Thomas Petzoldt - Homepage
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Tutorials, Tools, Downloads
Most downloads and examples below use the R software and you
may ask why. R is known as a system for statistical data
analysis and graphics, but R is more. It is an efficient
matrix-based programming language that can be used as a general
tool for data analysis, simulation and visualization.
Several years we were working with different systems and
languages like Fortran, Basic, Pascal, Delphi, JAVA, C/C++,
Spreadsheets, Simulation Dynamics tools and even other matrix
oriented environments. Now we do most (but not all) things in R
and some time critical parts in C. This has nothing to do with
any kind of "fundamentalism", it naturally developed because of
R's efficiency: it is fast enough, has packages for "almost
everything", can read and write data bases, produces good
graphics, has documentation facilities (esp. Sweave) and has a community that agreed to use
publications for getting scientific credit. We use, of
course, other software tools too, but only with R we reached
a level where we felt that it was worth to make our tools
publicly available.
Differential Equation Solvers
- Package deSolve (Soetaert, Petzoldt,
Setzer) is the main workhorse for solving initial value
problems of differential equations.
- It contains:
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- state of the art solvers for ODE, DAE, DDE and
PDE-Models from ODEPACK (lsoda, lsode, daspk, vode,
...)
- explicit Runge-Kutta solvers (euler, rk4, ode23, ode45,
rk78f, ...) and
- implicit Runge-Kutta (RADAU II A).
- Functions ode.1D, ode.2D and ode.3D for solving
1, 2 and 3 dimensional problems.
- Most solvers support events and/or delays.
- The model equations can be writtern in pure R or in
compiled languages (C, Fortran) to circumvent speed
limitations of R. If a model can be written in matrix
notation, R is usually fast enough.
- deSolve website: http://desolve.r-forge.r-project.org
(with a overview over related documents and
publications)
- Main publication: http://www.jstatsoft.org/v33/i09 (Soetaert,
Petzoldt, Setzer)
- Download: http://cran.r-project.org/package=deSolve
- Books that use deSolve: Soetaert & Hermann (2008), Ellner & Guckenheimer (2006), Stevens (2009)
- Talks given at the useR!2009 conference in Rennes,
France:
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- Karline Soetaert: Mathematical modelling of the
environment - are there enough data? [slides]
- Thomas Petzoldt: Dynamic simulation models - is R
powerful enough? [slides]
==> More differential equation solvers (e.g. for
boundary value problems) and related R packages (e.g. reactive
transport equations) can be found on the homepage of Karline Soetaert.
Packages for Analysis of the Model Output and Confronting
Models with Data
- R package qualV (Jachner, Boogaart,
Petzoldt contains model validation criteria, especially for
models with time delay)
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- R package FME (Soetaert, Petzoldt) implements tools
for model fitting and analysis of model results, e.g.
sensitivity indicators and Markov chain Monte Carlo
(MCMC)
-
Packages for Object Oriented Implementation of Dynamic
Models
In contrast to other object oriented (OOP) approaches that
implement an object oriented model of the original system,
simecol implements an "object model of models". Here the main
parts of a model are the equations, parameters, time steps and
a solver function. This structure is rather close to a
mathematical notation, so it is easy to re-implement existing
models from the literature or to share own models with
colleagues. This approach is rather general and can be used
for differential equations as well as individual-based and
other approaches, not only in ecology but also for social
sciences, economy or engineering. The advantage is that an
object encapsulates everything needed, so that you can easily
compare models with different data or equations within the
same session.
- R package proto (Grothendieck and
Petzoldt)
The package "simecol" uses the standard S4 class system of R,
in order to be "mainstream compatible". In contrast to this
"proto" implements an own
prototype-based (i.e. classless) object orientation. It
shows that R is also suitable as playground for exploring
(and using) different object oriented systems.
Specific packages for Aquatic Sciences
- Package marelac (Soetaert, Petzoldt, Meysman)
contains: (1) chemical and physical constants and datasets,
e.g. atomic weights, gas constants, the earths bathymetry;
(2) conversion factors (e.g. gram to mol to liter,
barometric units, temperature, salinity); (3) physical
functions, e.g. to estimate concentrations of conservative
substances, gas transfer and diffusion coefficients, the
Coriolis force and gravity; (4) thermophysical properties
of the seawater, as from the UNESCO polynomial or from the
more recent derivation based on a Gibbs function.
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- R package cardidates (Rolinski, Sachse,
Petzoldt) can be used for peak-fitting and determination of
"cardinal dates" in phytoplankton time series)
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- Publication (of the methods): Rolinski, S., Horn, H.,
Petzoldt, T., & Paul, L. (2007): Identification of
cardinal dates in phytoplankton time series to enable the
analysis of long-term trends. Oecologia
153, 997 - 1008.
- Project website: http://cardidates.r-forge.r-project.org/
- More information: cardidates tutorial
Other Tutorials and Examples about Modeling and Statistics
with R
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thomas.petzoldt@