BLAS/SRC/zgbmv.f(3)        Library Functions Manual        BLAS/SRC/zgbmv.f(3)

NAME
       BLAS/SRC/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 (character trans, integer m, integer n, integer kl,
       integer ku, 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)
       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, 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, 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, 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.
                      If either m or n is zero, then Y not referenced and the function
                      performs a quick return.

           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.

       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
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0             BLAS/SRC/zgbmv.f(3)