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.

UPLO

          UPLO is 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 supplied.


              UPLO = 'L' or 'l'   The lower triangular part of A is


                                  being supplied.

N

          N is INTEGER


           On entry, N specifies the order of the matrix A.


           N must be at least zero.

K

          K is INTEGER


           On entry, K specifies the number of super-diagonals of the


           matrix A. K must satisfy  0 .le. K.

ALPHA

          ALPHA is DOUBLE PRECISION.


           On entry, ALPHA specifies the scalar alpha.

A

          A is DOUBLE PRECISION array, 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 referenced.


           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

LDA

          LDA is INTEGER


           On entry, LDA specifies the first dimension of A as declared


           in the calling (sub) program. LDA must be at least


           ( k + 1 ).

X

          X is DOUBLE PRECISION array, dimension at least


           ( 1 + ( n - 1 )*abs( INCX ) ).


           Before entry, the incremented array X must contain the


           vector x.

INCX

          INCX is INTEGER


           On entry, INCX specifies the increment for the elements of


           X. INCX must not be zero.

BETA

          BETA is DOUBLE PRECISION.


           On entry, BETA specifies the scalar beta.

Y

          Y is DOUBLE PRECISION array, 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

          INCY is INTEGER


           On entry, INCY specifies the increment for the elements of


           Y. INCY must not be zero.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

December 2016

  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.