uncert *= chifactor
# Re-calculate chisq with the new uncertainties:
for c in np.arange(nchains):
if wlike: # Wavelet-based likelihood (chi-squared, actually)
currchisq[c], c2[c] = dwt.wlikelihood(params[c,mpars:], models[c]-data,
(params[c]-prior)[iprior], priorlow[iprior], priorlow[iprior])
else:
currchisq[c], c2[c] = cs.chisq(models[c], data, uncert,
(params[c]-prior)[iprior], priorlow[iprior], priorlow[iprior])
if leastsq:
fitchisq = currchisq[0]
# Get lowest chi-square and best fitting parameters:
bestchisq = np.amin(c2)
bestp = np.copy(params[np.argmin(c2)])
bestmodel = np.copy(models[np.argmin(c2)])
if savemodel is not None:
allmodel[:,:,0] = models
# Set up the random walks:
if walk == "mrw":
# Generate proposal jumps from Normal Distribution for MRW:
mstep = np.random.normal(0, stepsize[ifree], (chainsize, nchains, nfree))
elif walk == "demc":
# Support random distribution:
support = np.random.normal(0, stepsize[ifree], (chainsize, nchains, nfree))
# Generate indices for the chains such r[c] != c:
r1 = np.random.randint(0, nchains-1, (nchains, chainsize))
r2 = np.random.randint(0, nchains-1, (nchains, chainsize))
for c in np.arange(nchains):
r1[c][np.where(r1[c]==c)] = nchains-1
r2[c][np.where(r2[c]==c)] = nchains-1
# Uniform random distribution for the Metropolis acceptance rule:
unif = np.random.uniform(0, 1, (chainsize, nchains))
# Proposed iteration parameters and chi-square (per chain):
nextp = np.copy(params) # Proposed parameters
nextchisq = np.zeros(nchains) # Chi square of nextp
# Gelman-Rubin exit flag:
grflag = False
# ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
# Start loop:
mu.msg(1, "Start MCMC chains ({:s})".format(time.ctime()), log)
for i in np.arange(chainsize):
# Proposal jump:
if walk == "mrw":
jump = mstep[i]
elif walk == "demc":
jump = (gamma * (params[r1[:,i]]-params[r2[:,i]])[:,ifree] +
gamma2 * support[i] )
# Propose next point:
nextp[:,ifree] = params[:,ifree] + jump
# Check it's within boundaries:
outpars = np.asarray(((nextp < pmin) | (nextp > pmax))[:,ifree])
outflag = np.any(outpars, axis=1)
outbounds += ((nextp < pmin) | (nextp > pmax))[:,ifree]
for p in ifree:
nextp[np.where(nextp[:, p] < pmin[p]), p] = pmin[p]
nextp[np.where(nextp[:, p] > pmax[p]), p] = pmax[p]
# Update shared parameters:
for s in ishare:
nextp[:, s] = nextp[:, -int(stepsize[s])-1]
# Evaluate the models for the proposed parameters:
if mpi:
mu.comm_scatter(comm, nextp[:,0:mpars].flatten(), MPI.DOUBLE)
mu.comm_gather(comm, mpimodels)
models = np.reshape(mpimodels, (nchains, ndata))
else:
for c in np.where(~outflag)[0]:
fargs = [nextp[c, 0:mpars]] + indparams # List of function's arguments
models[c] = func(*fargs)
# Calculate chisq:
for c in np.where(~outflag)[0]:
if wlike: # Wavelet-based likelihood (chi-squared, actually)
nextchisq[c], c2[c] = dwt.wlikelihood(nextp[c,mpars:], models[c]-data,
(nextp[c]-prior)[iprior], priorlow[iprior], priorlow[iprior])
else:
nextchisq[c], c2[c] = cs.chisq(models[c], data, uncert,
(nextp[c]-prior)[iprior], priorlow[iprior], priorlow[iprior])
# Reject out-of-bound jumps:
nextchisq[np.where(outflag)] = np.inf
# Evaluate which steps are accepted and update values:
accept = np.exp(0.5 * (currchisq - nextchisq))
accepted = accept >= unif[i]
if i >= burnin:
numaccept += accepted
# Update params and chi square:
params [accepted] = nextp [accepted]
currchisq[accepted] = nextchisq[accepted]
# Check lowest chi-square:
if np.amin(c2) < bestchisq:
bestp = np.copy(params[np.argmin(c2)])
bestmodel = np.copy(models[np.argmin(c2)])
bestchisq = np.amin(c2)
# Store current iteration values:
allparams[:,:,i+nold] = params[:, ifree]
if savemodel is not None:
models[~accepted] = allmodel[~accepted,:,i+nold-1]
allmodel[:,:,i+nold] = models
# Print intermediate info:
if ((i+1) % intsteps == 0) and (i > 0):
mu.progressbar((i+1.0)/chainsize, log)
mu.msg(1, "Out-of-bound Trials:\n {:s}".
format(np.sum(outbounds, axis=0)), log)
mu.msg(1, "Best Parameters: (chisq={:.4f})\n{:s}".
format(bestchisq, str(bestp)), log)
# Gelman-Rubin statistic:
if grtest and (i+nold) > burnin:
psrf = gr.convergetest(allparams[:, :, burnin:i+nold+1:thinning])
mu.msg(1, "Gelman-Rubin statistic for free parameters:\n{:s}".
format(psrf), log)
if np.all(psrf < 1.01):
mu.msg(1, "All parameters have converged to within 1% of unity.", log)
# End the MCMC if all parameters satisfy GR two consecutive times:
if grexit and grflag:
# Let the workers know that the MCMC is stopping:
if mpi:
endflag = np.tile(np.inf, nchains*mpars)
mu.comm_scatter(comm, endflag, MPI.DOUBLE)
break
grflag = True
else:
grflag = False
# Save current results:
if savefile is not None:
np.save(savefile, allparams[:,:,0:i+nold])
if savemodel is not None:
np.save(savemodel, allmodel[:,:,0:i+nold])
# Stack together the chains:
chainlen = nold + i+1
allstack = allparams[0, :, burnin:chainlen]
for c in np.arange(1, nchains):
allstack = np.hstack((allstack, allparams[c, :, burnin:chainlen]))
# And the models:
if savemodel is not None:
modelstack = allmodel[0,:,burnin:chainlen]
for c in np.arange(1, nchains):
modelstack = np.hstack((modelstack, allmodel[c, :, burnin:chainlen]))
# Print out Summary:
mu.msg(1, "\nFin, MCMC Summary:\n------------------", log)
nsample = (i+1-burnin)*nchains
ntotal = np.size(allstack[0])
BIC = bestchisq + nfree*np.log(ndata)
redchisq = bestchisq/(ndata-nfree)
sdr = np.std(bestmodel-data)
fmtlen = len(str(ntotal))
mu.msg(1, "Burned in iterations per chain: {:{}d}".
format(burnin, fmtlen), log, 1)
mu.msg(1, "Number of iterations per chain: {:{}d}".
format(i+1, fmtlen), log, 1)
mu.msg(1, "MCMC sample size: {:{}d}".
format(nsample, fmtlen), log, 1)
mu.msg(resume, "Total MCMC sample size: {:{}d}".
format(ntotal, fmtlen), log, 1)
mu.msg(1, "Acceptance rate: {:.2f}%\n ".
format(np.sum(numaccept)*100.0/nsample), log, 1)
meanp = np.mean(allstack, axis=1) # Parameters mean
uncertp = np.std(allstack, axis=1) # Parameter standard deviation
mu.msg(1, "Best-fit params Uncertainties Signal/Noise Sample "
"Mean", log, 1)
for i in np.arange(nfree):
mu.msg(1, "{: 15.7e} {: 15.7e} {:12.2f} {: 15.7e}".
format(bestp[ifree][i], uncertp[i],
np.abs(bestp[ifree][i])/uncertp[i], meanp[i]), log, 1)
if leastsq and np.any(np.abs((bestp[ifree]-fitbestp)/fitbestp) > 1e-08):
np.set_printoptions(precision=8)
mu.warning("MCMC found a better fit than the minimizer:\n"
" MCMC best-fitting parameters: (chisq={:.8g})\n {:s}\n"
" Minimizer best-fitting parameters: (chisq={:.8g})\n"
" {:s}".format(bestchisq, str(bestp[ifree]),
fitchisq, str(fitbestp)), log)
fmtl = len("%.4f"%BIC) # Length of string formatting
mu.msg(1, " ", log)
if chisqscale:
mu.msg(1, "sqrt(reduced chi-squared) factor: {:{}.4f}".
format(chifactor, fmtl), log, 1)
mu.msg(1, "Best-parameter's chi-squared: {:{}.4f}".
format(bestchisq, fmtl), log, 1)
mu.msg(1, "Bayesian Information Criterion: {:{}.4f}".
format(BIC, fmtl), log, 1)
mu.msg(1, "Reduced chi-squared: {:{}.4f}".
format(redchisq, fmtl), log, 1)
mu.msg(1, "Standard deviation of residuals: {:.6g}\n".format(sdr), log, 1)
if rms:
rms, rmse, stderr, bs = ta.binrms(bestmodel-data)
if plots:
print("Plotting figures ...")
# Extract filename from savefile:
if savefile is not None:
if savefile.rfind(".") == -1:
fname = savefile[savefile.rfind("/")+1:] # Cut out file extention.
else:
fname = savefile[savefile.rfind("/")+1:savefile.rfind(".")]
else:
fname = "MCMC"
# Trace plot:
mp.trace(allstack, thinning=thinning, savefile=fname+"_trace.png",
sep=np.size(allstack[0])/nchains)
# Pairwise posteriors:
mp.pairwise(allstack, thinning=thinning, savefile=fname+"_pairwise.png")
# Histograms:
mp.histogram(allstack, thinning=thinning, savefile=fname+"_posterior.png")
# RMS vs bin size:
if rms:
mp.RMS(bs, rms, stderr, rmse, binstep=len(bs)/500+1,
savefile=fname+"_RMS.png")
if indparams != [] and np.size(indparams[0]) == ndata:
mp.modelfit(data, uncert, indparams[0], bestmodel,
savefile=fname+"_model.png")
# Save definitive results:
if savefile is not None:
np.save(savefile, allparams[:,:,:chainlen])
if savemodel is not None:
np.save(savemodel, allmodel [:,:,:chainlen])
return allstack, bestp
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()
def main(): """ One function to run them all. Developer Team: --------------- Patricio Cubillos [email protected] Jasmina Blecic [email protected] Joseph Harrington [email protected] Madison Stemm [email protected] (FINDME) Modification History: --------------------- 2014-07-25 Jasmina Initial version. 2014-08-15 Patricio put code into main() function. 2014-08-18 Patricio Merged with MC3 module. Added flag to sort read/execute steps. 2014-09-20 Jasmina Made call to makeRadius() function. Added progress statements. 2014-10-12 Jasmina Updated to new TEA structure. 2014-12-13 patricio Added Opacity calculation step (through Transit), added flags to break after TEA or Opacity calculation. 2015-05-03 jasmina Added best-fit Transit run. """ mu.msg(1, "\n======= Bayesian Atmospheric Radiative Transfer (BART) ===============" "\nA code to infer planetary atmospheric properties based on observed " "\nspectroscopic information." "\n\nCopyright (C) 2015 University of Central Florida. All rights reserved." "\n\nDevelopers contact: Patricio Cubillos [email protected]" "\n Jasmina Blecic [email protected]" "\n Joseph Harrington [email protected]" "\n======================================================================") mu.msg(1, "\nInitialization:") # 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") # Parser for the MCMC arguments: parser = argparse.ArgumentParser(parents=[cparser]) parser.add_argument("--justTEA", action='store_true', help="Run only TEA.") parser.add_argument("--justOpacity", action='store_true', help="Run only Transit to generate the Opacity table.") parser.add_argument("--resume", action='store_true', help="Resume a previous run.") # Directories and files options: group = parser.add_argument_group("Directories and files") group.add_argument("--loc_dir", dest="loc_dir", help="Output directory to store results [default: %(default)s]", type=str, action="store", default="outdir") group.add_argument("--tep_name", dest="tep_name", help="Transiting exoplanet file name.", type=str, action="store", default=None) group.add_argument("--logfile", dest="logfile", help="Help me!", type=str, action="store", default=None) # Pressure layers options: group = parser.add_argument_group("Layers pressure sampling") group.add_argument("--n_layers", dest="n_layers", help="Number of atmospheric layers [default: %(default)s]", type=int, action="store", default=100) group.add_argument("--p_top", dest="p_top", help="Pressure at the top of the atmosphere (bars) " "[default: %(default)s]", type=np.double, action="store", default=1.0e-5) group.add_argument("--p_bottom", dest="p_bottom", help="Pressure at the botom of the atmosphere (bars) " "[default: %(default)s]", type=np.double, action="store", default=100.0) group.add_argument("--log", dest="log", help="Use log (True) or linear (False) scale sampling " "[default: %(default)s]", type=eval, action="store", default=True) group.add_argument("--press_file", dest="press_file", help="Input/Output file with pressure array.", type=str, action="store", default=None) # Elemental abundance options: group = parser.add_argument_group("Elemental abundances") group.add_argument("--abun_basic", dest="abun_basic", help="Input elemental abundances file " "[default: 'BART/inputs/abundances_Asplund2009.txt']", type=str, action="store", default=None) group.add_argument("--abun_file", dest="abun_file", help="Input/Output modified elemental abundances file", type=str, action="store", default=None) group.add_argument("--solar_times", dest="solar_times", help="Multiplication factor for metal-element abundances", type=int, action="store", default=1.0) group.add_argument("--COswap", dest="COswap", help="Swap C and O abundances if True [default: %(default)s]", type=eval, action="store", default=False) # Temperature profile options: group = parser.add_argument_group("Temperature profile") group.add_argument("--PTtype", dest="PTtype", help="Temperature profile model [default: %(default)s]", type=str, action="store", default="line", choices=("line","madhu")) group.add_argument("--PTinit", dest="PTinit", help="Temperature profile model parameters", type=mu.parray, action="store", default=None) # Atmospheric model options: group = parser.add_argument_group("Atmospheric model") group.add_argument("--in_elem", dest="in_elem", help="Input elements to consider in TEA [default: %(default)s]", type=str, action="store", default='H He C N O') group.add_argument("--out_spec", dest="out_spec", help="Output species to include in the atmospheric model " "[default: %(default)s]", type=str, action="store", default='H_g He_ref C_g N_g O_g H2_ref CO_g CO2_g CH4_g H2O_g') group.add_argument("--preatm_file", dest="preatm_file", help="Pre-atmospheric file with elemental abundances per layer " "[default: %(default)s]", type=str, action="store", default="elem.atm") group.add_argument("--atmfile", dest="atmfile", help="Atmospheric model file [default: %(default)s]", type=str, action="store", default="") group.add_argument("--uniform", dest="uniform", help="If not None, set uniform abundances with the specified " "values for each species in out_spec [default: %(default)s]", type=mu.parray, action="store", default=None) # MCMC options: group = parser.add_argument_group("MCMC") group.add_argument("--func", dest="func", help="", type=mu.parray, action="store", default=None) group.add_argument("--params", dest="params", help="Model-fitting parameters [default: %(default)s]", type=mu.parray, action="store", default=None) group.add_argument("--molfit", dest="molfit", help="Molecules fit [default: %(default)s]", type=mu.parray, action="store", default=None) group.add_argument("--Tmin", dest="Tmin", help="Lower Temperature boundary [default: %(default)s]", type=float, action="store", default=400.0) group.add_argument("--Tmax", dest="Tmax", help="Higher Temperature boundary [default: %(default)s]", type=float, action="store", default=3000.0) group.add_argument("--quiet", dest="quiet", help="Set verbosity level to minimum", action="store_true") group.add_argument("--stepsize", dest="stepsize", help="Parameters stepsize", type=mu.parray, action="store", default=None) # Input converter options: group = parser.add_argument_group("Input Converter Options") group.add_argument("--tint", dest="tint", help="Internal temperature of the planet [default: %(default)s].", type=float, action="store", default=100.0) # Output-Converter Options: group = parser.add_argument_group("Output Converter Options") group.add_argument("--filter", action="store", help="Waveband filter name [default: %(default)s]", dest="filter", type=mu.parray, default=None) group.add_argument("--kurucz_file", action="store", help="Stellar Kurucz file [default: %(default)s]", dest="kurucz", type=str, default=None) group.add_argument("--solution", action="store", help="Solution geometry [default: %(default)s]", dest="solution", type=str, default="None", choices=('transit', 'eclipse')) # Transit options: group = parser.add_argument_group("Transit variables") group.add_argument("--tconfig", dest="tconfig", help="Transit configuration file [default: %(default)s]", type=str, action="store", default="transit.cfg") group.add_argument("--opacityfile", dest="opacityfile", help="Opacity table file [default: %(default)s]", type=str, action="store", default=None) # Remaining_argv contains all other command-line-arguments: cargs, remaining_argv = cparser.parse_known_args() # Get only the arguments defined above: known, unknown = parser.parse_known_args(remaining_argv) # Get configuration file from command-line: cfile = cargs.config_file # Default: if cfile is None: cfile = "./BART.cfg" # Always require a configuration file: if not os.path.isfile(cfile): mu.error("Configuration file: '{:s}' not found.".format(cfile)) # Read values from configuration file: config = ConfigParser.SafeConfigParser() config.optionxform = str # This one enable Uppercase in arguments config.read([cfile]) defaults = dict(config.items("MCMC")) mu.msg(1, "The configuration file is: '{:s}'.".format(cfile), indent=2) # Set the defaults from the configuration file: parser.set_defaults(**defaults) # Set values from command line: args, unknown = parser.parse_known_args(remaining_argv) # Unpack the variables from args: variables = dir(args) for var in dir(known): if not var.startswith("_"): exec("{:s} = args.{:s}".format(var, var)) # Make output directory: # Make a subdirectory with the date and time dirfmt = loc_dir + "%4d-%02d-%02d_%02d:%02d:%02d" date_dir = dirfmt % time.localtime()[0:6] # FINDME: Temporary hack (temporary?): date_dir = os.path.normpath(loc_dir) + "/" if not os.path.isabs(date_dir): date_dir = os.getcwd() + "/" + date_dir mu.msg(1, "Output folder: '{:s}'".format(date_dir), indent=2) try: os.mkdir(date_dir) except OSError, e: if e.errno == 17: # Allow overwritting while we debug pass else: mu.error("Cannot create folder '{:s}'. {:s}.".format(date_dir, os.strerror(e.errno)))
date_dir = os.getcwd() + "/" + date_dir
mu.msg(1, "Output folder: '{:s}'".format(date_dir), indent=2)
try:
os.mkdir(date_dir)
except OSError, e:
if e.errno == 17: # Allow overwritting while we debug
pass
else:
mu.error("Cannot create folder '{:s}'. {:s}.".format(date_dir,
os.strerror(e.errno)))
# Copy files to date dir:
# BART configuration file:
shutil.copy2(cfile, date_dir)
# TEP file:
if not os.path.isfile(tep_name):
mu.error("Tepfile ('{:s}') Not found.".format(tep_name))
else:
shutil.copy2(tep_name, date_dir + os.path.basename(tep_name))
# Check if files already exist:
runMCMC = 0 # Flag that indicate which steps to run
# Atmospheric file:
if os.path.isfile(atmfile):
atmfile = os.path.realpath(atmfile)
shutil.copy2(atmfile, date_dir + os.path.basename(atmfile))
mu.msg(1, "Atmospheric file copied from: '{:s}'.".format(atmfile),indent=2)
runMCMC |= 8
# Pre-atmospheric file:
if os.path.isfile(preatm_file):
preatm_file = os.path.realpath(preatm_file)
shutil.copy2(preatm_file, date_dir + os.path.basename(preatm_file))
def mcmc(data, uncert=None, func=None, indparams=[],
params=None, pmin=None, pmax=None, stepsize=None,
prior=None, priorlow=None, priorup=None,
numit=10, nchains=10, walk='demc', wlike=False,
leastsq=True, chisqscale=False, grtest=True, burnin=0,
thinning=1, plots=False, savefile=None, savemodel=None,
comm=None, resume=False, log=None, rms=False):
"""
This beautiful piece of code runs a Markov-chain Monte Carlo algoritm.
Parameters:
-----------
data: 1D ndarray
Dependent data fitted by func.
uncert: 1D ndarray
Uncertainty of data.
func: callable or string-iterable
The callable function that models data as:
model = func(params, *indparams)
Or an iterable (list, tuple, or ndarray) of 3 strings:
(funcname, modulename, path)
that specify the function name, function module, and module path.
If the module is already in the python-path scope, path can be omitted.
indparams: tuple
Additional arguments required by func.
params: 1D or 2D ndarray
Set of initial fitting parameters for func. If 2D, of shape
(nparams, nchains), it is assumed that it is one set for each chain.
pmin: 1D ndarray
Lower boundaries of the posteriors.
pmax: 1D ndarray
Upper boundaries of the posteriors.
stepsize: 1D ndarray
Proposal jump scale. If a values is 0, keep the parameter fixed.
Negative values indicate a shared parameter (See Note 1).
prior: 1D ndarray
Parameter prior distribution means (See Note 2).
priorlow: 1D ndarray
Lower prior uncertainty values (See Note 2).
priorup: 1D ndarray
Upper prior uncertainty values (See Note 2).
numit: Scalar
Total number of iterations.
nchains: Scalar
Number of simultaneous chains to run.
walk: String
Random walk algorithm:
- 'mrw': Metropolis random walk.
- 'demc': Differential Evolution Markov chain.
wlike: Boolean
If True, calculate the likelihood in a wavelet-base. This requires
three additional parameters (See Note 3).
leastsq: Boolean
Perform a least-square minimization before the MCMC run.
chisqscale: Boolean
Scale the data uncertainties such that the reduced chi-squared = 1.
grtest: Boolean
Run Gelman & Rubin test.
burnin: Scalar
Burned-in (discarded) number of iterations at the beginning
of the chains.
thinning: Integer
Thinning factor of the chains (use every thinning-th iteration) used
in the GR test and plots.
plots: Boolean
If True plot parameter traces, pairwise-posteriors, and posterior
histograms.
savefile: String
If not None, filename to store allparams (with np.save).
savemodel: String
If not None, filename to store the values of the evaluated function
(with np.save).
comm: MPI Communicator
A communicator object to transfer data through MPI.
resume: Boolean
If True resume a previous run.
log: FILE pointer
File object to write log into.
Returns:
--------
allparams: 2D ndarray
An array of shape (nfree, numit-nchains*burnin) with the MCMC
posterior distribution of the fitting parameters.
bestp: 1D ndarray
Array of the best fitting parameters.
Notes:
------
1.- To set one parameter equal to another, set its stepsize to the
negative index in params (Starting the count from 1); e.g.: to set
the second parameter equal to the first one, do: stepsize[1] = -1.
2.- If any of the fitting parameters has a prior estimate, e.g.,
param[i] = p0 +up/-low,
with up and low the 1sigma uncertainties. This information can be
considered in the MCMC run by setting:
prior[i] = p0
priorup[i] = up
priorlow[i] = low
All three: prior, priorup, and priorlow must be set and, furthermore,
priorup and priorlow must be > 0 to be considered as prior.
3.- FINDME WAVELET LIKELIHOOD
Examples:
---------
>>> # See examples: https://github.com/pcubillos/MCcubed/tree/master/examples
Developers:
-----------
Kevin Stevenson UCF [email protected]
Patricio Cubillos UCF [email protected]
Modification History:
---------------------
2008-05-02 kevin Initial implementation
2008-06-21 kevin Finished updating
2009-11-01 kevin Updated for multi events:
2010-06-09 kevin Updated for ipspline, nnint & bilinint
2011-07-06 kevin Updated for Gelman-Rubin statistic
2011-07-22 kevin Added principal component analysis
2011-10-11 kevin Added priors
2012-09-03 patricio Added Differential Evolution MC. Documented.
2013-01-31 patricio Modified for general purposes.
2013-02-21 patricio Added support distribution for DEMC.
2014-03-31 patricio Modified to be completely agnostic of the
fitting function, updated documentation.
2014-04-17 patricio Revamped use of 'func': no longer requires a
wrapper. Alternatively, can take a string list with
the function, module, and path names.
2014-04-19 patricio Added savefile, thinning, plots, and mpi arguments.
2014-05-04 patricio Added Summary print out.
2014-05-09 patricio Added Wavelet-likelihood calculation.
2014-05-09 patricio Changed figure types from pdf to png, because it's
much faster.
2014-05-26 patricio Changed mpi bool argument by comm. Re-engineered
MPI communications to make direct calls to func.
2014-06-09 patricio Fixed glitch with leastsq+informative priors.
2014-10-17 patricio Added savemodel argument.
2014-10-23 patricio Added support for func hack.
2015-02-04 patricio Added resume argument.
2015-05-15 patricio Added log argument.
"""
# Import the model function:
if type(func) in [list, tuple, np.ndarray]:
if func[0] != 'hack':
if len(func) == 3:
sys.path.append(func[2])
exec('from %s import %s as func'%(func[1], func[0]))
elif not callable(func):
mu.error("'func' must be either, a callable, or an iterable (list, "
"tuple, or ndarray) of strings with the model function, file, "
"and path names.", log)
if np.ndim(params) == 1: # Force it to be 2D (one for each chain)
params = np.atleast_2d(params)
nparams = len(params[0]) # Number of model params
ndata = len(data) # Number of data values
# Set default uncertainties:
if uncert is None:
uncert = np.ones(ndata)
# Set default boundaries:
if pmin is None:
pmin = np.zeros(nparams) - np.inf
if pmax is None:
pmax = np.zeros(nparams) + np.inf
# Set default stepsize:
if stepsize is None:
stepsize = 0.1 * np.abs(params[0])
# Set prior parameter indices:
if (prior is None) or (priorup is None) or (priorlow is None):
prior = priorup = priorlow = np.zeros(nparams) # Zero arrays
iprior = np.where(priorlow != 0)[0]
ilog = np.where(priorlow < 0)[0]
nfree = np.sum(stepsize > 0) # Number of free parameters
chainlen = int(np.ceil(numit/nchains)) # Number of iterations per chain
ifree = np.where(stepsize > 0)[0] # Free parameter indices
ishare = np.where(stepsize < 0)[0] # Shared parameter indices
# Number of model parameters (excluding wavelet parameters):
if wlike:
mpars = nparams - 3
else:
mpars = nparams
# Intermediate steps to run GR test and print progress report:
intsteps = chainlen / 10
# Allocate arrays with variables:
numaccept = np.zeros(nchains) # Number of accepted proposal jumps
outbounds = np.zeros((nchains, nfree), np.int) # Out of bounds proposals
allparams = np.zeros((nchains, nfree, chainlen)) # Parameter's record
if savemodel is not None:
allmodel = np.zeros((nchains, ndata, chainlen)) # Fit model
if resume:
oldparams = np.load(savefile)
nold = np.shape(oldparams)[2] # Number of old-run iterations
allparams = np.dstack((oldparams, allparams))
if savemodel is not None:
allmodel = np.dstack((np.load(savemodel), allmodel))
# Set params to the last-iteration state of the previous run:
params = np.repeat(params, nchains, 0)
params[:,ifree] = oldparams[:,:,-1]
else:
nold = 0
# Set MPI flag:
mpi = comm is not None
if mpi:
from mpi4py import MPI
# Send sizes info to other processes:
array1 = np.asarray([mpars, chainlen], np.int)
mu.comm_bcast(comm, array1, MPI.INT)
# DEMC parameters:
gamma = 2.4 / np.sqrt(2*nfree)
gamma2 = 0.001 # Jump scale factor of support distribution
# Least-squares minimization:
if leastsq:
fitargs = (params[0], func, data, uncert, indparams, stepsize, pmin, pmax,
prior, priorlow, priorup)
fitchisq, dummy = mf.modelfit(params[0,ifree], args=fitargs)
fitbestp = np.copy(params[0, ifree])
mu.msg(1, "Least-squares best-fitting parameters: \n{:s}\n\n".
format(str(fitbestp)), log)
# Replicate to make one set for each chain: (nchains, nparams):
if np.shape(params)[0] != nchains:
params = np.repeat(params, nchains, 0)
# Start chains with an initial jump:
for p in ifree:
# For each free param, use a normal distribution:
params[1:, p] = np.random.normal(params[0, p], stepsize[p], nchains-1)
# Stay within pmin and pmax boundaries:
params[np.where(params[:, p] < pmin[p]), p] = pmin[p]
params[np.where(params[:, p] > pmax[p]), p] = pmax[p]
# Update shared parameters:
for s in ishare:
params[:, s] = params[:, -int(stepsize[s])-1]
# Calculate chi-squared for model using current params:
models = np.zeros((nchains, ndata))
if mpi:
# Scatter (send) parameters to func:
mu.comm_scatter(comm, params[:,0:mpars].flatten(), MPI.DOUBLE)
# Gather (receive) evaluated models:
mpimodels = np.zeros(nchains*ndata, np.double)
mu.comm_gather(comm, mpimodels)
# Store them in models variable:
models = np.reshape(mpimodels, (nchains, ndata))
else:
for c in np.arange(nchains):
fargs = [params[c, 0:mpars]] + indparams # List of function's arguments
models[c] = func(*fargs)
# Calculate chi-squared for each chain:
currchisq = np.zeros(nchains)
c2 = np.zeros(nchains) # No-Jeffrey's chisq
for c in np.arange(nchains):
if wlike: # Wavelet-based likelihood (chi-squared, actually)
currchisq[c], c2[c] = dwt.wlikelihood(params[c, mpars:], models[c]-data,
(params[c]-prior)[iprior], priorlow[iprior], priorlow[iprior])
else:
currchisq[c], c2[c] = cs.chisq(models[c], data, uncert,
(params[c]-prior)[iprior], priorlow[iprior], priorlow[iprior])
# Scale data-uncertainties such that reduced chisq = 1:
if chisqscale:
chifactor = np.sqrt(np.amin(currchisq)/(ndata-nfree))
uncert *= chifactor
# Re-calculate chisq with the new uncertainties:
for c in np.arange(nchains):
if wlike: # Wavelet-based likelihood (chi-squared, actually)
currchisq[c], c2[c] = dwt.wlikelihood(params[c,mpars:], models[c]-data,
(params[c]-prior)[iprior], priorlow[iprior], priorlow[iprior])
else:
currchisq[c], c2[c] = cs.chisq(models[c], data, uncert,
(params[c]-prior)[iprior], priorlow[iprior], priorlow[iprior])
if leastsq:
fitchisq = currchisq[0]
# Get lowest chi-square and best fitting parameters:
bestchisq = np.amin(c2)
bestp = np.copy(params[np.argmin(c2)])
bestmodel = np.copy(models[np.argmin(c2)])
if savemodel is not None:
allmodel[:,:,0] = models
# Set up the random walks:
if walk == "mrw":
# Generate proposal jumps from Normal Distribution for MRW:
mstep = np.random.normal(0, stepsize[ifree], (chainlen, nchains, nfree))
elif walk == "demc":
# Support random distribution:
support = np.random.normal(0, stepsize[ifree], (chainlen, nchains, nfree))
# Generate indices for the chains such r[c] != c:
r1 = np.random.randint(0, nchains-1, (nchains, chainlen))
r2 = np.random.randint(0, nchains-1, (nchains, chainlen))
for c in np.arange(nchains):
r1[c][np.where(r1[c]==c)] = nchains-1
r2[c][np.where(r2[c]==c)] = nchains-1
# Uniform random distribution for the Metropolis acceptance rule:
unif = np.random.uniform(0, 1, (chainlen, nchains))
# Proposed iteration parameters and chi-square (per chain):
nextp = np.copy(params) # Proposed parameters
nextchisq = np.zeros(nchains) # Chi square of nextp
# Start loop:
mu.msg(1, "Start MCMC chains ({:s})".format(time.ctime()), log)
for i in np.arange(chainlen):
# Proposal jump:
if walk == "mrw":
jump = mstep[i]
elif walk == "demc":
jump = (gamma * (params[r1[:,i]]-params[r2[:,i]])[:,ifree] +
gamma2 * support[i] )
# Propose next point:
nextp[:,ifree] = params[:,ifree] + jump
# Check it's within boundaries:
outpars = np.asarray(((nextp < pmin) | (nextp > pmax))[:,ifree])
outflag = np.any(outpars, axis=1)
outbounds += ((nextp < pmin) | (nextp > pmax))[:,ifree]
for p in ifree:
nextp[np.where(nextp[:, p] < pmin[p]), p] = pmin[p]
nextp[np.where(nextp[:, p] > pmax[p]), p] = pmax[p]
# Update shared parameters:
for s in ishare:
nextp[:, s] = nextp[:, -int(stepsize[s])-1]
# Evaluate the models for the proposed parameters:
if mpi:
mu.comm_scatter(comm, nextp[:,0:mpars].flatten(), MPI.DOUBLE)
mu.comm_gather(comm, mpimodels)
models = np.reshape(mpimodels, (nchains, ndata))
else:
for c in np.where(~outflag)[0]:
fargs = [nextp[c, 0:mpars]] + indparams # List of function's arguments
models[c] = func(*fargs)
# Calculate chisq:
for c in np.where(~outflag)[0]:
if wlike: # Wavelet-based likelihood (chi-squared, actually)
nextchisq[c], c2[c] = dwt.wlikelihood(nextp[c,mpars:], models[c]-data,
(nextp[c]-prior)[iprior], priorlow[iprior], priorlow[iprior])
else:
nextchisq[c], c2[c] = cs.chisq(models[c], data, uncert,
(nextp[c]-prior)[iprior], priorlow[iprior], priorlow[iprior])
# Reject out-of-bound jumps:
nextchisq[np.where(outflag)] = np.inf
# Evaluate which steps are accepted and update values:
accept = np.exp(0.5 * (currchisq - nextchisq))
accepted = accept >= unif[i]
if i >= burnin:
numaccept += accepted
# Update params and chi square:
params [accepted] = nextp [accepted]
currchisq[accepted] = nextchisq[accepted]
# Check lowest chi-square:
if np.amin(c2) < bestchisq:
bestp = np.copy(params[np.argmin(c2)])
bestmodel = np.copy(models[np.argmin(c2)])
bestchisq = np.amin(c2)
# Store current iteration values:
allparams[:,:,i+nold] = params[:, ifree]
if savemodel is not None:
models[~accepted] = allmodel[~accepted,:,i+nold-1]
allmodel[:,:,i+nold] = models
# Print intermediate info:
if ((i+1) % intsteps == 0) and (i > 0):
mu.progressbar((i+1.0)/chainlen, log)
mu.msg(1, "Out-of-bound Trials:\n {:s}".
format(np.sum(outbounds, axis=0)), log)
mu.msg(1, "Best Parameters: (chisq={:.4f})\n{:s}".
format(bestchisq, str(bestp)), log)
# Gelman-Rubin statistic:
if grtest and (i+nold) > burnin:
psrf = gr.convergetest(allparams[:, :, burnin:i+nold+1:thinning])
mu.msg(1, "Gelman-Rubin statistic for free parameters:\n{:s}".
format(psrf), log)
if np.all(psrf < 1.01):
mu.msg(1, "All parameters have converged to within 1% of unity.", log)
# Save current results:
if savefile is not None:
np.save(savefile, allparams[:,:,0:i+nold])
if savemodel is not None:
np.save(savemodel, allmodel[:,:,0:i+nold])
# Stack together the chains:
allstack = allparams[0, :, burnin:]
for c in np.arange(1, nchains):
allstack = np.hstack((allstack, allparams[c, :, burnin:]))
# And the models:
if savemodel is not None:
modelstack = allmodel[0,:,burnin:]
for c in np.arange(1, nchains):
modelstack = np.hstack((modelstack, allmodel[c, :, burnin:]))
# Print out Summary:
mu.msg(1, "\nFin, MCMC Summary:\n------------------", log)
nsample = (chainlen-burnin)*nchains # This sample
ntotal = (nold+chainlen-burnin)*nchains
BIC = bestchisq + nfree*np.log(ndata)
redchisq = bestchisq/(ndata-nfree)
sdr = np.std(bestmodel-data)
fmtlen = len(str(ntotal))
mu.msg(1, "Burned in iterations per chain: {:{}d}".
format(burnin, fmtlen), log, 1)
mu.msg(1, "Number of iterations per chain: {:{}d}".
format(chainlen, fmtlen), log, 1)
mu.msg(1, "MCMC sample size: {:{}d}".
format(nsample, fmtlen), log, 1)
mu.msg(resume, "Total MCMC sample size: {:{}d}".
format(ntotal, fmtlen), log, 1)
mu.msg(1, "Acceptance rate: {:.2f}%\n ".
format(np.sum(numaccept)*100.0/nsample), log, 1)
meanp = np.mean(allstack, axis=1) # Parameters mean
uncertp = np.std(allstack, axis=1) # Parameter standard deviation
mu.msg(1, "Best-fit params Uncertainties Signal/Noise Sample "
"Mean", log, 1)
for i in np.arange(nfree):
mu.msg(1, "{: 15.7e} {: 15.7e} {:12.2f} {: 15.7e}".
format(bestp[ifree][i], uncertp[i],
np.abs(bestp[ifree][i])/uncertp[i], meanp[i]), log, 1)
if leastsq and np.any(np.abs((bestp[ifree]-fitbestp)/fitbestp) > 1e-08):
np.set_printoptions(precision=8)
mu.warning("MCMC found a better fit than the minimizer:\n"
" MCMC best-fitting parameters: (chisq={:.8g})\n {:s}\n"
" Minimizer best-fitting parameters: (chisq={:.8g})\n"
" {:s}".format(bestchisq, str(bestp[ifree]),
fitchisq, str(fitbestp)), log)
fmtl = len("%.4f"%BIC) # Length of string formatting
mu.msg(1, " ", log)
if chisqscale:
mu.msg(1, "sqrt(reduced chi-squared) factor: {:{}.4f}".
format(chifactor, fmtl), log, 1)
mu.msg(1, "Best-parameter's chi-squared: {:{}.4f}".
format(bestchisq, fmtl), log, 1)
mu.msg(1, "Bayesian Information Criterion: {:{}.4f}".
format(BIC, fmtl), log, 1)
mu.msg(1, "Reduced chi-squared: {:{}.4f}".
format(redchisq, fmtl), log, 1)
mu.msg(1, "Standard deviation of residuals: {:.6g}\n".format(sdr), log, 1)
if rms:
rms, rmse, stderr, bs = ta.binrms(bestmodel-data)
if plots:
print("Plotting figures ...")
# Extract filename from savefile:
if savefile is not None:
if savefile.rfind(".") == -1:
fname = savefile[savefile.rfind("/")+1:] # Cut out file extention.
else:
fname = savefile[savefile.rfind("/")+1:savefile.rfind(".")]
else:
fname = "MCMC"
# Trace plot:
mp.trace(allstack, thinning=thinning, savefile=fname+"_trace.png",
sep=np.size(allstack[0])/nchains)
# Pairwise posteriors:
mp.pairwise(allstack, thinning=thinning, savefile=fname+"_pairwise.png")
# Histograms:
mp.histogram(allstack, thinning=thinning, savefile=fname+"_posterior.png")
# RMS vs bin size:
if rms:
mp.RMS(bs, rms, stderr, rmse, binstep=len(bs)/500+1,
savefile=fname+"_RMS.png")
if indparams != [] and np.size(indparams[0]) == ndata:
mp.modelfit(data, uncert, indparams[0], bestmodel,
savefile=fname+"_model.png")
# Save definitive results:
if savefile is not None:
np.save(savefile, allparams)
if savemodel is not None:
np.save(savemodel, allmodel)
return allstack, bestp
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.
Modification History:
---------------------
2014-04-19 patricio Initial implementation. [email protected]
2014-05-04 patricio Added cfile argument for Interpreter support.
2014-05-26 patricio Re-engineered the MPI support.
2014-06-26 patricio Fixed bug with copy when uncert is None.
2014-09-14 patricio Write/read now binary files.
2014-10-23 patricio Added support for func hack.
2015-02-04 patricio Added resume argument.
2015-05-15 patricio Added logfile argument.
"""
# 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("-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
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 not found.", log)
array = mu.read2array(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 not found.", log)
pmin = mu.read2array(pmin[0])[0]
if pmax is not None and isinstance(pmax[0], str):
if not os.path.isfile(pmax[0]):
mu.error("'pmax' file not found.", log)
pmax = mu.read2array(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 not found.", log)
stepsize = mu.read2array(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 not found.", log)
prior = mu.read2array(prior[0])[0]
if priorlow is not None and isinstance(priorlow[0], str):
if not os.path.isfile(priorlow[0]):
mu.error("'priorlow' file not found.", log)
priorlow = mu.read2array(priorlow[0])[0]
if priorup is not None and isinstance(priorup[0], str):
if not os.path.isfile(priorup[0]):
mu.error("'priorup' file not found.", log)
priorup = mu.read2array(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 not found.", log)
array = mu.readbin(data[0])
data = array[0]
if len(array) == 2:
uncert = array[1]
if uncert is not None and isinstance(uncert[0], str):
if not os.path.isfile(uncert[0]):
mu.error("'uncert' file not found.", log)
uncert = mu.readbin(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 not found.", log)
indparams = mu.readbin(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, 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()
