zgbmv.f(3)

NAME
zgbmv.f -

SYNOPSIS

  Functions/Subroutines
subroutine ZGBMV (TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
ZGBMV

Function/Subroutine Documentation

  subroutine ZGBMV (CHARACTERTRANS, INTEGERM, INTEGERN, INTEGERKL, INTEGERKU, COMPLEX*16ALPHA, COMPLEX*16, dimension(lda,*)A, INTEGERLDA, COMPLEX*16, dimension(*)X, INTEGERINCX, COMPLEX*16BETA, COMPLEX*16, dimension(*)Y, INTEGERINCY)

ZGBMV Purpose:

     ZGBMV  performs one of the matrix-vector operations
        y := alpha*A*x + beta*y,   or   y := alpha*A**T*x + beta*y,   or
        y := alpha*A**H*x + beta*y,
     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.

Parameters:
    TRANS

              TRANS is 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**T*x + beta*y.
                  TRANS = 'C' or 'c'   y := alpha*A**H*x + beta*y.

    M

              M is INTEGER
               On entry, M specifies the number of rows of the matrix A.
               M must be at least zero.

    N

              N is INTEGER
               On entry, N specifies the number of columns of the matrix A.
               N must be at least zero.

    KL

              KL is INTEGER
               On entry, KL specifies the number of sub-diagonals of the
               matrix A. KL must satisfy  0 .le. KL.

    KU

              KU is INTEGER
               On entry, KU specifies the number of super-diagonals of the
               matrix A. KU must satisfy  0 .le. KU.

    ALPHA

              ALPHA is COMPLEX*16
               On entry, ALPHA specifies the scalar alpha.

    A

              A is COMPLEX*16 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

    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
               ( kl + ku + 1 ).

    X

              X is COMPLEX*16 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.

    INCX

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

    BETA

              BETA is COMPLEX*16
               On entry, BETA specifies the scalar beta. When BETA is
               supplied as zero then Y need not be set on input.

    Y

              Y is COMPLEX*16 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

              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 188 of file zgbmv.f'.

Author

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