zggbal.f - Online Linux Manual PageSection : 3
Updated : Tue Nov 14 2017
Source : Version 3.8.0
Note : LAPACK
NAMEzggbal.f
SYNOPSIS
Functions/Subroutinessubroutine zggbal (JOB, N, A, LDA, B, LDB, ILO, IHI, LSCALE, RSCALE, WORK, INFO)
ZGGBAL
Function/Subroutine Documentation
subroutine zggbal (character JOB, integer N, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( ldb, * ) B, integer LDB, integer ILO, integer IHI, double precision, dimension( * ) LSCALE, double precision, dimension( * ) RSCALE, double precision, dimension( * ) WORK, integer INFO)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 DOUBLE PRECISION 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: June 2016 Further Details: See R.C. WARD, Balancing the generalized eigenvalue problem,
SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.Definition at line 179 of file zggbal.f.
AuthorGenerated automatically by Doxygen for LAPACK from the source code. 0
Johanes Gumabo
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