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NAME

        ZGBBRD  -  reduce  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’ * A * P = B.  The
        routine computes B, and optionally forms Q or P’, or computes Q’*C  for
        a given matrix C.
 

ARGUMENTS

        VECT    (input) CHARACTER*1
                Specifies  whether  or  not  the  matrices  Q  and P’ are to be
                formed.  = ’N’: do not form Q or P’;
                = ’Q’: form Q only;
                = ’P’: form P’ 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 gen‐
                erated 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’*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.
 

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