determines pion mass and pcac mass from online measured correlator of the HMC code
onlinemeas(data, t1, t2, stat_range, S = 1.5, pl = FALSE, skip = 0,
iobs = 1, ind.vec = c(1, 3, 4, 5), mu = 0.1, kappa = 0.125,
boot.R = 99, boot.l = 10, tsboot.sim = "geom", method = "uwerr",
fit.routine = "optim", nrep, oldnorm = FALSE)data to be fitted to as e.g. the output of
readcmicor. Currently only cmicor format is supported.
lower bound for the fitrange in time (t1,t2). Counting starts with 0.
upper bound for the fitrange in time (t1,t2). Counting starts with 0.
range of data to be included in the analysis.
passed to uwerr, see documentation of uwerr.
logical: if set to TRUE the function produces plots
number of measurements to be discarded at the beginning of the
time series. skip has no effect if two or more replica are used, see
argument nrep.
if there are several operators available (local-local, local-smeared, etc.), then this labels these (for cmi format)
index vector indexing the column numbers in cmicor to be used
twisted mass parameter.
hopping parameter.
number of bootstrap samples for bootstrap analysis
average block size for blocking analysis with tsboot
The type of simulation required to generate the replicate
time series. See tsboot for details.
the type of error analysis to be used. Can be either “uwerr”, “boot”, “all” or “no”. For “no” (or any other string) no error analysis is performed. This might be helpful for a first impression and also to test different initial values for the fitting parameters. The latter is in particular needed for more than one state in the fit.
The fit routine to be used. Default is “gsl”, which uses the gnu scientific library “gsl_multifit_fdfsolver” solver to minimise the chisquare. All other values lead to the usage of R's optim function. The latter choice might be significantly slower.
vector (N1, N2, ...) of replica length N1, N2. If missing it is
assumed that there is only one ensemble. If there are two or more replica
the parameter skip has no effect.
If set to “TRUE”, the old online measurement normalisation of “tmLQCD” prior to version 5.2.0 is used in order to get correct values for the pion decay constant.
returns an object of class ofit with the following
items
result from the fit as returned by optim
Fit result of the PP correlator only
lower bound for the fitrange in time (t1,t2). Counting starts with 0.
upper bound for the fitrange in time (t1,t2). Counting starts with 0.
number of measurements found in the data
Time extent found in the data
data.frame
containing the time values used in the fit, the averaged correlator and its
error and the value of Chi for each time value
the
result of the time series analysis for the lowest mass as carried out by
uwerr
the result of the time series
analysis for the PCAC mass carried out by uwerr, see details
effective masses in the pion channel
size of the data matrix, copied from input
object returned by
the call to boot if method was set correspodingly.
Otherwise NULL.
object returned by the call to
tsboot if method was set correspodingly. Otherwise
NULL.
error analysis method as copied from input
fit.routine as copied from input
nrep as copied from input
data.frame
containing the pcac masses computed not with a fit, but with the derivative
method for all time values in between t1 and t2
The online measurements in the HMC code compute the PP and PA correlation functions summed over spatial x for all t. We analyse these correlators in different ways:
First, only the PP correlator is analysed and fitted by \(p_1^2\cosh(-m(t-T/2))\) for \(m\) and \(p_1\).
Second, PP and PA correlators are fitted together with three parameters as \(C_\mathrm{PP} = p_1^2\cosh(-m(t-T/2))\) and \(C_\mathrm{PA} = \)\( p_1p_2\cosh(-m(t-T/2))\) in a simultaneous fit. \(m\) is then the pseudo scalar mass and the pcac mass is determined from $$m_\mathrm{PCAC} = m_\mathrm{PS} \frac{p_2}{2p_1}$$
Finally, the PCAC mass can also be determined computing $$m_\mathrm{PCAC}(t) =% $$$$ \frac{C_\mathrm{PA}(t+1)-C_\mathrm{PA}(t-1)}{4C_\mathrm{PP}(t)}$$ using the symmetric finite difference operator.