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sgebal.f(3)				      LAPACK				      sgebal.f(3)

       sgebal.f -

       subroutine sgebal (JOB, N, A, LDA, ILO, IHI, SCALE, INFO)

Function/Subroutine Documentation
   subroutine sgebal (characterJOB, integerN, real, dimension( lda, * )A, integerLDA, integerILO,
       integerIHI, real, dimension( * )SCALE, integerINFO)


	    SGEBAL balances a general real matrix A.  This involves, first,
	    permuting A by a similarity transformation 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 matrix, and improve the
	    accuracy of the computed eigenvalues and/or eigenvectors.


		     JOB is CHARACTER*1
		     Specifies the operations to be performed on A:
		     = 'N':  none:  simply set ILO = 1, IHI = N, SCALE(I) = 1.0
			     for i = 1,...,N;
		     = 'P':  permute only;
		     = 'S':  scale only;
		     = 'B':  both permute and scale.


		     N is INTEGER
		     The order of the matrix A.  N >= 0.


		     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.
		     See Further Details.


		     LDA is INTEGER
		     The leading dimension of the array A.  LDA >= max(1,N).


		     ILO is INTEGER


		     IHI is INTEGER
		     ILO and IHI are set to integers such that on exit
		     A(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.


		     SCALE is REAL array, dimension (N)
		     Details of the permutations and scaling factors applied to
		     A.  If P(j) is the index of the row and column interchanged
		     with row and column j and D(j) is the scaling factor
		     applied to row and column j, then
		     SCALE(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.


		     INFO is INTEGER
		     = 0:  successful exit.
		     < 0:  if INFO = -i, the i-th argument had an illegal value.

	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

	   November 2011

       Further Details:

	     The permutations consist of row and column interchanges which put
	     the matrix in the form

			( T1   X   Y  )
		P A P = (  0   B   Z  )
			(  0   0   T2 )

	     where T1 and T2 are upper triangular matrices whose eigenvalues lie
	     along the diagonal.  The column indices ILO and IHI mark the starting
	     and ending columns of the submatrix B. Balancing consists of applying
	     a diagonal similarity transformation inv(D) * B * D to make the
	     1-norms of each row of B and its corresponding column nearly equal.
	     The output matrix is

		( T1	 X*D	      Y    )
		(  0  inv(D)*B*D  inv(D)*Z ).
		(  0	  0	      T2   )

	     Information about the permutations P and the diagonal matrix D is
	     returned in the vector SCALE.

	     This subroutine is based on the EISPACK routine BALANC.

	     Modified by Tzu-Yi Chen, Computer Science Division, University of
	       California at Berkeley, USA

       Definition at line 161 of file sgebal.f.

       Generated automatically by Doxygen for LAPACK from the source code.

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