Calculates ranges of the unknowns of a linear inverse problem
Given the linear constraints
finds the minimum and maximum values of all elements of vector x
This is done by successively minimising and maximising each
using linear programming.
numeric matrix containing the coefficients of the equalities Ex=F.
numeric vector containing the right-hand side of the equalities.
numeric matrix containing the coefficients of the inequalities Gx>=H.
numeric vector containing the right-hand side of the inequalities.
tolerance for equality and inequality constraints.
if TRUE, the mean value of all range solutions is also outputted.
The ranges are estimated by successively minimising and maximising each
unknown, and using linear programming (based on function
By default linear programming assumes that all unknowns are positive.
If all unknowns are indeed to be positive, then it will generally be faster
ispos equal to TRUE
FALSE, then a system double the size of the
original system must be solved.
xranges outputs only the minimum and maximum value of each flow unless:
TRUE. In this case, all the results of the successive
minimisation and maximisation will be outputted, i.e. for each linear
programming application, not just the value of the unknown being optimised
but also the corresponding values of the other unknowns will be outputted.
TRUE, then the mean of all the results of the
linear programming will be outputted.
This may be a good starting value for
Note: the columns corresponding to the
central value and the
full results are valid solutions of the equations Ex=F
and Gx>=H. This is not the case for the first two columns (with
the minimal and maximal values).
a matrix with at least two columns:
column 1 and 2: the minimum and maximum value of each
central is TRUE: column 3 = the central value
full is TRUE: next columns contain all valid range solutions
Karline Soetaert <email@example.com>
Michel Berkelaar and others (2010). lpSolve: Interface to Lp_solve v. 5.5 to solve linear/integer programs. R package version 5.6.5. http://CRAN.R-project.org/package=lpSolve
Minkdiet, for a description of the Mink diet example.
varranges, for range estimation of variables,
xsample, to randomly sample the lsei problem
lp: linear programming from package lpSolve
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