sgbmv

SGBMV(1)                         BLAS routine                         SGBMV(1)



NAME
       SGBMV - performs one of the matrix-vector operations   y := alpha*A*x +
       beta*y, or y := alpha*A'*x + beta*y,

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

           REAL                                                         ALPHA,BETA

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

           CHARACTER                                                    TRANS

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

PURPOSE
       SGBMV  performs one of the matrix-vector operations

       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.


ARGUMENTS
       TRANS  - CHARACTER*1.
              On entry, TRANS specifies the operation to be performed as
              follows:

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

       A      - REAL             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
              correspond to elements in the band matrix (such as the top left
              ku by ku triangle) are not referenced.  The following program
              segment 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      - REAL             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            .
              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             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.

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                        SGBMV(1)