DORMBR(3F) DORMBR(3F)
DORMBR - VECT = 'Q', DORMBR overwrites the general real M-by-N matrix C
with SIDE = 'L' SIDE = 'R' TRANS = 'N'
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(
LWORK )
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).
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.
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DORMBR(3F) DORMBR(3F)
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 reflector
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 (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
DORMBR(3F) DORMBR(3F)
DORMBR - VECT = 'Q', DORMBR overwrites the general real M-by-N matrix C
with SIDE = 'L' SIDE = 'R' TRANS = 'N'
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(
LWORK )
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).
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.
Page 1
DORMBR(3F) DORMBR(3F)
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 reflector
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 (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
PPPPaaaaggggeeee 2222 [ Back ]
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