R: Solving Linear Inverse Models

limSolve-package {limSolve} | R Documentation

## Solving Linear Inverse Models

### Description

Functions that:

(1.) Find the minimum/maximum of a linear or quadratic function: min or max (f(x)), where f(x) = ||Ax-b||^2 or f(x) = sum(ai*xi) subject to equality constraints Ex=f and/or inequality constraints Gx>=h.

(2.) Sample an underdetermined- or overdetermined system Ex=f subject to Gx>=h, and if applicable Ax~=b.

(3.) Solve a linear system Ax=B for the unknown x. Includes banded and tridiagonal linear systems.

The package calls Fortran functions from LINPACK

### Details

Package: | limSolve
Type: | Package
Version: | 1.5.4
Date: | 2013-23-01
License: | GNU Public License 2 or above

limSolve is designed for solving linear inverse models (LIM).

These consist of linear equality and, or inequality conditions, which can be solved either by least squares or by linear programming techniques.

Amongst the possible applications are: food web quantification, flux balance analysis (e.g. metabolic networks), compositional estimation, and operations research problems.

The package contains several examples to exemplify its use

### Author(s)

Karline Soetaert (Maintainer),

Karel Van den Meersche

Dick van Oevelen

### References

Van den Meersche K, Soetaert K, Van Oevelen D (2009). xsample(): An R Function for Sampling Linear Inverse Problems. Journal of Statistical Software, Code Snippets, 30(1), 1-15.

http://www.jstatsoft.org/v30/c01/

### See Also

`Blending`, `Chemtax`, `RigaWeb`, `E_coli`, `Minkdiet` the examples.

`ldei`, `lsei`,`linp`, `ldp`, `nnls` to solve LIM

`xranges`, `varranges` to estimate ranges of unknowns and variables

`xsample`, `varsample` to create a random sample of unknowns and variables

`Solve`, `Solve.banded`, `Solve.tridiag`, to solve non-square, banded and tridiagonal linear systems of equations.

`resolution` row and column resolution of a matrix

package vignette `limSolve`

### Examples

    ## Not run:
    ## show examples (see respective help pages for details)
    example(Blending)
    example(Chemtax)
    example(E_coli)
    example(Minkdiet)

    ## run demos
    demo("limSolve")

    ## open the directory with original E_coli input file
    browseURL(paste(system.file(package="limSolve"), "/doc", sep=""))

    ## show package vignette with tutorial about xsample
    vignette("xsample")

    ## show main package vignette
    vignette("limSolve")

    ## End(Not run)

[Package limSolve version 1.5.5.3 Index]