CGBBRD - reduce 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 )
CHARACTER VECT
INTEGER INFO, KL, KU, LDAB, LDC, LDPT, LDQ, M,
N, NCC
REAL D( * ), E( * ), RWORK( * )
COMPLEX AB( LDAB, * ), C( LDC, * ), PT( LDPT, *
), Q( LDQ, * ), WORK( * )
PURPOSE
CGBBRD 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 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
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 = 'Q' or 'B', the m-by-m unitary matrix Q.
If VECT = 'N' or 'P', the array Q is not refer
enced.
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 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 other
wise.
C (input/output) COMPLEX 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 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 ille
gal value.
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