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version 1.4, 2010/12/21 13:53:39 version 1.5, 2011/11/21 20:43:04
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       SUBROUTINE DSYEQUB( UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO )  *> \brief \b DSYEQUB
 *  *
 *     -- LAPACK routine (version 3.2.2)                                 --  *  =========== DOCUMENTATION ===========
 *     -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --  
 *     -- Jason Riedy of Univ. of California Berkeley.                 --  
 *     -- June 2010                                                    --  
 *  *
 *     -- LAPACK is a software package provided by Univ. of Tennessee, --  * Online html documentation available at 
 *     -- Univ. of California Berkeley and NAG Ltd.                    --  *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download DSYEQUB + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsyequb.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsyequb.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsyequb.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DSYEQUB( UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO )
   * 
   *       .. Scalar Arguments ..
   *       INTEGER            INFO, LDA, N
   *       DOUBLE PRECISION   AMAX, SCOND
   *       CHARACTER          UPLO
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION   A( LDA, * ), S( * ), WORK( * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DSYEQUB 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
   *> scalings.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] UPLO
   *> \verbatim
   *>          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.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The order of the matrix A.  N >= 0.
   *> \endverbatim
   *>
   *> \param[in] A
   *> \verbatim
   *>          A is DOUBLE PRECISION 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.
   *> \endverbatim
   *>
   *> \param[in] LDA
   *> \verbatim
   *>          LDA is INTEGER
   *>          The leading dimension of the array A.  LDA >= max(1,N).
   *> \endverbatim
   *>
   *> \param[out] S
   *> \verbatim
   *>          S is DOUBLE PRECISION array, dimension (N)
   *>          If INFO = 0, S contains the scale factors for A.
   *> \endverbatim
   *>
   *> \param[out] SCOND
   *> \verbatim
   *>          SCOND is DOUBLE PRECISION
   *>          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.
   *> \endverbatim
   *>
   *> \param[out] AMAX
   *> \verbatim
   *>          AMAX is DOUBLE PRECISION
   *>          Absolute value of largest matrix element.  If AMAX is very
   *>          close to overflow or very close to underflow, the matrix
   *>          should be scaled.
   *> \endverbatim
   *>
   *> \param[out] WORK
   *> \verbatim
   *>          WORK is DOUBLE PRECISION array, dimension (3*N)
   *> \endverbatim
   *>
   *> \param[out] INFO
   *> \verbatim
   *>          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.
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup doubleSYcomputational
   *
   *> \par References:
   *  ================
   *>
   *>  Livne, O.E. and Golub, G.H., "Scaling by Binormalization", \n
   *>  Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004. \n
   *>  DOI 10.1023/B:NUMA.0000016606.32820.69 \n
   *>  Tech report version: http://ruready.utah.edu/archive/papers/bin.pdf
   *>
   *  =====================================================================
         SUBROUTINE DSYEQUB( UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO )
   *
   *  -- LAPACK computational routine (version 3.4.0) --
   *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
   *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
   *     November 2011
 *  *
       IMPLICIT NONE  
 *     ..  
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, N        INTEGER            INFO, LDA, N
       DOUBLE PRECISION   AMAX, SCOND        DOUBLE PRECISION   AMAX, SCOND
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       DOUBLE PRECISION   A( LDA, * ), S( * ), WORK( * )        DOUBLE PRECISION   A( LDA, * ), S( * ), WORK( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DSYEQUB 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  
 *  scalings.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  UPLO    (input) 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       (input) INTEGER  
 *          The order of the matrix A.  N >= 0.  
 *  
 *  A       (input) DOUBLE PRECISION 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     (input) INTEGER  
 *          The leading dimension of the array A.  LDA >= max(1,N).  
 *  
 *  S       (output) DOUBLE PRECISION array, dimension (N)  
 *          If INFO = 0, S contains the scale factors for A.  
 *  
 *  SCOND   (output) DOUBLE PRECISION  
 *          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    (output) DOUBLE PRECISION  
 *          Absolute value of largest matrix element.  If AMAX is very  
 *          close to overflow or very close to underflow, the matrix  
 *          should be scaled.  
 *  
 *  WORK    (workspace) DOUBLE PRECISION array, dimension (3*N)  
 *  
 *  INFO    (output) 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.  
 *  
 *  Further Details  
 *  ======= =======  
 *  
 *  Reference: 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  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Removed from v.1.4  
changed lines
  Added in v.1.5

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