CGBBRD(3)      LAPACK routine of NEC Numeric Library Collection      CGBBRD(3)



NAME
       CGBBRD

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



PURPOSE
            CGBBRD 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)
                     VECT is 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)
                     M is INTEGER
                     The number of rows of the matrix A.  M >= 0.

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

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

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

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

           AB        (input/output)
                     AB is COMPLEX 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)
                     LDAB is INTEGER
                     The leading dimension of the array A. LDAB >= KL+KU+1.

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

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

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

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

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

           WORK      (output)
                     WORK is COMPLEX array, dimension (max(M,N))

           RWORK     (output)
                     RWORK is REAL array, dimension (max(M,N))

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



LAPACK routine                  31 October 2017                      CGBBRD(3)