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csyequb.f(3)				      LAPACK				     csyequb.f(3)

       csyequb.f -

       subroutine csyequb (UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO)

Function/Subroutine Documentation
   subroutine csyequb (characterUPLO, integerN, complex, dimension( lda, * )A, integerLDA, real,
       dimension( * )S, realSCOND, realAMAX, complex, dimension( * )WORK, integerINFO)


	    CSYEQUB computes row and column scalings intended to equilibrate a
	    symmetric matrix A and reduce its condition number
	    (with respect to the two-norm).  S contains the scale factors,
	    S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with
	    elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal.  This
	    choice of S puts the condition number of B within a factor N of the
	    smallest possible condition number over all possible diagonal


		     UPLO is CHARACTER*1
		     Specifies whether the details of the factorization are stored
		     as an upper or lower triangular matrix.
		     = 'U':  Upper triangular, form is A = U*D*U**T;
		     = 'L':  Lower triangular, form is A = L*D*L**T.


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


		     A is COMPLEX array, dimension (LDA,N)
		     The N-by-N symmetric matrix whose scaling
		     factors are to be computed.  Only the diagonal elements of A
		     are referenced.


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


		     S is REAL array, dimension (N)
		     If INFO = 0, S contains the scale factors for A.


		     SCOND is REAL
		     If INFO = 0, S contains the ratio of the smallest S(i) to
		     the largest S(i).	If SCOND >= 0.1 and AMAX is neither too
		     large nor too small, it is not worth scaling by S.


		     AMAX is REAL
		     Absolute value of largest matrix element.	If AMAX is very
		     close to overflow or very close to underflow, the matrix
		     should be scaled.


		     WORK is COMPLEX array, dimension (3*N)


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

	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

	   November 2011

	   Livne, O.E. and Golub, G.H., 'Scaling by Binormalization',
	    Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004.
	    DOI 10.1023/B:NUMA.0000016606.32820.69
	    Tech report version: http://ruready.utah.edu/archive/papers/bin.pdf

       Definition at line 137 of file csyequb.f.

       Generated automatically by Doxygen for LAPACK from the source code.

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