TESTING/LIN/zsbmv.f(3)

NAME
TESTING/LIN/zsbmv.f

SYNOPSIS

  Functions/Subroutines
subroutine zsbmv (uplo, n, k, alpha, a, lda, x, incx, beta, y, incy)
ZSBMV

Function/Subroutine Documentation

  subroutine zsbmv (character uplo, integer n, integer k, complex*16 alpha, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) x, integer incx, complex*16 beta, complex*16, dimension( * ) y, integer incy)

ZSBMV

Purpose:

    !>
    !> ZSBMV  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   - 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  - COMPLEX*16
    !>           On entry, ALPHA specifies the scalar alpha.
    !>           Unchanged on exit.
    !>
    !>  A      - COMPLEX*16 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
    !>
    !>           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      - COMPLEX*16 array, 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   - COMPLEX*16
    !>           On entry, BETA specifies the scalar beta.
    !>           Unchanged on exit.
    !>
    !>  Y      - COMPLEX*16 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   - INTEGER
    !>           On entry, INCY specifies the increment for the elements of
    !>           Y. INCY must not be zero.
    !>           Unchanged on exit.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 150 of file zsbmv.f.

Author

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