Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3  - reduces a complex general m-by-n band matrix A to real upper bidiagonal form B
       by a unitary transformation

SYNOPSIS

       SUBROUTINE ZGBBRD( VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q,  LDQ,  PT,  LDPT,  C,  LDC,
                          WORK, RWORK, INFO )

           CHARACTER      VECT

           INTEGER        INFO, KL, KU, LDAB, LDC, LDPT, LDQ, M, N, NCC

           DOUBLE         PRECISION D( * ), E( * ), RWORK( * )

           COMPLEX*16     AB( LDAB, * ), C( LDC, * ), PT( LDPT, * ), Q( LDQ, * ), WORK( * )

PURPOSE

       ZGBBRD reduces a complex general m-by-n band matrix A to real upper bidiagonal form B by a
       unitary transformation: Q**H * A * P = B.
        The routine computes B, and optionally forms Q or P**H, or computes
        Q**H*C for a given matrix C.

ARGUMENTS

        VECT    (input) CHARACTER*1
                Specifies whether or not the matrices Q and P**H are to be
                formed.
                = 'N': do not form Q or P**H;
                = 'Q': form Q only;
                = 'P': form P**H only;
                = 'B': form both.

        M       (input) INTEGER
                The number of rows of the matrix A.  M >= 0.

        N       (input) INTEGER
                The number of columns of the matrix A.  N >= 0.

        NCC     (input) INTEGER
                The number of columns of the matrix C.  NCC >= 0.

        KL      (input) INTEGER
                The number of subdiagonals of the matrix A. KL >= 0.

        KU      (input) INTEGER
                The number of superdiagonals of the matrix A. KU >= 0.

        AB      (input/output) COMPLEX*16 array, dimension (LDAB,N)
                On entry, the m-by-n band matrix A, stored in rows 1 to
                KL+KU+1. The j-th column of A is stored in the j-th column of
                the array AB as follows:
                AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl).
                On exit, A is overwritten by values generated during the
                reduction.

        LDAB    (input) INTEGER
                The leading dimension of the array A. LDAB >= KL+KU+1.

        D       (output) DOUBLE PRECISION array, dimension (min(M,N))
                The diagonal elements of the bidiagonal matrix B.

        E       (output) DOUBLE PRECISION array, dimension (min(M,N)-1)
                The superdiagonal elements of the bidiagonal matrix B.

        Q       (output) COMPLEX*16 array, dimension (LDQ,M)
                If VECT = 'Q' or 'B', the m-by-m unitary matrix Q.
                If VECT = 'N' or 'P', the array Q is not referenced.

        LDQ     (input) INTEGER
                The leading dimension of the array Q.
                LDQ >= max(1,M) if VECT = 'Q' or 'B'; LDQ >= 1 otherwise.

        PT      (output) COMPLEX*16 array, dimension (LDPT,N)
                If VECT = 'P' or 'B', the n-by-n unitary matrix P'.
                If VECT = 'N' or 'Q', the array PT is not referenced.

        LDPT    (input) INTEGER
                The leading dimension of the array PT.
                LDPT >= max(1,N) if VECT = 'P' or 'B'; LDPT >= 1 otherwise.

        C       (input/output) COMPLEX*16 array, dimension (LDC,NCC)
                On entry, an m-by-ncc matrix C.
                On exit, C is overwritten by Q**H*C.
                C is not referenced if NCC = 0.

        LDC     (input) INTEGER
                The leading dimension of the array C.
                LDC >= max(1,M) if NCC > 0; LDC >= 1 if NCC = 0.

        WORK    (workspace) COMPLEX*16 array, dimension (max(M,N))

        RWORK   (workspace) DOUBLE PRECISION array, dimension (max(M,N))

        INFO    (output) INTEGER
                = 0:  successful exit.
                < 0:  if INFO = -i, the i-th argument had an illegal value.

 LAPACK routine (version 3.3.1)             April 2011                            ZGBBRD(3lapack)