BGEMV(3)        BLAS routine of NEC Numeric Library Collection        BGEMV(3)



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

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

           REAL(kind=2) (bfloat16 format)
                        ALPHA, BETA

           INTEGER      INCX, INCY, LDA, M, N

           CHARACTER*1  TRANS

           REAL(kind=2) (bfloat16 format)
                        A( LDA, * ), X( * ), Y( * )

PURPOSE
       BGEMV  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 matrix.


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.

       ALPHA  - REAL(kind=2) (bfloat16 format).
              On  entry, ALPHA specifies the scalar alpha.  Unchanged on exit.

       A      - REAL(kind=2) (bfloat16 format)
              array of DIMENSION ( LDA, n ).  Before entry, the leading m by n
              part  of  the  array  A must contain the matrix of coefficients.
              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 max( 1, m ).
              Unchanged on exit.

       X      - REAL(kind=2) (bfloat16 format)
              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   - REAL(kind=2) (bfloat16 format).
              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      - REAL(kind=2) (bfloat16 format)
              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  with  BETA non-zero, 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                       BGEMV(3)