*> \brief \b SGBMV
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 
*
*  Definition:
*  ===========
*
*       SUBROUTINE SGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
* 
*       .. Scalar Arguments ..
*       REAL ALPHA,BETA
*       INTEGER INCX,INCY,KL,KU,LDA,M,N
*       CHARACTER TRANS
*       ..
*       .. Array Arguments ..
*       REAL A(LDA,*),X(*),Y(*)
*       ..
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> SGBMV  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 REAL
*>           On entry, ALPHA specifies the scalar alpha.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*>          A is REAL 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 REAL 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 REAL
*>           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 REAL 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 2015
*
*> \ingroup single_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 SGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
*
*  -- Reference BLAS level2 routine (version 3.6.0) --
*  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2015
*
*     .. Scalar Arguments ..
      REAL ALPHA,BETA
      INTEGER INCX,INCY,KL,KU,LDA,M,N
      CHARACTER TRANS
*     ..
*     .. Array Arguments ..
      REAL A(LDA,*),X(*),Y(*)
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL ONE,ZERO
      PARAMETER (ONE=1.0E+0,ZERO=0.0E+0)
*     ..
*     .. Local Scalars ..
      REAL TEMP
      INTEGER I,INFO,IX,IY,J,JX,JY,K,KUP1,KX,KY,LENX,LENY
*     ..
*     .. External Functions ..
      LOGICAL LSAME
      EXTERNAL LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC MAX,MIN
*     ..
*
*     Test the input parameters.
*
      INFO = 0
      IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
     +    .NOT.LSAME(TRANS,'C')) THEN
          INFO = 1
      ELSE IF (M.LT.0) THEN
          INFO = 2
      ELSE IF (N.LT.0) THEN
          INFO = 3
      ELSE IF (KL.LT.0) THEN
          INFO = 4
      ELSE IF (KU.LT.0) THEN
          INFO = 5
      ELSE IF (LDA.LT. (KL+KU+1)) THEN
          INFO = 8
      ELSE IF (INCX.EQ.0) THEN
          INFO = 10
      ELSE IF (INCY.EQ.0) THEN
          INFO = 13
      END IF
      IF (INFO.NE.0) THEN
          CALL XERBLA('SGBMV ',INFO)
          RETURN
      END IF
*
*     Quick return if possible.
*
      IF ((M.EQ.0) .OR. (N.EQ.0) .OR.
     +    ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
*
*     Set  LENX  and  LENY, the lengths of the vectors x and y, and set
*     up the start points in  X  and  Y.
*
      IF (LSAME(TRANS,'N')) THEN
          LENX = N
          LENY = M
      ELSE
          LENX = M
          LENY = N
      END IF
      IF (INCX.GT.0) THEN
          KX = 1
      ELSE
          KX = 1 - (LENX-1)*INCX
      END IF
      IF (INCY.GT.0) THEN
          KY = 1
      ELSE
          KY = 1 - (LENY-1)*INCY
      END IF
*
*     Start the operations. In this version the elements of A are
*     accessed sequentially with one pass through the band part of A.
*
*     First form  y := beta*y.
*
      IF (BETA.NE.ONE) THEN
          IF (INCY.EQ.1) THEN
              IF (BETA.EQ.ZERO) THEN
                  DO 10 I = 1,LENY
                      Y(I) = ZERO
   10             CONTINUE
              ELSE
                  DO 20 I = 1,LENY
                      Y(I) = BETA*Y(I)
   20             CONTINUE
              END IF
          ELSE
              IY = KY
              IF (BETA.EQ.ZERO) THEN
                  DO 30 I = 1,LENY
                      Y(IY) = ZERO
                      IY = IY + INCY
   30             CONTINUE
              ELSE
                  DO 40 I = 1,LENY
                      Y(IY) = BETA*Y(IY)
                      IY = IY + INCY
   40             CONTINUE
              END IF
          END IF
      END IF
      IF (ALPHA.EQ.ZERO) RETURN
      KUP1 = KU + 1
      IF (LSAME(TRANS,'N')) THEN
*
*        Form  y := alpha*A*x + y.
*
          JX = KX
          IF (INCY.EQ.1) THEN
              DO 60 J = 1,N
                  TEMP = ALPHA*X(JX)
                  K = KUP1 - J
                  DO 50 I = MAX(1,J-KU),MIN(M,J+KL)
                      Y(I) = Y(I) + TEMP*A(K+I,J)
   50             CONTINUE
                  JX = JX + INCX
   60         CONTINUE
          ELSE
              DO 80 J = 1,N
                  TEMP = ALPHA*X(JX)
                  IY = KY
                  K = KUP1 - J
                  DO 70 I = MAX(1,J-KU),MIN(M,J+KL)
                      Y(IY) = Y(IY) + TEMP*A(K+I,J)
                      IY = IY + INCY
   70             CONTINUE
                  JX = JX + INCX
                  IF (J.GT.KU) KY = KY + INCY
   80         CONTINUE
          END IF
      ELSE
*
*        Form  y := alpha*A**T*x + y.
*
          JY = KY
          IF (INCX.EQ.1) THEN
              DO 100 J = 1,N
                  TEMP = ZERO
                  K = KUP1 - J
                  DO 90 I = MAX(1,J-KU),MIN(M,J+KL)
                      TEMP = TEMP + A(K+I,J)*X(I)
   90             CONTINUE
                  Y(JY) = Y(JY) + ALPHA*TEMP
                  JY = JY + INCY
  100         CONTINUE
          ELSE
              DO 120 J = 1,N
                  TEMP = ZERO
                  IX = KX
                  K = KUP1 - J
                  DO 110 I = MAX(1,J-KU),MIN(M,J+KL)
                      TEMP = TEMP + A(K+I,J)*X(IX)
                      IX = IX + INCX
  110             CONTINUE
                  Y(JY) = Y(JY) + ALPHA*TEMP
                  JY = JY + INCY
                  IF (J.GT.KU) KX = KX + INCX
  120         CONTINUE
          END IF
      END IF
*
      RETURN
*
*     End of SGBMV .
*
      END
