Linear Inverse Model examples and solution methods

Description

functions that read and solve linear inverse problems (food web problems, linear programming problems, flux balance analysis).

These problems find solutions to linear or quadratic functions: min or max (f(x)), where f(x) = ||Ax-b||^2 or f(x) = sum(ai*xi)

subject to equality constraints Ex=f and inequality constraints Gx>=h.

Uses package limSolve.

Details

The model problem is formulated in text files in a way that is natural and comprehensible. Functions in LIM then converts this input into the required linear equality and inequality conditions, which can be solved either by least squares or by linear programming techniques. By letting an algorithm formulate the mathematics, it is simple to reformulate the model in case a parameter value changes, or a component is added or removed.

Three different types of problems are supported:

flow networks,

reaction networks (e.g. flux balance analysis).

and other (operations research) problems.

The first two cases are based on mass balances of the components.

The package includes many examples

Author(s)

Karline Soetaert (Maintainer),

Dick van Oevelen

References

Description of the software:

van Oevelen D, Van den Meersche K, Meysman FJR Soetaert K, Middelburg JJ, Vezina AF., 2009. Quantifying Food Web Flows Using Linear Inverse Models. Ecosystems 13: 32-45 DOI: 10.1007/s10021-009-9297-6. http://www.springerlink.com/content/4q6h4011511731m5/fulltext.pdf

(please use the above citation when using the software)

About food web modelling:

Soetaert, K., van Oevelen, D., 2009. Modeling food web interactions in benthic deep-sea ecosystems: a practical guide. Oceanography (22) 1: 130-145.

Application of deep-water food web:

van Oevelen, Dick, Gerard Duineveld, Marc Lavaleye, Furu Mienis, Karline Soetaert, and Carlo H. R. Heip, 2009. The cold-water coral community as hotspot of carbon cycling on continental margins: A food web analysis from Rockall Bank (northeast Atlantic). Limnology and Oceangraphy 54:1829-1844.

http://www.aslo.org/lo/toc/vol_54/issue_6/1829.pdf

A flux balance analysis application:

Karline Soetaert. Escherichia coli Core Metabolism Model in LIM. LIM package vignette (see also below).

See Also

Read, Setup for reading files and creating the model

Ldei, Lsei,Linp,

Flowmatrix, Plotranges, Variables,

Varranges, Xranges, Xsample.

Examples

## Not run: 
## show examples (see respective help pages for details)
example(Lsei)
example(LIMRigaSpring)
example(Ldei)
example(Xsample)
example(Varranges)

## run demos
demo("LIMexamples")

## open the directory with R sourcecode examples
browseURL(paste(system.file(package="LIM"), "/doc/examples/Foodweb", sep=""))
browseURL(paste(system.file(package="LIM"), "/doc/examples/LinearProg", sep=""))
browseURL(paste(system.file(package="LIM"), "/doc/examples/Reactions", sep=""))

## the deep-water coral food -web
browseURL(paste(system.file(package="LIM"), "/doc/examples/Foodweb/coral", sep=""))

## show package vignette with tutorial about how to create input files
vignette("LIM")

## E.coli example vignette - flux balance analysis
vignette("LIMecoli")

browseURL(paste(system.file(package="LIM"), "/doc", sep=""))

## End(Not run)

Results