Dormbr.f -
subroutine dormbr (VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
DORMBR
DORMBR
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).
Parameters:
VECT
VECT is CHARACTER*1
= 'Q': apply Q or Q**T;
= 'P': apply P or P**T.
SIDE
SIDE is 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
TRANS is CHARACTER*1
= 'N': No transpose, apply Q or P;
= 'T': Transpose, apply Q**T or P**T.
M
M is INTEGER
The number of rows of the matrix C. M >= 0.
N
N is INTEGER
The number of columns of the matrix C. N >= 0.
K
K is 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
A is 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
LDA is 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
TAU is DOUBLE PRECISION 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 DGEBRD in the array argument TAUQ or TAUP.
C
C is 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
LDC is INTEGER
The leading dimension of the array C. LDC >= max(1,M).
WORK
WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK
LWORK is 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.
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
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Definition at line 195 of file dormbr.f.
Generated automatically by Doxygen for LAPACK from the source code.