dsbmv.f(3)

NAME
dsbmv.f -

SYNOPSIS

  Functions/Subroutines
subroutine dsbmv (UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
DSBMV

Function/Subroutine Documentation

  subroutine dsbmv (characterUPLO, integerN, integerK, double precisionALPHA, double precision, dimension(lda,*)A, integerLDA, double precision, dimension(*)X, integerINCX, double precisionBETA, double precision, dimension(*)Y, integerINCY)

DSBMV 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

              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 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

    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 of 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 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

              INCY is INTEGER
               On entry, INCY specifies the increment for the elements of
               Y. INCY must not be zero.

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    November 2011

Further Details:

      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.

Definition at line 185 of file dsbmv.f.

Author

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