.TH "zggbal.f" 3 "Wed Oct 15 2014" "Version 3.4.2" "LAPACK" \" -*- nroff -*-
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.SH NAME
zggbal.f \- 
.SH SYNOPSIS
.br
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.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBzggbal\fP (JOB, N, A, LDA, B, LDB, ILO, IHI, LSCALE, RSCALE, WORK, INFO)"
.br
.RI "\fI\fBZGGBAL\fP \fP"
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "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)"

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\fBZGGBAL\fP  
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\fBPurpose: \fP
.RS 4

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.nf
 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.
.fi
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.RE
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\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 
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          N is INTEGER
          The order of the matrices A and B.  N >= 0.
.fi
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\fIA\fP 
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          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.
.fi
.PP
.br
\fILDA\fP 
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.nf
          LDA is INTEGER
          The leading dimension of the array A. LDA >= max(1,N).
.fi
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\fIB\fP 
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.nf
          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.
.fi
.PP
.br
\fILDB\fP 
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          LDB is INTEGER
          The leading dimension of the array B. LDB >= max(1,N).
.fi
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\fIILO\fP 
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          ILO is INTEGER
.fi
.PP
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\fIIHI\fP 
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.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
            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.
.fi
.PP
.br
\fIWORK\fP 
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.nf
          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'.
.fi
.PP
.br
\fIINFO\fP 
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          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value.
.fi
.PP
 
.RE
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\fBAuthor:\fP
.RS 4
Univ\&. of Tennessee 
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Univ\&. of California Berkeley 
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Univ\&. of Colorado Denver 
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NAG Ltd\&. 
.RE
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\fBDate:\fP
.RS 4
November 2011 
.RE
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\fBFurther Details: \fP
.RS 4

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.nf
  See R.C. WARD, Balancing the generalized eigenvalue problem,
                 SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.
.fi
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.RE
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Definition at line 177 of file zggbal\&.f\&.
.SH "Author"
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Generated automatically by Doxygen for LAPACK from the source code\&.