normalize | R Documentation |
Bring a system of (in)equalities in a standard form
normalize(A, b, operators, unit = 0)
A |
|
b |
|
operators |
|
unit |
|
A list
with the folowing components
A
: the A
corresponding to the normalized sytem.
b
: the constant vector corresponding to the normalized system
neq
: the number of equations
nleq
: the number of non-strict inequations (<=)
order
: the index vector used to permute the original rows of A
.
For this package, a set of equations is in normal form when
The first neq
rows represent linear equalities.
The next nleq
rows represent inequalities of the form a.x <= b
All other rows are strict inequalities of the form a.x < b
If unit>0
, the strict inequalities a.x < b
are replaced with
inequations of the form a.x <= b-unit
, where unit
represents
the precision of measurement.
A <- matrix(1:12,nrow=4) b <- 1:4 ops <- c("<=","==","==","<") normalize(A,b,ops) normalize(A,b,ops,unit=0.1)
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