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zggbal.f(3) LAPACK zggbal.f(3)

zggbal.f -


subroutine zggbal (JOB, N, A, LDA, B, LDB, ILO, IHI, LSCALE, RSCALE, WORK, INFO)
 
ZGGBAL

ZGGBAL
Purpose:
 ZGGBAL 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
 elements on the diagonal; and second, applying a diagonal similarity
 transformation to rows and columns ILO to IHI to make the rows
 and columns 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.
Parameters:
JOB
          JOB is 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
          N is INTEGER
          The order of the matrices A and B.  N >= 0.
A
          A is COMPLEX*16 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
          LDA is INTEGER
          The leading dimension of the array A. LDA >= max(1,N).
B
          B is COMPLEX*16 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
          LDB is INTEGER
          The leading dimension of the array B. LDB >= max(1,N).
ILO
          ILO is INTEGER
IHI
          IHI is 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
          LSCALE is DOUBLE PRECISION 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 interchanged 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
          RSCALE is DOUBLE PRECISION 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
          WORK is 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
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Further Details:
  See R.C. WARD, Balancing the generalized eigenvalue problem,
                 SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.
Definition at line 177 of file zggbal.f.

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