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version 1.7, 2011/07/22 07:38:01 version 1.8, 2011/11/21 20:37:07
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   *> \brief \b DGBMV
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
   * 
   *       .. Scalar Arguments ..
   *       DOUBLE PRECISION ALPHA,BETA
   *       INTEGER INCX,INCY,KL,KU,LDA,M,N
   *       CHARACTER TRANS
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION A(LDA,*),X(*),Y(*)
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DGBMV  performs one of the matrix-vector operations
   *>
   *>    y := alpha*A*x + beta*y,   or   y := alpha*A**T*x + beta*y,
   *>
   *> where alpha and beta are scalars, x and y are vectors and A is an
   *> m by n band matrix, with kl sub-diagonals and ku super-diagonals.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] TRANS
   *> \verbatim
   *>          TRANS is CHARACTER*1
   *>           On entry, TRANS specifies the operation to be performed as
   *>           follows:
   *>
   *>              TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.
   *>
   *>              TRANS = 'T' or 't'   y := alpha*A**T*x + beta*y.
   *>
   *>              TRANS = 'C' or 'c'   y := alpha*A**T*x + beta*y.
   *> \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.
   *> \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.
   *> \endverbatim
   *>
   *> \param[in] KL
   *> \verbatim
   *>          KL is INTEGER
   *>           On entry, KL specifies the number of sub-diagonals of the
   *>           matrix A. KL must satisfy  0 .le. KL.
   *> \endverbatim
   *>
   *> \param[in] KU
   *> \verbatim
   *>          KU is INTEGER
   *>           On entry, KU specifies the number of super-diagonals of the
   *>           matrix A. KU must satisfy  0 .le. KU.
   *> \endverbatim
   *>
   *> \param[in] ALPHA
   *> \verbatim
   *>          ALPHA is DOUBLE PRECISION.
   *>           On entry, ALPHA specifies the scalar alpha.
   *> \endverbatim
   *>
   *> \param[in] A
   *> \verbatim
   *>          A is DOUBLE PRECISION array of DIMENSION ( LDA, n ).
   *>           Before entry, the leading ( kl + ku + 1 ) by n part of the
   *>           array A must contain the matrix of coefficients, supplied
   *>           column by column, with the leading diagonal of the matrix in
   *>           row ( ku + 1 ) of the array, the first super-diagonal
   *>           starting at position 2 in row ku, the first sub-diagonal
   *>           starting at position 1 in row ( ku + 2 ), and so on.
   *>           Elements in the array A that do not correspond to elements
   *>           in the band matrix (such as the top left ku by ku triangle)
   *>           are not referenced.
   *>           The following program segment will transfer a band matrix
   *>           from conventional full matrix storage to band storage:
   *>
   *>                 DO 20, J = 1, N
   *>                    K = KU + 1 - J
   *>                    DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL )
   *>                       A( K + I, J ) = matrix( I, J )
   *>              10    CONTINUE
   *>              20 CONTINUE
   *> \endverbatim
   *>
   *> \param[in] LDA
   *> \verbatim
   *>          LDA is INTEGER
   *>           On entry, LDA specifies the first dimension of A as declared
   *>           in the calling (sub) program. LDA must be at least
   *>           ( kl + ku + 1 ).
   *> \endverbatim
   *>
   *> \param[in] X
   *> \verbatim
   *>          X is DOUBLE PRECISION array of DIMENSION at least
   *>           ( 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.
   *> \endverbatim
   *>
   *> \param[in] INCX
   *> \verbatim
   *>          INCX is INTEGER
   *>           On entry, INCX specifies the increment for the elements of
   *>           X. INCX must not be zero.
   *> \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.
   *> \endverbatim
   *>
   *> \param[in,out] Y
   *> \verbatim
   *>          Y is DOUBLE PRECISION array of DIMENSION at least
   *>           ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
   *>           and at least
   *>           ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
   *>           Before entry, 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.
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup double_blas_level2
   *
   *> \par Further Details:
   *  =====================
   *>
   *> \verbatim
   *>
   *>  Level 2 Blas routine.
   *>  The vector and matrix arguments are not referenced when N = 0, or M = 0
   *>
   *>  -- Written on 22-October-1986.
   *>     Jack Dongarra, Argonne National Lab.
   *>     Jeremy Du Croz, Nag Central Office.
   *>     Sven Hammarling, Nag Central Office.
   *>     Richard Hanson, Sandia National Labs.
   *> \endverbatim
   *>
   *  =====================================================================
       SUBROUTINE DGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)        SUBROUTINE DGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
   *
   *  -- Reference BLAS level2 routine (version 3.4.0) --
   *  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
   *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
   *     November 2011
   *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       DOUBLE PRECISION ALPHA,BETA        DOUBLE PRECISION ALPHA,BETA
       INTEGER INCX,INCY,KL,KU,LDA,M,N        INTEGER INCX,INCY,KL,KU,LDA,M,N
Line 8 Line 199
       DOUBLE PRECISION A(LDA,*),X(*),Y(*)        DOUBLE PRECISION A(LDA,*),X(*),Y(*)
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DGBMV  performs one of the matrix-vector operations  
 *  
 *     y := alpha*A*x + beta*y,   or   y := alpha*A**T*x + beta*y,  
 *  
 *  where alpha and beta are scalars, x and y are vectors and A is an  
 *  m by n band matrix, with kl sub-diagonals and ku super-diagonals.  
 *  
 *  Arguments  
 *  ==========  
 *  
 *  TRANS  - CHARACTER*1.  
 *           On entry, TRANS specifies the operation to be performed as  
 *           follows:  
 *  
 *              TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.  
 *  
 *              TRANS = 'T' or 't'   y := alpha*A**T*x + beta*y.  
 *  
 *              TRANS = 'C' or 'c'   y := alpha*A**T*x + beta*y.  
 *  
 *           Unchanged on exit.  
 *  
 *  M      - INTEGER.  
 *           On entry, M specifies the number of rows of the matrix A.  
 *           M must be at least zero.  
 *           Unchanged on exit.  
 *  
 *  N      - INTEGER.  
 *           On entry, N specifies the number of columns of the matrix A.  
 *           N must be at least zero.  
 *           Unchanged on exit.  
 *  
 *  KL     - INTEGER.  
 *           On entry, KL specifies the number of sub-diagonals of the  
 *           matrix A. KL must satisfy  0 .le. KL.  
 *           Unchanged on exit.  
 *  
 *  KU     - INTEGER.  
 *           On entry, KU specifies the number of super-diagonals of the  
 *           matrix A. KU must satisfy  0 .le. KU.  
 *           Unchanged on exit.  
 *  
 *  ALPHA  - DOUBLE PRECISION.  
 *           On entry, ALPHA specifies the scalar alpha.  
 *           Unchanged on exit.  
 *  
 *  A      - DOUBLE PRECISION array of DIMENSION ( LDA, n ).  
 *           Before entry, the leading ( kl + ku + 1 ) by n part of the  
 *           array A must contain the matrix of coefficients, supplied  
 *           column by column, with the leading diagonal of the matrix in  
 *           row ( ku + 1 ) of the array, the first super-diagonal  
 *           starting at position 2 in row ku, the first sub-diagonal  
 *           starting at position 1 in row ( ku + 2 ), and so on.  
 *           Elements in the array A that do not correspond to elements  
 *           in the band matrix (such as the top left ku by ku triangle)  
 *           are not referenced.  
 *           The following program segment will transfer a band matrix  
 *           from conventional full matrix storage to band storage:  
 *  
 *                 DO 20, J = 1, N  
 *                    K = KU + 1 - J  
 *                    DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL )  
 *                       A( K + I, J ) = matrix( I, J )  
 *              10    CONTINUE  
 *              20 CONTINUE  
 *  
 *           Unchanged on exit.  
 *  
 *  LDA    - INTEGER.  
 *           On entry, LDA specifies the first dimension of A as declared  
 *           in the calling (sub) program. LDA must be at least  
 *           ( kl + ku + 1 ).  
 *           Unchanged on exit.  
 *  
 *  X      - DOUBLE PRECISION array of DIMENSION at least  
 *           ( 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   - INTEGER.  
 *           On entry, INCX specifies the increment for the elements of  
 *           X. INCX must not be zero.  
 *           Unchanged on exit.  
 *  
 *  BETA   - 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      - DOUBLE PRECISION array of DIMENSION at least  
 *           ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'  
 *           and at least  
 *           ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.  
 *           Before entry, the incremented array Y must contain the  
 *           vector y. On exit, Y is overwritten by the updated vector y.  
 *  
 *  INCY   - INTEGER.  
 *           On entry, INCY specifies the increment for the elements of  
 *           Y. INCY must not be zero.  
 *           Unchanged on exit.  
 *  
 *  Further Details  
 *  ===============  
 *  
 *  Level 2 Blas routine.  
 *  The vector and matrix arguments are not referenced when N = 0, or M = 0  
 *  
 *  -- Written on 22-October-1986.  
 *     Jack Dongarra, Argonne National Lab.  
 *     Jeremy Du Croz, Nag Central Office.  
 *     Sven Hammarling, Nag Central Office.  
 *     Richard Hanson, Sandia National Labs.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
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  Added in v.1.8

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