Generates bootstrap samples for effective mass values computed from an
object of class cf (a correlation function)
bootstrap.effectivemass(cf, type = "solve")a correlation function as an object of type cf, preferably
after a call to bootstrap.cf. If the latter has not been
called yet, it will be called in this function.
The function to be used to compute the effective mass values.
Possibilities are "acosh", "solve", "log", "temporal", "shifted" and
"weighted". While the first three assume normal cosh behaviour of the
correlation function, "temporal" is desigend to remove an additional
constant stemming from temporal states in two particle correlation
functions. The same for "shifted" and "weighted", the latter for the case of
two particle energies with the two particle having different energies. In
the latter case only the leading polution is removed by
removeTemporal.cf and taken into account here.
An object of class effectivemass is invisibly returned. It
has objects: effMass: The computed effective mass values as a
vector of length Time/2. For type="acosh" also the first value
is NA, because this definition requires three time slices.
deffMass: The computed bootstrap errors for the effective masses
of the same length as effMass.
effMass.tsboot: The boostrap samples of the effective masses as an
array of dimension RxN, where R=boot.R is the number of bootstrap
samples and N=(Time/2+1).
and boot.R, boot.l, Time
A number of types is implemented to compute effective mass values from the correlation function:
"solve": the ratio \(C(t+1) / C(t) = \cosh(-m*(t+1)) / \cosh(-m*t)\) is numerically solved for m.
"acosh": the effective mass is computed from \(m=acosh((C(t-1)+C(t+1)) / (2C(t)))\) Note that this definition is less tolerant against noise.
"log": the effective mass is defined via \(m=\log(C(t) / C(t+1))\) which has artifacts of the periodicity at large t-values.
"temporal": the ratio \([C(t)-C(t+1)] / [C(t-1)-C(t)] = [\cosh(-m*(t))-\cosh(-m*(t+1))] / [\cosh(-m*(t-1))-\cosh(-m(t))]\) is numerically solved for \(m(t)\).
"shifted": like "temporal", but the differences \(C(t)-C(t+1)\) are
assumed to be taken already at the correlator matrix level using
removeTemporal.cf and hence the ratio \([C(t+1)] / [C(t)] =
[\cosh(-m*(t))-\cosh(-m*(t+1))] / [\cosh(-m*(t-1))-\cosh(-m(t))]\) is
numerically solved for \(m(t)\).
"weighted": like "shifted", but now there is an additional weight factor
\(w\) from removeTemporal.cf to be taken into account, such that
the ratio \([C(t+1)] / [C(t)] = [\cosh(-m*(t))-w*\cosh(-m*(t+1))] /
[\cosh(-m*(t-1))-w*\cosh(-m(t))]\) is numerically solved for \(m(t)\)
with \(w\) as input.
arXiv:1203.6041
fit.effectivemass, bootstrap.cf,
removeTemporal.cf
# NOT RUN {
data(samplecf)
samplecf <- bootstrap.cf(cf=samplecf, boot.R=99, boot.l=2, seed=1442556)
effmass <- bootstrap.effectivemass(cf=samplecf)
summary(effmass)
plot(effmass, ylim=c(0.14,0.15))
# }
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