cggbal man page on Scientific

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```CGGBAL(1)		 LAPACK routine (version 3.2)		     CGGBAL(1)

NAME
CGGBAL - balances a pair of general complex matrices (A,B)

SYNOPSIS
SUBROUTINE CGGBAL( JOB,	N,  A,	LDA, B, LDB, ILO, IHI, LSCALE, RSCALE,
WORK, INFO )

CHARACTER	  JOB

INTEGER	  IHI, ILO, INFO, LDA, LDB, N

REAL		  LSCALE( * ), RSCALE( * ), WORK( * )

COMPLEX	  A( LDA, * ), B( LDB, * )

PURPOSE
CGGBAL balances	a  pair	 of  general  complex  matrices	 (A,B).	  This
involves,  first,  permuting  A	and B by similarity transformations to
isolate eigenvalues in the first 1 to ILO\$-\$1 and last IHI+1 to N  ele‐
ments  on  the  diagonal;  and  second,	applying a diagonal similarity
transformation to rows and columns ILO to IHI to make the rows and col‐
umns  as close in norm as possible. Both steps are optional.  Balancing
may reduce the 1-norm of the matrices, and improve the accuracy of  the
computed	 eigenvalues and/or eigenvectors in the generalized eigenvalue
problem A*x = lambda*B*x.

ARGUMENTS
JOB     (input) CHARACTER*1
Specifies the operations to be performed on A and B:
= 'N':  none:  simply set ILO = 1, IHI = N, LSCALE(I) = 1.0 and
RSCALE(I) = 1.0 for i=1,...,N; = 'P':  permute only;
= 'S':  scale only;
= 'B':  both permute and scale.

N       (input) INTEGER
The order of the matrices A and B.  N >= 0.

A       (input/output) COMPLEX array, dimension (LDA,N)
On entry, the input matrix A.  On exit, A is overwritten by the
balanced matrix.	 If JOB = 'N', A is not referenced.

LDA     (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).

B       (input/output) COMPLEX array, dimension (LDB,N)
On entry, the input matrix B.  On exit, B is overwritten by the
balanced matrix.	 If JOB = 'N', B is not referenced.

LDB     (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).

ILO     (output) INTEGER
IHI	(output)  INTEGER ILO and IHI are set to integers such
that on exit A(i,j) = 0 and B(i,j) =  0	if  i  >  j  and  j  =
1,...,ILO-1  or	i = IHI+1,...,N.  If JOB = 'N' or 'S', ILO = 1
and IHI = N.

LSCALE  (output) REAL array, dimension (N)
Details of the permutations and scaling factors applied to  the
left  side  of A and B.	If P(j) is the index of the row inter‐
changed with row j, and D(j) is the scaling factor  applied  to
row  j,	then  LSCALE(j)	 =  P(j)    for J = 1,...,ILO-1 = D(j)
for J = ILO,...,IHI = P(j)    for J = IHI+1,...,N.   The	 order
in  which  the  interchanges  are made is N to IHI+1, then 1 to
ILO-1.

RSCALE  (output) REAL array, dimension (N)
Details of the permutations and scaling factors applied to  the
right  side  of	A  and	B.  If P(j) is the index of the column
interchanged with column j, and	D(j)  is  the  scaling	factor
applied	to  column  j,	then  RSCALE(j)	 =  P(j)     for  J  =
1,...,ILO-1 = D(j)    for J = ILO,...,IHI =  P(j)     for  J  =
IHI+1,...,N.  The order in which the interchanges are made is N
to IHI+1, then 1 to ILO-1.

WORK    (workspace) REAL array, dimension (lwork)
lwork must be at least max(1,6*N) when JOB = 'S' or 'B', and at
least 1 when JOB = 'N' or 'P'.

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value.

FURTHER DETAILS
See R.C. WARD, Balancing the generalized eigenvalue problem,
SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.

LAPACK routine (version 3.2)	 November 2008			     CGGBAL(1)
```
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