Calculates ranges of the unknowns of a linear inverse problem
Description
Given the linear constraints
Ex=f
Gx>=h
finds the minimum and maximum values of all elements of vector x
This is done by successively minimising and maximising each x
,
using linear programming.
Usage
1 2 |
Arguments
E |
numeric matrix containing the coefficients of the equalities Ex=F. |
F |
numeric vector containing the right-hand side of the equalities. |
G |
numeric matrix containing the coefficients of the inequalities Gx>=H. |
H |
numeric vector containing the right-hand side of the inequalities. |
ispos |
if |
tol |
tolerance for equality and inequality constraints. |
central |
if TRUE, the mean value of all range solutions is also outputted. |
full |
if |
Details
The ranges are estimated by successively minimising and maximising each
unknown, and using linear programming (based on function lp
from
R-package lpSolve
.
By default linear programming assumes that all unknowns are positive.
If all unknowns are indeed to be positive, then it will generally be faster
to set ispos
equal to TRUE
If ispos
is 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:
full
is 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.
If central
is TRUE
, then the mean of all the results of the
linear programming will be outputted.
This may be a good starting value for xsample
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).
Value
a matrix with at least two columns:
column 1 and 2: the minimum and maximum value of each x
if central
is TRUE: column 3 = the central value
if full
is TRUE: next columns contain all valid range solutions
Author(s)
Karline Soetaert <karline.soetaert@nioz.nl>
References
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
See Also
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
Examples
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