CUNMBR - VECT = 'Q', CUNMBR overwrites the general complex
M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
SYNOPSIS
SUBROUTINE CUNMBR( VECT, SIDE, TRANS, M, N, K, A, LDA,
TAU, C, LDC, WORK, LWORK, INFO )
CHARACTER SIDE, TRANS, VECT
INTEGER INFO, K, LDA, LDC, LWORK, M, N
COMPLEX A( LDA, * ), C( LDC, * ), TAU( * ),
WORK( * )
PURPOSE
If VECT = 'Q', CUNMBR overwrites the general complex M-by-
N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C
* Q TRANS = 'C': Q**H * C C * Q**H
If VECT = 'P', CUNMBR overwrites the general complex M-by-
N matrix C with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': P * C C * P
TRANS = 'C': P**H * C C * P**H
Here Q and P**H are the unitary matrices determined by
CGEBRD when reducing a complex matrix A to bidiagonal
form: A = Q * B * P**H. Q and P**H are defined as products
of elementary reflectors H(i) and G(i) respectively.
Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq
is the order of the unitary matrix Q or P**H that is
applied.
If VECT = 'Q', A is assumed to have been an NQ-by-K
matrix: if nq >= k, Q = H(1) H(2) . . . H(k);
if nq < k, Q = H(1) H(2) . . . H(nq-1).
If VECT = 'P', A is assumed to have been a K-by-NQ matrix:
if k < nq, P = G(1) G(2) . . . G(k);
if k >= nq, P = G(1) G(2) . . . G(nq-1).
ARGUMENTS
VECT (input) CHARACTER*1
= 'Q': apply Q or Q**H;
= 'P': apply P or P**H.
SIDE (input) CHARACTER*1
= 'L': apply Q, Q**H, P or P**H from the Left;
= 'R': apply Q, Q**H, P or P**H from the Right.
= 'N': No transpose, apply Q or P;
= 'C': Conjugate transpose, apply Q**H or P**H.
M (input) INTEGER
The number of rows of the matrix C. M >= 0.
N (input) INTEGER
The number of columns of the matrix C. N >= 0.
K (input) INTEGER
If VECT = 'Q', the number of columns in the origi
nal matrix reduced by CGEBRD. If VECT = 'P', the
number of rows in the original matrix reduced by
CGEBRD. K >= 0.
A (input) COMPLEX array, dimension
(LDA,min(nq,K)) if VECT = 'Q' (LDA,nq) if
VECT = 'P' The vectors which define the elementary
reflectors H(i) and G(i), whose products determine
the matrices Q and P, as returned by CGEBRD.
LDA (input) INTEGER
The leading dimension of the array A. If VECT =
'Q', LDA >= max(1,nq); if VECT = 'P', LDA >=
max(1,min(nq,K)).
TAU (input) COMPLEX array, dimension (min(nq,K))
TAU(i) must contain the scalar factor of the ele
mentary reflector H(i) or G(i) which determines Q
or P, as returned by CGEBRD in the array argument
TAUQ or TAUP.
C (input/output) COMPLEX array, dimension (LDC,N)
On entry, the M-by-N matrix C. On exit, C is
overwritten by Q*C or Q**H*C or C*Q**H or C*Q or
P*C or P**H*C or C*P or C*P**H.
LDC (input) INTEGER
The leading dimension of the array C. LDC >=
max(1,M).
WORK (workspace/output) COMPLEX array, dimension
(LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal
LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. If SIDE = 'L',
LWORK >= max(1,N); if SIDE = 'R', LWORK >=
max(1,M). For optimum performance LWORK >= N*NB
if SIDE = 'L', and LWORK >= M*NB if SIDE = 'R',
where NB is the optimal blocksize.
the routine only calculates the optimal size of
the WORK array, returns this value as the first
entry of the WORK array, and no error message
related to LWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille
gal value
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