g_analyze Main Table of Contents

VERSION 4.6.5 Mon 2 Dec 2013

Description

g_analyze reads an ASCII file and analyzes data sets. A line in the input file may start with a time (see option -time) and any number of y-values may follow. Multiple sets can also be read when they are separated by & (option -n); in this case only one y-value is read from each line. All lines starting with # and @ are skipped. All analyses can also be done for the derivative of a set (option -d).

All options, except for -av and -power, assume that the points are equidistant in time.

g_analyze always shows the average and standard deviation of each set, as well as the relative deviation of the third and fourth cumulant from those of a Gaussian distribution with the same standard deviation.

Option -ac produces the autocorrelation function(s). Be sure that the time interval between data points is much shorter than the time scale of the autocorrelation.

Option -cc plots the resemblance of set i with a cosine of i/2 periods. The formula is:
2 (integral from 0 to T of y(t) cos(i π t) dt)^2 / integral from 0 to T of y^2(t) dt
This is useful for principal components obtained from covariance analysis, since the principal components of random diffusion are pure cosines.

Option -msd produces the mean square displacement(s).

Option -dist produces distribution plot(s).

Option -av produces the average over the sets. Error bars can be added with the option -errbar. The errorbars can represent the standard deviation, the error (assuming the points are independent) or the interval containing 90% of the points, by discarding 5% of the points at the top and the bottom.

Option -ee produces error estimates using block averaging. A set is divided in a number of blocks and averages are calculated for each block. The error for the total average is calculated from the variance between averages of the m blocks B_i as follows: error^2 = sum (B_i - )^2 / (m*(m-1)). These errors are plotted as a function of the block size. Also an analytical block average curve is plotted, assuming that the autocorrelation is a sum of two exponentials. The analytical curve for the block average is:
f(t) = σ*sqrt(2/T ( α (τ_1 ((exp(-t/τ_1) - 1) τ_1/t + 1)) +
(1-α) (τ_2 ((exp(-t/τ_2) - 1) τ_2/t + 1)))),
where T is the total time. α, τ_1 and τ_2 are obtained by fitting f^2(t) to error^2. When the actual block average is very close to the analytical curve, the error is σ*sqrt(2/T (a τ_1 + (1-a) τ_2)). The complete derivation is given in B. Hess, J. Chem. Phys. 116:209-217, 2002.

Option -bal finds and subtracts the ultrafast "ballistic" component from a hydrogen bond autocorrelation function by the fitting of a sum of exponentials, as described in e.g. O. Markovitch, J. Chem. Phys. 129:084505, 2008. The fastest term is the one with the most negative coefficient in the exponential, or with -d, the one with most negative time derivative at time 0. -nbalexp sets the number of exponentials to fit.

Option -gem fits bimolecular rate constants ka and kb (and optionally kD) to the hydrogen bond autocorrelation function according to the reversible geminate recombination model. Removal of the ballistic component first is strongly advised. The model is presented in O. Markovitch, J. Chem. Phys. 129:084505, 2008.

Option -filter prints the RMS high-frequency fluctuation of each set and over all sets with respect to a filtered average. The filter is proportional to cos(π t/len) where t goes from -len/2 to len/2. len is supplied with the option -filter. This filter reduces oscillations with period len/2 and len by a factor of 0.79 and 0.33 respectively.

Option -g fits the data to the function given with option -fitfn.

Option -power fits the data to b t^a, which is accomplished by fitting to a t + b on log-log scale. All points after the first zero or with a negative value are ignored.

Option -luzar performs a Luzar & Chandler kinetics analysis on output from g_hbond. The input file can be taken directly from g_hbond -ac, and then the same result should be produced.

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