dgbmv.f

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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, 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, 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, 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.
*
*> \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)
*
*  -- Reference BLAS level2 routine --
*  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      DOUBLE PRECISION ALPHA,BETA
      INTEGER INCX,INCY,KL,KU,LDA,M,N
      CHARACTER TRANS
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION A(LDA,*),X(*),Y(*)
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION ONE,ZERO
      parameter(one=1.0d+0,zero=0.0d+0)
*     ..
*     .. Local Scalars ..
      DOUBLE PRECISION 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('DGBMV ',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 DGBMV
*
      END