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version 1.7, 2010/12/21 13:53:45 version 1.8, 2011/11/21 20:43:11
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   *> \brief \b ZHBTRD
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download ZHBTRD + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhbtrd.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhbtrd.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhbtrd.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE ZHBTRD( VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ,
   *                          WORK, INFO )
   * 
   *       .. Scalar Arguments ..
   *       CHARACTER          UPLO, VECT
   *       INTEGER            INFO, KD, LDAB, LDQ, N
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION   D( * ), E( * )
   *       COMPLEX*16         AB( LDAB, * ), Q( LDQ, * ), WORK( * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> ZHBTRD reduces a complex Hermitian band matrix A to real symmetric
   *> tridiagonal form T by a unitary similarity transformation:
   *> Q**H * A * Q = T.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] VECT
   *> \verbatim
   *>          VECT is CHARACTER*1
   *>          = 'N':  do not form Q;
   *>          = 'V':  form Q;
   *>          = 'U':  update a matrix X, by forming X*Q.
   *> \endverbatim
   *>
   *> \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] 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,out] AB
   *> \verbatim
   *>          AB is COMPLEX*16 array, dimension (LDAB,N)
   *>          On entry, 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).
   *>          On exit, the diagonal elements of AB are overwritten by the
   *>          diagonal elements of the tridiagonal matrix T; if KD > 0, the
   *>          elements on the first superdiagonal (if UPLO = 'U') or the
   *>          first subdiagonal (if UPLO = 'L') are overwritten by the
   *>          off-diagonal elements of T; the rest of AB is overwritten by
   *>          values generated during the reduction.
   *> \endverbatim
   *>
   *> \param[in] LDAB
   *> \verbatim
   *>          LDAB is INTEGER
   *>          The leading dimension of the array AB.  LDAB >= KD+1.
   *> \endverbatim
   *>
   *> \param[out] D
   *> \verbatim
   *>          D is DOUBLE PRECISION array, dimension (N)
   *>          The diagonal elements of the tridiagonal matrix T.
   *> \endverbatim
   *>
   *> \param[out] E
   *> \verbatim
   *>          E is DOUBLE PRECISION array, dimension (N-1)
   *>          The off-diagonal elements of the tridiagonal matrix T:
   *>          E(i) = T(i,i+1) if UPLO = 'U'; E(i) = T(i+1,i) if UPLO = 'L'.
   *> \endverbatim
   *>
   *> \param[in,out] Q
   *> \verbatim
   *>          Q is COMPLEX*16 array, dimension (LDQ,N)
   *>          On entry, if VECT = 'U', then Q must contain an N-by-N
   *>          matrix X; if VECT = 'N' or 'V', then Q need not be set.
   *>
   *>          On exit:
   *>          if VECT = 'V', Q contains the N-by-N unitary matrix Q;
   *>          if VECT = 'U', Q contains the product X*Q;
   *>          if VECT = 'N', the array Q is not referenced.
   *> \endverbatim
   *>
   *> \param[in] LDQ
   *> \verbatim
   *>          LDQ is INTEGER
   *>          The leading dimension of the array Q.
   *>          LDQ >= 1, and LDQ >= N if VECT = 'V' or 'U'.
   *> \endverbatim
   *>
   *> \param[out] WORK
   *> \verbatim
   *>          WORK is COMPLEX*16 array, dimension (N)
   *> \endverbatim
   *>
   *> \param[out] INFO
   *> \verbatim
   *>          INFO is INTEGER
   *>          = 0:  successful exit
   *>          < 0:  if INFO = -i, the i-th argument had an illegal value
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup complex16OTHERcomputational
   *
   *> \par Further Details:
   *  =====================
   *>
   *> \verbatim
   *>
   *>  Modified by Linda Kaufman, Bell Labs.
   *> \endverbatim
   *>
   *  =====================================================================
       SUBROUTINE ZHBTRD( VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ,        SUBROUTINE ZHBTRD( VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ,
      $                   WORK, INFO )       $                   WORK, 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, VECT        CHARACTER          UPLO, VECT
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       COMPLEX*16         AB( LDAB, * ), Q( LDQ, * ), WORK( * )        COMPLEX*16         AB( LDAB, * ), Q( LDQ, * ), WORK( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  ZHBTRD reduces a complex Hermitian band matrix A to real symmetric  
 *  tridiagonal form T by a unitary similarity transformation:  
 *  Q**H * A * Q = T.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  VECT    (input) CHARACTER*1  
 *          = 'N':  do not form Q;  
 *          = 'V':  form Q;  
 *          = 'U':  update a matrix X, by forming X*Q.  
 *  
 *  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.  
 *  
 *  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/output) COMPLEX*16 array, dimension (LDAB,N)  
 *          On entry, 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).  
 *          On exit, the diagonal elements of AB are overwritten by the  
 *          diagonal elements of the tridiagonal matrix T; if KD > 0, the  
 *          elements on the first superdiagonal (if UPLO = 'U') or the  
 *          first subdiagonal (if UPLO = 'L') are overwritten by the  
 *          off-diagonal elements of T; the rest of AB is overwritten by  
 *          values generated during the reduction.  
 *  
 *  LDAB    (input) INTEGER  
 *          The leading dimension of the array AB.  LDAB >= KD+1.  
 *  
 *  D       (output) DOUBLE PRECISION array, dimension (N)  
 *          The diagonal elements of the tridiagonal matrix T.  
 *  
 *  E       (output) DOUBLE PRECISION array, dimension (N-1)  
 *          The off-diagonal elements of the tridiagonal matrix T:  
 *          E(i) = T(i,i+1) if UPLO = 'U'; E(i) = T(i+1,i) if UPLO = 'L'.  
 *  
 *  Q       (input/output) COMPLEX*16 array, dimension (LDQ,N)  
 *          On entry, if VECT = 'U', then Q must contain an N-by-N  
 *          matrix X; if VECT = 'N' or 'V', then Q need not be set.  
 *  
 *          On exit:  
 *          if VECT = 'V', Q contains the N-by-N unitary matrix Q;  
 *          if VECT = 'U', Q contains the product X*Q;  
 *          if VECT = 'N', the array Q is not referenced.  
 *  
 *  LDQ     (input) INTEGER  
 *          The leading dimension of the array Q.  
 *          LDQ >= 1, and LDQ >= N if VECT = 'V' or 'U'.  
 *  
 *  WORK    (workspace) COMPLEX*16 array, dimension (N)  
 *  
 *  INFO    (output) INTEGER  
 *          = 0:  successful exit  
 *          < 0:  if INFO = -i, the i-th argument had an illegal value  
 *  
 *  Further Details  
 *  ===============  
 *  
 *  Modified by Linda Kaufman, Bell Labs.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Removed from v.1.7  
changed lines
  Added in v.1.8

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