ssbmv

SSBMV(1)                         BLAS routine                         SSBMV(1)



NAME
       SSBMV - performs the matrix-vector operation   y := alpha*A*x + beta*y,

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

           REAL                                                  ALPHA,BETA

           INTEGER                                               INCX,INCY,K,LDA,N

           CHARACTER                                             UPLO

           REAL                                                  A(LDA,*),X(*),Y(*)

PURPOSE
       SSBMV  performs the matrix-vector  operation

       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.


ARGUMENTS
       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
              supplied.

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

              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  - REAL            .
              On entry, ALPHA specifies the scalar alpha.  Unchanged on exit.

       A      - REAL             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
              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

              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      - REAL             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   - REAL            .
              On entry, BETA specifies the scalar beta.  Unchanged on exit.

       Y      - REAL             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.

FURTHER DETAILS
       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                     November 2008                        SSBMV(1)