BLAS/SRC/ztbmv.f(3)

NAME
BLAS/SRC/ztbmv.f

SYNOPSIS

  Functions/Subroutines
subroutine ztbmv (uplo, trans, diag, n, k, a, lda, x, incx)
ZTBMV

Function/Subroutine Documentation

  subroutine ztbmv (character uplo, character trans, character diag, integer n, integer k, complex*16, dimension(lda,*) a, integer lda, complex*16, dimension(*) x, integer incx)

ZTBMV

Purpose:

    !>
    !> ZTBMV  performs one of the matrix-vector operations
    !>
    !>    x := A*x,   or   x := A**T*x,   or   x := A**H*x,
    !>
    !> where x is an n element vector and  A is an n by n unit, or non-unit,
    !> upper or lower triangular band matrix, with ( k + 1 ) diagonals.
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>           On entry, UPLO specifies whether the matrix is an upper or
    !>           lower triangular matrix as follows:
    !>
    !>              UPLO = 'U' or 'u'   A is an upper triangular matrix.
    !>
    !>              UPLO = 'L' or 'l'   A is a lower triangular matrix.
    !>

    TRANS

    !>          TRANS is CHARACTER*1
    !>           On entry, TRANS specifies the operation to be performed as
    !>           follows:
    !>
    !>              TRANS = 'N' or 'n'   x := A*x.
    !>
    !>              TRANS = 'T' or 't'   x := A**T*x.
    !>
    !>              TRANS = 'C' or 'c'   x := A**H*x.
    !>

    DIAG

    !>          DIAG is CHARACTER*1
    !>           On entry, DIAG specifies whether or not A is unit
    !>           triangular as follows:
    !>
    !>              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
    !>
    !>              DIAG = 'N' or 'n'   A is not assumed to be unit
    !>                                  triangular.
    !>

    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 with UPLO = 'U' or 'u', K specifies the number of
    !>           super-diagonals of the matrix A.
    !>           On entry with UPLO = 'L' or 'l', K specifies the number of
    !>           sub-diagonals of the matrix A.
    !>           K must satisfy  0 .le. K.
    !>

    A

    !>          A is 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 matrix of coefficients, 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 an upper
    !>           triangular 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 matrix of coefficients, 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 a lower
    !>           triangular 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
    !>
    !>           Note that when DIAG = 'U' or 'u' the elements of the array A
    !>           corresponding to the diagonal elements of the matrix are not
    !>           referenced, but are assumed to be unity.
    !>

    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 COMPLEX*16 array, dimension at least
    !>           ( 1 + ( n - 1 )*abs( INCX ) ).
    !>           Before entry, the incremented array X must contain the n
    !>           element vector x. On exit, X is overwritten with the
    !>           transformed vector x.
    !>

    INCX

    !>          INCX is INTEGER
    !>           On entry, INCX specifies the increment for the elements of
    !>           X. INCX must not be zero.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

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 ztbmv.f.

Author

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