SORGBR(3F) SORGBR(3F)
SORGBR - generate one of the real orthogonal matrices Q or P**T
determined by SGEBRD when reducing a real matrix A to bidiagonal form
SUBROUTINE SORGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
CHARACTER VECT
INTEGER INFO, K, LDA, LWORK, M, N
REAL A( LDA, * ), TAU( * ), WORK( LWORK )
SORGBR generates one of the real orthogonal matrices Q or P**T determined
by SGEBRD 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)
or G(i) respectively.
If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q is of
order M:
if m >= k, Q = H(1) H(2) . . . H(k) and SORGBR returns the first n
columns of Q, where m >= n >= k;
if m < k, Q = H(1) H(2) . . . H(m-1) and SORGBR returns Q as an M-by-M
matrix.
If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T is of
order N:
if k < n, P**T = G(k) . . . G(2) G(1) and SORGBR returns the first m rows
of P**T, where n >= m >= k;
if k >= n, P**T = G(n-1) . . . G(2) G(1) and SORGBR returns P**T as an
N-by-N matrix.
VECT (input) CHARACTER*1
Specifies whether the matrix Q or the matrix P**T is required, as
defined in the transformation applied by SGEBRD:
= 'Q': generate Q;
= 'P': generate P**T.
M (input) INTEGER
The number of rows of the matrix Q or P**T to be returned. M >=
0.
N (input) INTEGER
The number of columns of the matrix Q or P**T to be returned. N
>= 0. If VECT = 'Q', M >= N >= min(M,K); if VECT = 'P', N >= M
>= min(N,K).
Page 1
SORGBR(3F) SORGBR(3F)
K (input) INTEGER
If VECT = 'Q', the number of columns in the original M-by-K
matrix reduced by SGEBRD. If VECT = 'P', the number of rows in
the original K-by-N matrix reduced by SGEBRD. K >= 0.
A (input/output) REAL array, dimension (LDA,N)
On entry, the vectors which define the elementary reflectors, as
returned by SGEBRD. On exit, the M-by-N matrix Q or P**T.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
TAU (input) REAL array, dimension
(min(M,K)) if VECT = 'Q' (min(N,K)) if VECT = 'P' TAU(i) must
contain the scalar factor of the elementary reflector H(i) or
G(i), which determines Q or P**T, as returned by SGEBRD in its
array argument TAUQ or TAUP.
WORK (workspace/output) REAL array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= max(1,min(M,N)). For
optimum performance LWORK >= min(M,N)*NB, where NB is the optimal
blocksize.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
SORGBR(3F) SORGBR(3F)
SORGBR - generate one of the real orthogonal matrices Q or P**T
determined by SGEBRD when reducing a real matrix A to bidiagonal form
SUBROUTINE SORGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
CHARACTER VECT
INTEGER INFO, K, LDA, LWORK, M, N
REAL A( LDA, * ), TAU( * ), WORK( LWORK )
SORGBR generates one of the real orthogonal matrices Q or P**T determined
by SGEBRD 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)
or G(i) respectively.
If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q is of
order M:
if m >= k, Q = H(1) H(2) . . . H(k) and SORGBR returns the first n
columns of Q, where m >= n >= k;
if m < k, Q = H(1) H(2) . . . H(m-1) and SORGBR returns Q as an M-by-M
matrix.
If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T is of
order N:
if k < n, P**T = G(k) . . . G(2) G(1) and SORGBR returns the first m rows
of P**T, where n >= m >= k;
if k >= n, P**T = G(n-1) . . . G(2) G(1) and SORGBR returns P**T as an
N-by-N matrix.
VECT (input) CHARACTER*1
Specifies whether the matrix Q or the matrix P**T is required, as
defined in the transformation applied by SGEBRD:
= 'Q': generate Q;
= 'P': generate P**T.
M (input) INTEGER
The number of rows of the matrix Q or P**T to be returned. M >=
0.
N (input) INTEGER
The number of columns of the matrix Q or P**T to be returned. N
>= 0. If VECT = 'Q', M >= N >= min(M,K); if VECT = 'P', N >= M
>= min(N,K).
Page 1
SORGBR(3F) SORGBR(3F)
K (input) INTEGER
If VECT = 'Q', the number of columns in the original M-by-K
matrix reduced by SGEBRD. If VECT = 'P', the number of rows in
the original K-by-N matrix reduced by SGEBRD. K >= 0.
A (input/output) REAL array, dimension (LDA,N)
On entry, the vectors which define the elementary reflectors, as
returned by SGEBRD. On exit, the M-by-N matrix Q or P**T.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
TAU (input) REAL array, dimension
(min(M,K)) if VECT = 'Q' (min(N,K)) if VECT = 'P' TAU(i) must
contain the scalar factor of the elementary reflector H(i) or
G(i), which determines Q or P**T, as returned by SGEBRD in its
array argument TAUQ or TAUP.
WORK (workspace/output) REAL array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= max(1,min(M,N)). For
optimum performance LWORK >= min(M,N)*NB, 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 ]
|
