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# LAPACK-3

## man page of LAPACK-3

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

```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' * 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 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'*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 3.2)     March 2011                       LAPACK-3(3)
```