NAME

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( LWORK )

#include <sunperf.h>

void cunmbr(char vect, char side, char trans, int m, int n, int k, complex ∗ca, int lda, complex ∗tau, complex ∗cc, int ldc, int ∗info) ;

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.

TRANS (input) CHARACTER∗1
= ’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 original 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 elementary 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.

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

SunOS 5.0  —  Last change: 10 Dec 1998