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version 1.7, 2010/12/21 13:53:53 version 1.8, 2011/11/21 20:43:18
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   *> \brief \b ZPBEQU
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download ZPBEQU + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zpbequ.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zpbequ.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zpbequ.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE ZPBEQU( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, INFO )
   * 
   *       .. Scalar Arguments ..
   *       CHARACTER          UPLO
   *       INTEGER            INFO, KD, LDAB, N
   *       DOUBLE PRECISION   AMAX, SCOND
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION   S( * )
   *       COMPLEX*16         AB( LDAB, * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> ZPBEQU computes row and column scalings intended to equilibrate a
   *> Hermitian positive definite band 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
   *>          = 'U':  Upper triangular of A is stored;
   *>          = 'L':  Lower triangular of A is stored.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The order of the matrix A.  N >= 0.
   *> \endverbatim
   *>
   *> \param[in] KD
   *> \verbatim
   *>          KD is INTEGER
   *>          The number of superdiagonals of the matrix A if UPLO = 'U',
   *>          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
   *> \endverbatim
   *>
   *> \param[in] AB
   *> \verbatim
   *>          AB is COMPLEX*16 array, dimension (LDAB,N)
   *>          The upper or lower triangle of the Hermitian band matrix A,
   *>          stored in the first KD+1 rows of the array.  The j-th column
   *>          of A is stored in the j-th column of the array AB as follows:
   *>          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
   *>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
   *> \endverbatim
   *>
   *> \param[in] LDAB
   *> \verbatim
   *>          LDAB is INTEGER
   *>          The leading dimension of the array A.  LDAB >= KD+1.
   *> \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 complex16OTHERcomputational
   *
   *  =====================================================================
       SUBROUTINE ZPBEQU( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, INFO )        SUBROUTINE ZPBEQU( UPLO, N, KD, AB, LDAB, 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
Line 15 Line 145
       COMPLEX*16         AB( LDAB, * )        COMPLEX*16         AB( LDAB, * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  ZPBEQU computes row and column scalings intended to equilibrate a  
 *  Hermitian positive definite band 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  
 *          = 'U':  Upper triangular of A is stored;  
 *          = 'L':  Lower triangular of A is stored.  
 *  
 *  N       (input) INTEGER  
 *          The order of the matrix A.  N >= 0.  
 *  
 *  KD      (input) INTEGER  
 *          The number of superdiagonals of the matrix A if UPLO = 'U',  
 *          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.  
 *  
 *  AB      (input) COMPLEX*16 array, dimension (LDAB,N)  
 *          The upper or lower triangle of the Hermitian band matrix A,  
 *          stored in the first KD+1 rows of the array.  The j-th column  
 *          of A is stored in the j-th column of the array AB as follows:  
 *          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;  
 *          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).  
 *  
 *  LDAB     (input) INTEGER  
 *          The leading dimension of the array A.  LDAB >= KD+1.  
 *  
 *  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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