DORMBR(1) LAPACK routine (version 3.2) DORMBR(1)NAME
DORMBR - VECT = 'Q', DORMBR overwrites the general real M-by-N matrix C
with SIDE = 'L' SIDE = 'R' TRANS = 'N'
SYNOPSIS
SUBROUTINE DORMBR( 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
DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK(
* )
PURPOSE
If VECT = 'Q', DORMBR overwrites the general real M-by-N matrix C with
SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C
C * Q TRANS = 'T': Q**T * C C * Q**T
If VECT = 'P', DORMBR overwrites the general real M-by-N matrix C with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': P * C C * P
TRANS = 'T': P**T * C C * P**T
Here Q and P**T are the orthogonal matrices determined by DGEBRD when
reducing a real matrix A to bidiagonal form: A = Q * B * P**T. Q and
P**T 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 orthogonal matrix Q or P**T 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**T;
= 'P': apply P or P**T.
SIDE (input) CHARACTER*1
= 'L': apply Q, Q**T, P or P**T from the Left;
= 'R': apply Q, Q**T, P or P**T from the Right.
TRANS (input) CHARACTER*1
= 'N': No transpose, apply Q or P;
= 'T': Transpose, apply Q**T or P**T.
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 DGEBRD. If VECT = 'P', the number of rows in the
original matrix reduced by DGEBRD. K >= 0.
A (input) DOUBLE PRECISION 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
DGEBRD.
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) DOUBLE PRECISION array, dimension (min(nq,K))
TAU(i) must contain the scalar factor of the elementary reflec‐
tor H(i) or G(i) which determines Q or P, as returned by DGEBRD
in the array argument TAUQ or TAUP.
C (input/output) DOUBLE PRECISION array, dimension (LDC,N)
On entry, the M-by-N matrix C. On exit, C is overwritten by
Q*C or Q**T*C or C*Q**T or C*Q or P*C or P**T*C or C*P or
C*P**T.
LDC (input) INTEGER
The leading dimension of the array C. LDC >= max(1,M).
WORK (workspace/output) DOUBLE PRECISION array, dimension
(MAX(1,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 per‐
formance LWORK >= N*NB if SIDE = 'L', and LWORK >= M*NB if SIDE
= 'R', where NB is the optimal blocksize. If LWORK = -1, then
a workspace query is assumed; 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 illegal value
LAPACK routine (version 3.2) November 2008 DORMBR(1)
