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



NAME
       DSBMV - perform the matrix-vector operation   y := alpha*A*x + beta*y

SYNOPSIS
       SUBROUTINE DSBMV ( UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y, INCY )

           DOUBLE       PRECISION ALPHA, BETA

           INTEGER      INCX, INCY, K, LDA, N

           CHARACTER*1  UPLO

           DOUBLE       PRECISION A( LDA, * ), X( * ), Y( * )

PURPOSE
       DSBMV  performs the matrix-vector  operation

          y := alpha*A*x + beta*y

       where  alpha  and beta are scalars, x and y are n element vectors and A
       is an n by n symmetric band matrix, with k super-diagonals.


PARAMETERS
       UPLO   - CHARACTER*1.
              On entry, UPLO specifies whether the upper or  lower  triangular
              part of the band matrix A is being supplied as follows:

              UPLO = 'U' or 'u'   The upper triangular part of A is being sup-
              plied.

              UPLO = 'L' or 'l'   The lower triangular part of A is being sup-
              plied.

              Unchanged on exit.

       N      - INTEGER.
              On  entry,  N specifies the order of the matrix A.  N must be at
              least zero.  Unchanged on exit.

       K      - INTEGER.
              On entry, K specifies  the  number  of  super-diagonals  of  the
              matrix A. K must satisfy  0 .le. K.  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 with UPLO = 'U' or 'u', the leading ( k + 1 ) by  n
              part  of the array A must contain the upper triangular band part
              of the symmetric matrix, supplied column  by  column,  with  the
              leading  diagonal  of  the matrix in row ( k + 1 ) of the array,
              the first super-diagonal starting at position 2 in row k, and so
              on.  The  top  left k by k triangle of the array A is not refer-
              enced.  The following program segment will  transfer  the  upper
              triangular  part  of  a  symmetric band matrix from conventional
              full matrix storage to band storage:

              DO 20, J = 1, N M = K + 1 - J DO 10, I = MAX( 1, J - K ), J A( M
              + I, J ) = matrix( I, J ) 10    CONTINUE 20 CONTINUE

              Before  entry with UPLO = 'L' or 'l', the leading ( k + 1 ) by n
              part of the array A must contain the lower triangular band  part
              of  the  symmetric  matrix,  supplied column by column, with the
              leading diagonal of the matrix in row 1 of the array, the  first
              sub-diagonal  starting  at  position  1 in row 2, and so on. The
              bottom right k by k triangle of the array A is  not  referenced.
              The following program segment will transfer the lower triangular
              part of a symmetric band matrix from  conventional  full  matrix
              storage to band storage:

              DO  20,  J = 1, N M = 1 - J DO 10, I = J, MIN( N, J + K ) A( M +
              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 ( k + 1 ).
              Unchanged on exit.

       X      - DOUBLE PRECISION array of DIMENSION at least
              ( 1 + ( n - 1 )*abs( INCX ) ).  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.  Unchanged on exit.

       Y      - DOUBLE PRECISION array of DIMENSION at least
              ( 1 + ( n - 1 )*abs( INCY ) ).  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                       DSBMV(3)