sggbal.f(3)							      LAPACK							       sggbal.f(3)

NAME

       sggbal.f -

SYNOPSIS

   Functions/Subroutines
       subroutine sggbal (JOB, N, A, LDA, B, LDB, ILO, IHI, LSCALE, RSCALE, WORK, INFO)
	   SGGBAL

Function/Subroutine Documentation
   subroutine sggbal (characterJOB, integerN, real, dimension( lda, * )A, integerLDA, real, dimension( ldb, * )B, integerLDB, integerILO,
       integerIHI, real, dimension( * )LSCALE, real, dimension( * )RSCALE, real, dimension( * )WORK, integerINFO)
       SGGBAL

       Purpose:

	    SGGBAL 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.

       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 REAL 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 REAL 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 REAL 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 REAL 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.

	   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 sggbal.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       sggbal.f(3)