DGBMV(3)                    MathKeisan BLAS routine                   DGBMV(3)



NAME
       DGBMV  - perform one of the matrix-vector operations   y := alpha*A*x +
       beta*y, y := alpha*A'*x + beta*y

SYNOPSIS
       SUBROUTINE DGBMV ( TRANS, M, N, KL, KU, ALPHA, A, LDA, X,  INCX,  BETA,
                        Y, INCY )

           DOUBLE       PRECISION ALPHA, BETA

           INTEGER      INCX, INCY, KL, KU, LDA, M, N

           CHARACTER*1  TRANS

           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'*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.


PARAMETERS
       TRANS  - CHARACTER*1.
              On entry, TRANS specifies the operation to be performed as  fol-
              lows:

              TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.

              TRANS = 'T' or 't'   y := alpha*A'*x + beta*y.

              TRANS = 'C' or 'c'   y := alpha*A'*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 cor-
              respond to elements in the band matrix (such as the top left  ku
              by  ku triangle) are not referenced.  The following program seg-
              ment 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.

              Level 2 Blas routine.

              -- 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.



BLAS routine                    16 October 1992                       DGBMV(3)