.TH "SRC/dggbal.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
SRC/dggbal.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBdggbal\fP (job, n, a, lda, b, ldb, ilo, ihi, lscale, rscale, work, info)"
.br
.RI "\fBDGGBAL\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine dggbal (character job, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb, integer ilo, integer ihi, double precision, dimension( * ) lscale, double precision, dimension( * ) rscale, double precision, dimension( * ) work, integer info)"

.PP
\fBDGGBAL\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> DGGBAL balances a pair of general real 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\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIJOB\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The order of the matrices A and B\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fIA\fP 
.PP
.nf
!>          A is DOUBLE PRECISION 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\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The leading dimension of the array A\&. LDA >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIB\fP 
.PP
.nf
!>          B is DOUBLE PRECISION 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\&.
!> 
.fi
.PP
.br
\fILDB\fP 
.PP
.nf
!>          LDB is INTEGER
!>          The leading dimension of the array B\&. LDB >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIILO\fP 
.PP
.nf
!>          ILO is INTEGER
!> 
.fi
.PP
.br
\fIIHI\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fILSCALE\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIRSCALE\fP 
.PP
.nf
!>          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
!>            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\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          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'\&.
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value\&.
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

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NAG Ltd\&. 
.RE
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\fBFurther Details:\fP
.RS 4

.PP
.nf
!>
!>  See R\&.C\&. WARD, Balancing the generalized eigenvalue problem,
!>                 SIAM J\&. Sci\&. Stat\&. Comp\&. 2 (1981), 141-152\&.
!> 
.fi
.PP
 
.RE
.PP

.PP
Definition at line \fB175\fP of file \fBdggbal\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.