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TWiSt
Langevin
Commits
7b8b9dbd
Commit
7b8b9dbd
authored
Feb 16, 2016
by
Philip Rinn
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^.*\.Rproj$
^\.Rproj\.user$
R/RcppExports.R
.gitignore
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.Rproj.user
.Rhistory
.RData
Langevin.Rproj
src/*.o
src/*.so
src/*.dll
ChangeLog
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2016-01-27 Philip Rinn <philip.rinn@uni-oldenburg.de>
* OpenMP: Use recommended method to set the number of used threads
2015-11-02 Philip Rinn <philip.rinn@uni-oldenburg.de>
* Add missing importFroms
* Tag as version 1.1.1
2015-11-02 Philip Rinn <philip.rinn@uni-oldenburg.de>
* Add citation file
* Update vignette
* Tag as version 1.1
2015-10-21 Philip Rinn <philip.rinn@uni-oldenburg.de>
* Add plot function for class 'Langevin' (only for 1D)
2015-10-19 Philip Rinn <philip.rinn@uni-oldenburg.de>
* Add print function for class 'Langevin'
2015-10-16 Philip Rinn <philip.rinn@uni-oldenburg.de>
* Add summary function for class 'Langevin'
2015-09-07 Philip Rinn <philip.rinn@uni-oldenburg.de>
* Langevin{1,2}D: read sampling frequency from time-series object
* Langevin2D: time-series need to be arranged as columns now!
2015-09-03 Philip Rinn <philip.rinn@uni-oldenburg.de>
* timeseries{1,2}D: output is a time-series object now
* timeseries2D: time-series are the columns of the returned object now!
2015-08-26 Philip Rinn <philip.rinn@uni-oldenburg.de>
* Use title case for package title
* Tag as version 1.0.3
2015-08-26 Philip Rinn <philip.rinn@uni-oldenburg.de>
* Don't install vignette source files in inst/doc
* Tag as version 1.0.2
2015-08-25 Philip Rinn <philip.rinn@uni-oldenburg.de>
* Add paper submitted to JSS as vignette
* Tag as version 1.0.1
2015-08-25 Philip Rinn <philip.rinn@uni-oldenburg.de>
* Update package description
* Tag as version 1.0
2015-07-21 Philip Rinn <philip.rinn@uni-oldenburg.de>
* Langevin1D: calculate error of the Diffusion
2015-07-21 Philip Rinn <philip.rinn@uni-oldenburg.de>
* Add description of package
* Langevin1D: move part of the documentation to package description
2015-07-16 Philip Rinn <philip.rinn@uni-oldenburg.de>
* timeseries2D: major cleanup
* rewrite to use matrices as input for the coefficients
* use cubic drift and quadratic diffusion polynomial
* output is a matrix with two rows now
* timeseries1D: use cubic drift and quadratic diffusion polynomial
2015-07-15 Philip Rinn <philip.rinn@uni-oldenburg.de>
* Rename timeseries -> timeseries1D to be consistent with Langevin{1,2}D
* timeseries{1,2}D: remove argument seed:
* One should use set.seed(seed) before calling timeseries{1,2}D instead
2015-02-16 Philip Rinn <philip.rinn@uni-oldenburg.de>
* Use 'Rcpp Attributes' to generate the glue between C++ and R.
2015-01-13 Philip Rinn <philip.rinn@uni-oldenburg.de>
* Add Pedro G. Lind to package authors
2015-01-13 Pedro G. Lind <pedro.g.lind@forwind.de>
* Add function timeseries2D: Generate a two-dimensional Langevin process
2014-09-03 Philip Rinn <philip.rinn@uni-oldenburg.de>
* Langevin2D: Do the linear regression right
* linreg.h: catch situations where no solution is found
2014-02-24 Philip Rinn <philip.rinn@uni-oldenburg.de>
* Langevin{1,2}D: Make minimal number of events per bin configurable
2014-02-19 Philip Rinn <philip.rinn@uni-oldenburg.de>
* Langevin1D: Use weighted linear regression to determine D2
2014-02-17 Philip Rinn <philip.rinn@uni-oldenburg.de>
* Langevin2D: Use weighted linear regression to determine D1
2014-02-14 Philip Rinn <philip.rinn@uni-oldenburg.de>
* Langevin1D: Use weighted linear regression to determine D1
2013-06-11 Philip Rinn <philip.rinn@uni-oldenburg.de>
* Avoid extra copy of large input variables in C++ code
2013-05-31 Philip Rinn <philip.rinn@uni-oldenburg.de>
* timeseries: be a little smarter to allow longer time series
2013-03-26 Philip Rinn <philip.rinn@uni-oldenburg.de>
* timeseries: sampling frequency is a double now
2013-03-15 Philip Rinn <philip.rinn@uni-oldenburg.de>
* Switch documentation to in-source with roxygen2
2012-12-17 Philip Rinn <philip.rinn@uni-oldenburg.de>
* timeseries: if no seed it given use a random one to preserve old behavior
2012-12-10 Philip Rinn <philip.rinn@uni-oldenburg.de>
* timeseries: adding ability so set the seed for the RNG
2012-11-20 Philip Rinn <philip.rinn@uni-oldenburg.de>
* Add David Bastine to package contributors
2012-11-20 David Bastine <david.bastine@uni-oldenburg.de>
* timeseries: adding integration time step as optional argument
2012-09-03 Philip Rinn <philip.rinn@uni-oldenburg.de>
* Langevin{1,2}D: adding option to set the number of threads
2012-09-03 Philip Rinn <philip.rinn@uni-oldenburg.de>
* BugFix: Again: don't try to be smarter than you are in Langevin{1,2}D
2012-08-24 Philip Rinn <philip.rinn@uni-oldenburg.de>
* Add function timeseries
2012-08-15 Philip Rinn <philip.rinn@uni-oldenburg.de>
* BugFix: check for NAs when calculation mean_bins in Langevin2D
2012-08-13 Philip Rinn <philip.rinn@uni-oldenburg.de>
* BugFix: Don't over-optimize in Langevin{1,2}D
2012-08-09 Philip Rinn <philip.rinn@uni-oldenburg.de>
* Langevin2D: Mayor rewrite of the function:
* Pure C++ now
* Output of D2 changed from (bins,bins,2,2) to (bins,bins,3)!
2012-08-08 Philip Rinn <philip.rinn@uni-oldenburg.de>
* BugFix: corrected D2 estimation in Langevin1D
* Update documentation of Langevin{1,2}D
2012-08-06 Philip Rinn <philip.rinn@uni-oldenburg.de>
* Update documentation of Langevin1D
2012-07-04 Philip Rinn <philip.rinn@uni-oldenburg.de>
* Update the C++ and linker flags for Windows builds
* Byte-compile functions by default
2012-05-25 Philip Rinn <philip.rinn@uni-oldenburg.de>
* Add generic functions for 1D and 2D Langevin analysis: Langevin{1,2}D
* Initiate the package
DESCRIPTION
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Package: Langevin
Type: Package
Title: Langevin Analysis in One and Two Dimensions
Version: 1.1.1
Date: 2015-11-03
Authors@R: c(person('Philip', 'Rinn', email='philip.rinn@uni-oldenburg.de',
role=c('aut','cre')), person('Pedro G.', 'Lind', role='aut'),
person('David', 'Bastine', role='ctb'))
Description: Estimate drift and diffusion functions from time series and
generate synthetic time series from given drift and diffusion coefficients.
Encoding: UTF-8
License: GPL (>= 2)
LazyLoad: yes
ByteCompile: yes
NeedsCompilation: yes
Depends:
R (>= 3.0.2)
Imports:
Rcpp (>= 0.11.0)
LinkingTo: Rcpp, RcppArmadillo (>= 0.4.600.0)
RoxygenNote: 5.0.1
GPL-2
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NAMESPACE
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# Generated by roxygen2: do not edit by hand
S3method(plot,Langevin)
S3method(print,Langevin)
S3method(summary,Langevin)
export(Langevin1D)
export(Langevin2D)
export(timeseries1D)
export(timeseries2D)
import(Rcpp)
importFrom(graphics,par)
importFrom(graphics,plot)
importFrom(stats,frequency)
importFrom(stats,is.mts)
importFrom(stats,is.ts)
importFrom(stats,median)
useDynLib(Langevin)
R/Langevin-package.r
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#' An \R package for stochastic data analysis
#'
#' The \pkg{Langevin} package provides functions to estimate drift and
#' diffusion functions from data sets.
#'
#'
#' This package was developed by the research group
#' \emph{Turbulence, Wind energy and Stochastics} (TWiSt) at the Carl von
#' Ossietzky University of Oldenburg (Germany).
#'
#' @section Mathematical Background: A wide range of dynamic systems can be
#' described by a stochastic differential equation, the Langevin equation. The
#' time derivative of the system trajectory \eqn{\dot{X}(t)} can be expressed as
#' a sum of a deterministic part \eqn{D^{(1)}} and the product of a stochastic
#' force \eqn{\Gamma(t)} and a weight coefficient \eqn{D^{(2)}}. The stochastic
#' force \eqn{\Gamma(t)} is \eqn{\delta}-correlated Gaussian white noise.
#'
#' For stationary continuous Markov processes Siegert et al. and Friedrich et
#' al. developed a method to reconstruct drift \eqn{D^{(1)}} and diffusion
#' \eqn{D^{(2)}} directly from measured data.
#'
#' \deqn{ \dot{X}(t) = D^{(1)}(X(t),t) + \sqrt{D^{(2)}(X(t),t)}\,\Gamma(t)\quad
#' \mathrm{with} } \deqn{ D^{(n)}(x,t) = \lim_{\tau \rightarrow 0}
#' \frac{1}{\tau} M^{(n)}(x,t,\tau)\quad \mathrm{and} } \deqn{ M^{(n)}(x,t,\tau)
#' = \frac{1}{n!} \langle (X(t+\tau) - x)^n \rangle |_{X(t) = x} }
#'
#' The Langevin equation should be interpreted in the way that for every time
#' \eqn{t_i} where the system meets an arbitrary but fixed point \eqn{x} in
#' phase space, \eqn{X(t_i+\tau)} is defined by the deterministic function
#' \eqn{D^{(1)}(x)} and the stochastic function
#' \eqn{\sqrt{D^{(2)}(x)}\Gamma(t_i)}. Both, \eqn{D^{(1)}(x)} and
#' \eqn{D^{(2)}(x)} are constant for fixed \eqn{x}.
#'
#' One can integrate drift and diffusion numerically over small intervals. If
#' the system is at time \eqn{t} in the state \eqn{x = X(t)} the drift can be
#' calculated for small \eqn{\tau} by averaging over the difference of the
#' system state at \eqn{t+\tau} and the state at \eqn{t}. The average has to be
#' taken over the whole ensemble or in the stationary case over all \eqn{t =
#' t_i} with \eqn{X(t_i) = x}. Diffusion can be calculated analogously.
#'
#'
#' @name Langevin-package
#' @aliases Langevin-package
#' @docType package
#' @author Philip Rinn
#' @references
#'
#' \bold{A review of the Langevin method can be found at:}
#'
#' Friedrich, R.; et al. (2011) \emph{Approaching Complexity by Stochastic
#' Methods: From Biological Systems to Turbulence}. Physics Reports, 506(5), 87–162.
#'
#' \bold{For further reading:}
#'
#' Risken, H. (1996) \emph{The Fokker-Planck equation}. Springer.
#'
#' Siegert, S.; et al. (1998) \emph{Analysis of data sets of stochastic
#' systems}. Phys. Lett. A.
#'
#' Friedrich, R.; et al. (2000) \emph{Extracting model equations from
#' experimental data}. Phys. Lett. A.
NULL
R/Langevin1D.r
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#' Calculate the Drift and Diffusion of one-dimensional stochastic processes
#'
#' \code{Langevin1D} calculates the Drift and Diffusion vectors (with errors)
#' for a given time series.
#'
#'
#' @param data a vector containing the time series or a time-series object.
#' @param bins a scalar denoting the number of \code{bins} to calculate the
#' conditional moments on.
#' @param steps a vector giving the \eqn{\tau} steps to calculate the
#' conditional moments (in samples (=\eqn{\tau * sf})).
#' @param sf a scalar denoting the sampling frequency (optional if \code{data}
#' is a time-series object).
#' @param bin_min a scalar denoting the minimal number of events per \code{bin}.
#' Defaults to \code{100}.
#' @param reqThreads a scalar denoting how many threads to use. Defaults to
#' \code{-1} which means all available cores.
#'
#' @return \code{Langevin1D} returns a list with thirteen components:
#' @return \item{D1}{a vector of the Drift coefficient for each \code{bin}.}
#' @return \item{eD1}{a vector of the error of the Drift coefficient for each
#' \code{bin}.}
#' @return \item{D2}{a vector of the Diffusion coefficient for each \code{bin}.}
#' @return \item{eD2}{a vector of the error of the Driffusion coefficient for
#' each \code{bin}.}
#' @return \item{D4}{a vector of the fourth Kramers-Moyal coefficient for each
#' \code{bin}.}
#' @return \item{mean_bin}{a vector of the mean value per \code{bin}.}
#' @return \item{density}{a vector of the number of events per \code{bin}.}
#' @return \item{M1}{a matrix of the first conditional moment for each
#' \eqn{\tau}. Rows corespond to \code{bin}, columns to \eqn{\tau}.}
#' @return \item{eM1}{a matrix of the error of the first conditional moment
#' for each \eqn{\tau}. Rows corespond to \code{bin}, columns to \eqn{\tau}.}
#' @return \item{M2}{a matrix of the second conditional moment for each
#' \eqn{\tau}. Rows corespond to \code{bin}, columns to \eqn{\tau}.}
#' @return \item{eM2}{a matrix of the error of the second conditional moment
#' for each \eqn{\tau}. Rows corespond to \code{bin}, columns to \eqn{\tau}.}
#' @return \item{M4}{a matrix of the fourth conditional moment for each
#' \eqn{\tau}. Rows corespond to \code{bin}, columns to \eqn{\tau}.}
#' @return \item{U}{a vector of the \code{bin} borders.}
#'
#' @author Philip Rinn
#' @seealso \code{\link{Langevin2D}}
#' @examples
#'
#' # Set number of bins, steps and the sampling frequency
#' bins <- 20;
#' steps <- c(1:5);
#' sf <- 1000;
#'
#' #### Linear drift, constant diffusion
#'
#' # Generate a time series with linear D^1 = -x and constant D^2 = 1
#' x <- timeseries1D(N=1e6, d11=-1, d20=1, sf=sf);