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CGBBRD

Section: LAPACK routine (version 3.3.1) (1)
Updated: April 2011
Index

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 CGBBRD(: VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q,LDQ, PT, LDPT, C, LDC, WORK, RWORK, INFO )
: CHARACTERVECT
: INTEGERINFO, KL, KU, LDAB, LDC, LDPT, LDQ, M, N, NCC
: REALD( * ), E( * ), RWORK( * )
: COMPLEXAB( LDAB, * ), C( LDC, * ), PT( LDPT, * ),Q( LDQ, * ), WORK( * )

PURPOSE

CGBBRD reduces a complex general m-by-n band matrix A to real upperbidiagonal 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.
= aqNaq: do not form Q or P**H;

= aqQaq: form Q only;

= aqPaq: form P**H only;

= aqBaq: 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 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) REAL array, dimension (min(M,N)): The diagonal elements of the bidiagonal matrix B.
E (output) REAL array, dimension (min(M,N)-1): The superdiagonal elements of the bidiagonal matrix B.
Q (output) COMPLEX array, dimension (LDQ,M): If VECT = aqQaq or aqBaq, the m-by-m unitary matrix Q.
If VECT = aqNaq or aqPaq, the array Q is not referenced.
LDQ (input) INTEGER: The leading dimension of the array Q.
LDQ >= max(1,M) if VECT = aqQaq or aqBaq; LDQ >= 1 otherwise.
PT (output) COMPLEX array, dimension (LDPT,N): If VECT = aqPaq or aqBaq, the n-by-n unitary matrix Paq.
If VECT = aqNaq or aqQaq, the array PT is not referenced.
LDPT (input) INTEGER: The leading dimension of the array PT.
LDPT >= max(1,N) if VECT = aqPaq or aqBaq; LDPT >= 1 otherwise.
C (input/output) 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) INTEGER: The leading dimension of the array C.
LDC >= max(1,M) if NCC > 0; LDC >= 1 if NCC = 0.
WORK (workspace) COMPLEX array, dimension (max(M,N))
RWORK (workspace) REAL 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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