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version 1.5, 2011/07/22 07:38:06 version 1.6, 2011/11/21 20:42:53
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   *> \brief \b DLA_GBAMV
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download DLA_GBAMV + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dla_gbamv.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dla_gbamv.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dla_gbamv.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DLA_GBAMV( TRANS, M, N, KL, KU, ALPHA, AB, LDAB, X,
   *                             INCX, BETA, Y, INCY )
   * 
   *       .. Scalar Arguments ..
   *       DOUBLE PRECISION   ALPHA, BETA
   *       INTEGER            INCX, INCY, LDAB, M, N, KL, KU, TRANS
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION   AB( LDAB, * ), X( * ), Y( * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DLA_GBAMV  performs one of the matrix-vector operations
   *>
   *>         y := alpha*abs(A)*abs(x) + beta*abs(y),
   *>    or   y := alpha*abs(A)**T*abs(x) + beta*abs(y),
   *>
   *> where alpha and beta are scalars, x and y are vectors and A is an
   *> m by n matrix.
   *>
   *> This function is primarily used in calculating error bounds.
   *> To protect against underflow during evaluation, components in
   *> the resulting vector are perturbed away from zero by (N+1)
   *> times the underflow threshold.  To prevent unnecessarily large
   *> errors for block-structure embedded in general matrices,
   *> "symbolically" zero components are not perturbed.  A zero
   *> entry is considered "symbolic" if all multiplications involved
   *> in computing that entry have at least one zero multiplicand.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] TRANS
   *> \verbatim
   *>          TRANS is INTEGER
   *>           On entry, TRANS specifies the operation to be performed as
   *>           follows:
   *>
   *>             BLAS_NO_TRANS      y := alpha*abs(A)*abs(x) + beta*abs(y)
   *>             BLAS_TRANS         y := alpha*abs(A**T)*abs(x) + beta*abs(y)
   *>             BLAS_CONJ_TRANS    y := alpha*abs(A**T)*abs(x) + beta*abs(y)
   *>
   *>           Unchanged on exit.
   *> \endverbatim
   *>
   *> \param[in] M
   *> \verbatim
   *>          M is INTEGER
   *>           On entry, M specifies the number of rows of the matrix A.
   *>           M must be at least zero.
   *>           Unchanged on exit.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>           On entry, N specifies the number of columns of the matrix A.
   *>           N must be at least zero.
   *>           Unchanged on exit.
   *> \endverbatim
   *>
   *> \param[in] KL
   *> \verbatim
   *>          KL is INTEGER
   *>           The number of subdiagonals within the band of A.  KL >= 0.
   *> \endverbatim
   *>
   *> \param[in] KU
   *> \verbatim
   *>          KU is INTEGER
   *>           The number of superdiagonals within the band of A.  KU >= 0.
   *> \endverbatim
   *>
   *> \param[in] ALPHA
   *> \verbatim
   *>          ALPHA is DOUBLE PRECISION
   *>           On entry, ALPHA specifies the scalar alpha.
   *>           Unchanged on exit.
   *> \endverbatim
   *>
   *> \param[in] AB
   *> \verbatim
   *>          AB is DOUBLE PRECISION array of DIMENSION ( LDAB, n )
   *>           Before entry, the leading m by n part of the array AB must
   *>           contain the matrix of coefficients.
   *>           Unchanged on exit.
   *> \endverbatim
   *>
   *> \param[in] LDAB
   *> \verbatim
   *>          LDAB is INTEGER
   *>           On entry, LDA specifies the first dimension of AB as declared
   *>           in the calling (sub) program. LDAB must be at least
   *>           max( 1, m ).
   *>           Unchanged on exit.
   *> \endverbatim
   *>
   *> \param[in] X
   *> \verbatim
   *>          X is DOUBLE PRECISION array, dimension
   *>           ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
   *>           and at least
   *>           ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
   *>           Before entry, the incremented array X must contain the
   *>           vector x.
   *>           Unchanged on exit.
   *> \endverbatim
   *>
   *> \param[in] INCX
   *> \verbatim
   *>          INCX is INTEGER
   *>           On entry, INCX specifies the increment for the elements of
   *>           X. INCX must not be zero.
   *>           Unchanged on exit.
   *> \endverbatim
   *>
   *> \param[in] BETA
   *> \verbatim
   *>          BETA is DOUBLE PRECISION
   *>           On entry, BETA specifies the scalar beta. When BETA is
   *>           supplied as zero then Y need not be set on input.
   *>           Unchanged on exit.
   *> \endverbatim
   *>
   *> \param[in,out] Y
   *> \verbatim
   *>          Y is DOUBLE PRECISION array, dimension
   *>           ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
   *>           and at least
   *>           ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
   *>           Before entry with BETA non-zero, the incremented array Y
   *>           must contain the vector y. On exit, Y is overwritten by the
   *>           updated vector y.
   *> \endverbatim
   *>
   *> \param[in] INCY
   *> \verbatim
   *>          INCY is INTEGER
   *>           On entry, INCY specifies the increment for the elements of
   *>           Y. INCY must not be zero.
   *>           Unchanged on exit.
   *>
   *>  Level 2 Blas routine.
   *> \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 DLA_GBAMV( TRANS, M, N, KL, KU, ALPHA, AB, LDAB, X,        SUBROUTINE DLA_GBAMV( TRANS, M, N, KL, KU, ALPHA, AB, LDAB, X,
      $                      INCX, BETA, Y, INCY )       $                      INCX, BETA, Y, INCY )
 *  *
 *     -- LAPACK routine (version 3.3.1)                                 --  *  -- LAPACK computational routine (version 3.4.0) --
 *     -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *     -- Jason Riedy of Univ. of California Berkeley.                 --  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     -- June 2010                                                    --  *     November 2011
 *  
 *     -- LAPACK is a software package provided by Univ. of Tennessee, --  
 *     -- Univ. of California Berkeley and NAG Ltd.                    --  
 *  *
       IMPLICIT NONE  
 *     ..  
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       DOUBLE PRECISION   ALPHA, BETA        DOUBLE PRECISION   ALPHA, BETA
       INTEGER            INCX, INCY, LDAB, M, N, KL, KU, TRANS        INTEGER            INCX, INCY, LDAB, M, N, KL, KU, TRANS
Line 19 Line 198
       DOUBLE PRECISION   AB( LDAB, * ), X( * ), Y( * )        DOUBLE PRECISION   AB( LDAB, * ), X( * ), Y( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DLA_GBAMV  performs one of the matrix-vector operations  
 *  
 *          y := alpha*abs(A)*abs(x) + beta*abs(y),  
 *     or   y := alpha*abs(A)**T*abs(x) + beta*abs(y),  
 *  
 *  where alpha and beta are scalars, x and y are vectors and A is an  
 *  m by n matrix.  
 *  
 *  This function is primarily used in calculating error bounds.  
 *  To protect against underflow during evaluation, components in  
 *  the resulting vector are perturbed away from zero by (N+1)  
 *  times the underflow threshold.  To prevent unnecessarily large  
 *  errors for block-structure embedded in general matrices,  
 *  "symbolically" zero components are not perturbed.  A zero  
 *  entry is considered "symbolic" if all multiplications involved  
 *  in computing that entry have at least one zero multiplicand.  
 *  
 *  Arguments  
 *  ==========  
 *  
 *  TRANS   (input) INTEGER  
 *           On entry, TRANS specifies the operation to be performed as  
 *           follows:  
 *  
 *             BLAS_NO_TRANS      y := alpha*abs(A)*abs(x) + beta*abs(y)  
 *             BLAS_TRANS         y := alpha*abs(A**T)*abs(x) + beta*abs(y)  
 *             BLAS_CONJ_TRANS    y := alpha*abs(A**T)*abs(x) + beta*abs(y)  
 *  
 *           Unchanged on exit.  
 *  
 *  M        (input) INTEGER  
 *           On entry, M specifies the number of rows of the matrix A.  
 *           M must be at least zero.  
 *           Unchanged on exit.  
 *  
 *  N        (input) INTEGER  
 *           On entry, N specifies the number of columns of the matrix A.  
 *           N must be at least zero.  
 *           Unchanged on exit.  
 *  
 *  KL       (input) INTEGER  
 *           The number of subdiagonals within the band of A.  KL >= 0.  
 *  
 *  KU       (input) INTEGER  
 *           The number of superdiagonals within the band of A.  KU >= 0.  
 *  
 *  ALPHA    (input) DOUBLE PRECISION  
 *           On entry, ALPHA specifies the scalar alpha.  
 *           Unchanged on exit.  
 *  
 *  AB       (input) DOUBLE PRECISION array of DIMENSION ( LDAB, n )  
 *           Before entry, the leading m by n part of the array AB must  
 *           contain the matrix of coefficients.  
 *           Unchanged on exit.  
 *  
 *  LDAB     (input) INTEGER  
 *           On entry, LDA specifies the first dimension of AB as declared  
 *           in the calling (sub) program. LDAB must be at least  
 *           max( 1, m ).  
 *           Unchanged on exit.  
 *  
 *  X        (input) DOUBLE PRECISION array, dimension  
 *           ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'  
 *           and at least  
 *           ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.  
 *           Before entry, the incremented array X must contain the  
 *           vector x.  
 *           Unchanged on exit.  
 *  
 *  INCX     (input) INTEGER  
 *           On entry, INCX specifies the increment for the elements of  
 *           X. INCX must not be zero.  
 *           Unchanged on exit.  
 *  
 *  BETA     (input)  DOUBLE PRECISION  
 *           On entry, BETA specifies the scalar beta. When BETA is  
 *           supplied as zero then Y need not be set on input.  
 *           Unchanged on exit.  
 *  
 *  Y        (input/output) DOUBLE PRECISION  array, dimension  
 *           ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'  
 *           and at least  
 *           ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.  
 *           Before entry with BETA non-zero, the incremented array Y  
 *           must contain the vector y. On exit, Y is overwritten by the  
 *           updated vector y.  
 *  
 *  INCY     (input) INTEGER  
 *           On entry, INCY specifies the increment for the elements of  
 *           Y. INCY must not be zero.  
 *           Unchanged on exit.  
 *  
 *  
 *  Level 2 Blas routine.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Removed from v.1.5  
changed lines
  Added in v.1.6

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