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version 1.8, 2011/07/22 07:38:04 version 1.9, 2011/11/21 20:42:49
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   *> \brief \b DGBBRD
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download DGBBRD + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgbbrd.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgbbrd.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgbbrd.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DGBBRD( VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q,
   *                          LDQ, PT, LDPT, C, LDC, WORK, INFO )
   * 
   *       .. Scalar Arguments ..
   *       CHARACTER          VECT
   *       INTEGER            INFO, KL, KU, LDAB, LDC, LDPT, LDQ, M, N, NCC
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION   AB( LDAB, * ), C( LDC, * ), D( * ), E( * ),
   *      $                   PT( LDPT, * ), Q( LDQ, * ), WORK( * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DGBBRD reduces a real general m-by-n band matrix A to upper
   *> bidiagonal form B by an orthogonal transformation: Q**T * A * P = B.
   *>
   *> The routine computes B, and optionally forms Q or P**T, or computes
   *> Q**T*C for a given matrix C.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] VECT
   *> \verbatim
   *>          VECT is CHARACTER*1
   *>          Specifies whether or not the matrices Q and P**T are to be
   *>          formed.
   *>          = 'N': do not form Q or P**T;
   *>          = 'Q': form Q only;
   *>          = 'P': form P**T only;
   *>          = 'B': form both.
   *> \endverbatim
   *>
   *> \param[in] M
   *> \verbatim
   *>          M is INTEGER
   *>          The number of rows of the matrix A.  M >= 0.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The number of columns of the matrix A.  N >= 0.
   *> \endverbatim
   *>
   *> \param[in] NCC
   *> \verbatim
   *>          NCC is INTEGER
   *>          The number of columns of the matrix C.  NCC >= 0.
   *> \endverbatim
   *>
   *> \param[in] KL
   *> \verbatim
   *>          KL is INTEGER
   *>          The number of subdiagonals of the matrix A. KL >= 0.
   *> \endverbatim
   *>
   *> \param[in] KU
   *> \verbatim
   *>          KU is INTEGER
   *>          The number of superdiagonals of the matrix A. KU >= 0.
   *> \endverbatim
   *>
   *> \param[in,out] AB
   *> \verbatim
   *>          AB is DOUBLE PRECISION array, dimension (LDAB,N)
   *>          On entry, the m-by-n band matrix A, stored in rows 1 to
   *>          KL+KU+1. The j-th column of A is stored in the j-th column of
   *>          the array AB as follows:
   *>          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl).
   *>          On exit, A is overwritten by values generated during the
   *>          reduction.
   *> \endverbatim
   *>
   *> \param[in] LDAB
   *> \verbatim
   *>          LDAB is INTEGER
   *>          The leading dimension of the array A. LDAB >= KL+KU+1.
   *> \endverbatim
   *>
   *> \param[out] D
   *> \verbatim
   *>          D is DOUBLE PRECISION array, dimension (min(M,N))
   *>          The diagonal elements of the bidiagonal matrix B.
   *> \endverbatim
   *>
   *> \param[out] E
   *> \verbatim
   *>          E is DOUBLE PRECISION array, dimension (min(M,N)-1)
   *>          The superdiagonal elements of the bidiagonal matrix B.
   *> \endverbatim
   *>
   *> \param[out] Q
   *> \verbatim
   *>          Q is DOUBLE PRECISION array, dimension (LDQ,M)
   *>          If VECT = 'Q' or 'B', the m-by-m orthogonal matrix Q.
   *>          If VECT = 'N' or 'P', the array Q is not referenced.
   *> \endverbatim
   *>
   *> \param[in] LDQ
   *> \verbatim
   *>          LDQ is INTEGER
   *>          The leading dimension of the array Q.
   *>          LDQ >= max(1,M) if VECT = 'Q' or 'B'; LDQ >= 1 otherwise.
   *> \endverbatim
   *>
   *> \param[out] PT
   *> \verbatim
   *>          PT is DOUBLE PRECISION array, dimension (LDPT,N)
   *>          If VECT = 'P' or 'B', the n-by-n orthogonal matrix P'.
   *>          If VECT = 'N' or 'Q', the array PT is not referenced.
   *> \endverbatim
   *>
   *> \param[in] LDPT
   *> \verbatim
   *>          LDPT is INTEGER
   *>          The leading dimension of the array PT.
   *>          LDPT >= max(1,N) if VECT = 'P' or 'B'; LDPT >= 1 otherwise.
   *> \endverbatim
   *>
   *> \param[in,out] C
   *> \verbatim
   *>          C is DOUBLE PRECISION array, dimension (LDC,NCC)
   *>          On entry, an m-by-ncc matrix C.
   *>          On exit, C is overwritten by Q**T*C.
   *>          C is not referenced if NCC = 0.
   *> \endverbatim
   *>
   *> \param[in] LDC
   *> \verbatim
   *>          LDC is INTEGER
   *>          The leading dimension of the array C.
   *>          LDC >= max(1,M) if NCC > 0; LDC >= 1 if NCC = 0.
   *> \endverbatim
   *>
   *> \param[out] WORK
   *> \verbatim
   *>          WORK is DOUBLE PRECISION array, dimension (2*max(M,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 doubleGBcomputational
   *
   *  =====================================================================
       SUBROUTINE DGBBRD( VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q,        SUBROUTINE DGBBRD( VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q,
      $                   LDQ, PT, LDPT, C, LDC, WORK, INFO )       $                   LDQ, PT, LDPT, C, LDC, WORK, INFO )
 *  *
 *  -- LAPACK routine (version 3.3.1) --  *  -- 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..--
 *  -- April 2011                                                      --  *     November 2011
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          VECT        CHARACTER          VECT
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      $                   PT( LDPT, * ), Q( LDQ, * ), WORK( * )       $                   PT( LDPT, * ), Q( LDQ, * ), WORK( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DGBBRD reduces a real general m-by-n band matrix A to upper  
 *  bidiagonal form B by an orthogonal transformation: Q**T * A * P = B.  
 *  
 *  The routine computes B, and optionally forms Q or P**T, or computes  
 *  Q**T*C for a given matrix C.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  VECT    (input) CHARACTER*1  
 *          Specifies whether or not the matrices Q and P**T are to be  
 *          formed.  
 *          = 'N': do not form Q or P**T;  
 *          = 'Q': form Q only;  
 *          = 'P': form P**T only;  
 *          = 'B': form both.  
 *  
 *  M       (input) INTEGER  
 *          The number of rows of the matrix A.  M >= 0.  
 *  
 *  N       (input) INTEGER  
 *          The number of columns of the matrix A.  N >= 0.  
 *  
 *  NCC     (input) INTEGER  
 *          The number of columns of the matrix C.  NCC >= 0.  
 *  
 *  KL      (input) INTEGER  
 *          The number of subdiagonals of the matrix A. KL >= 0.  
 *  
 *  KU      (input) INTEGER  
 *          The number of superdiagonals of the matrix A. KU >= 0.  
 *  
 *  AB      (input/output) DOUBLE PRECISION array, dimension (LDAB,N)  
 *          On entry, the m-by-n band matrix A, stored in rows 1 to  
 *          KL+KU+1. The j-th column of A is stored in the j-th column of  
 *          the array AB as follows:  
 *          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl).  
 *          On exit, A is overwritten by values generated during the  
 *          reduction.  
 *  
 *  LDAB    (input) INTEGER  
 *          The leading dimension of the array A. LDAB >= KL+KU+1.  
 *  
 *  D       (output) DOUBLE PRECISION array, dimension (min(M,N))  
 *          The diagonal elements of the bidiagonal matrix B.  
 *  
 *  E       (output) DOUBLE PRECISION array, dimension (min(M,N)-1)  
 *          The superdiagonal elements of the bidiagonal matrix B.  
 *  
 *  Q       (output) DOUBLE PRECISION array, dimension (LDQ,M)  
 *          If VECT = 'Q' or 'B', the m-by-m orthogonal matrix Q.  
 *          If VECT = 'N' or 'P', the array Q is not referenced.  
 *  
 *  LDQ     (input) INTEGER  
 *          The leading dimension of the array Q.  
 *          LDQ >= max(1,M) if VECT = 'Q' or 'B'; LDQ >= 1 otherwise.  
 *  
 *  PT      (output) DOUBLE PRECISION array, dimension (LDPT,N)  
 *          If VECT = 'P' or 'B', the n-by-n orthogonal matrix P'.  
 *          If VECT = 'N' or 'Q', the array PT is not referenced.  
 *  
 *  LDPT    (input) INTEGER  
 *          The leading dimension of the array PT.  
 *          LDPT >= max(1,N) if VECT = 'P' or 'B'; LDPT >= 1 otherwise.  
 *  
 *  C       (input/output) DOUBLE PRECISION array, dimension (LDC,NCC)  
 *          On entry, an m-by-ncc matrix C.  
 *          On exit, C is overwritten by Q**T*C.  
 *          C is not referenced if NCC = 0.  
 *  
 *  LDC     (input) INTEGER  
 *          The leading dimension of the array C.  
 *          LDC >= max(1,M) if NCC > 0; LDC >= 1 if NCC = 0.  
 *  
 *  WORK    (workspace) DOUBLE PRECISION array, dimension (2*max(M,N))  
 *  
 *  INFO    (output) INTEGER  
 *          = 0:  successful exit.  
 *          < 0:  if INFO = -i, the i-th argument had an illegal value.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Removed from v.1.8  
changed lines
  Added in v.1.9

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