zggbal.f man page

zggbal.f —

Synopsis

Functions/Subroutines

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

Function/Subroutine Documentation

subroutine zggbal (characterJOB, integerN, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( ldb, * )B, integerLDB, integerILO, integerIHI, double precision, dimension( * )LSCALE, double precision, dimension( * )RSCALE, double precision, dimension( * )WORK, integerINFO)

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.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

zggbal(3) is an alias of zggbal.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK