a one-letter string specifying the ‘job’ for DGEBAL.
P
Permutation
S
Scaling
B
Both permutation and scaling
N
None
Details
An excerpt of the LAPACK documentation about DGEBAL(), describing the
result
i1 ("ILO")
(output) integer
i2 ("IHI")
(output) integer i1 and i2 are set to integers such that on exit
z[i,j] = 0 if i > j and j = 1,...,i1-1 or i = i2+1,...,n.
If job = 'N' or 'S', i1 = 1 and i2 = n.
scale
(output) numeric vector of length n.
Details of the permutations and scaling factors applied to
A. If P[j] is the index of the row and column interchanged
with row and column j and D[j] is the scaling factor
applied to row and column j, then
scale[j] = P[j] for j = 1,...,i1-1 = D[j] for j = i1,...,i2, = P[j] for j = i2+1,...,n.
The order in which the interchanges are made is n to i2+1,
then 1 to i1-1.
Look at the LAPACK documentation for more details.
Value
A list with components
z
the transformation of matrix A, after permutation and
or scaling.
scale
numeric vector of length n, containing the
permutation and/or scale vectors applied.
i1,i2
integers (length 1) in {1,2,…,n}, denoted by
ILO and IHI respectively in the LAPACK
documentation. Only relevant for "P" or "B", they
describe where permutations and where scaling took place; see the
Details section.
Author(s)
Martin Maechler
References
LAPACK Reference Manual
See Also
eigen, expm.
Examples
m4 <- rbind(c(-1,-1, 0, 0),
c( 0, 0,10,10),
c( 0, 0,10, 0),
c( 0,10, 0, 0))
(b4 <- balance(m4))
## --- for testing and didactical reasons : ----
demo(balanceTst) # also defines the balanceTst() function
# which in its tests ``defines'' what
# the return value means, notably (i1,i2,scale)