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version 1.7, 2010/12/21 13:53:36 version 1.8, 2011/11/21 20:43:02
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   *> \brief \b DPPEQU
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download DPPEQU + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dppequ.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dppequ.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dppequ.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DPPEQU( UPLO, N, AP, S, SCOND, AMAX, INFO )
   * 
   *       .. Scalar Arguments ..
   *       CHARACTER          UPLO
   *       INTEGER            INFO, N
   *       DOUBLE PRECISION   AMAX, SCOND
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION   AP( * ), S( * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DPPEQU computes row and column scalings intended to equilibrate a
   *> symmetric positive definite matrix A in packed storage 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
   *>          = 'U':  Upper triangle of A is stored;
   *>          = 'L':  Lower triangle of A is stored.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The order of the matrix A.  N >= 0.
   *> \endverbatim
   *>
   *> \param[in] AP
   *> \verbatim
   *>          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
   *>          The upper or lower triangle of the symmetric matrix A, packed
   *>          columnwise in a linear array.  The j-th column of A is stored
   *>          in the array AP as follows:
   *>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
   *>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=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] 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 doubleOTHERcomputational
   *
   *  =====================================================================
       SUBROUTINE DPPEQU( UPLO, N, AP, S, SCOND, AMAX, INFO )        SUBROUTINE DPPEQU( UPLO, N, AP, S, SCOND, AMAX, INFO )
 *  *
 *  -- LAPACK routine (version 3.2) --  *  -- LAPACK computational routine (version 3.4.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     November 2006  *     November 2011
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          UPLO        CHARACTER          UPLO
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       DOUBLE PRECISION   AP( * ), S( * )        DOUBLE PRECISION   AP( * ), S( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DPPEQU computes row and column scalings intended to equilibrate a  
 *  symmetric positive definite matrix A in packed storage 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  
 *          = 'U':  Upper triangle of A is stored;  
 *          = 'L':  Lower triangle of A is stored.  
 *  
 *  N       (input) INTEGER  
 *          The order of the matrix A.  N >= 0.  
 *  
 *  AP      (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)  
 *          The upper or lower triangle of the symmetric matrix A, packed  
 *          columnwise in a linear array.  The j-th column of A is stored  
 *          in the array AP as follows:  
 *          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;  
 *          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=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.  
 *  
 *  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.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Removed from v.1.7  
changed lines
  Added in v.1.8

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