![]() |
LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
|
subroutine sormbr | ( | character | vect, |
character | side, | ||
character | trans, | ||
integer | m, | ||
integer | n, | ||
integer | k, | ||
real, dimension( lda, * ) | a, | ||
integer | lda, | ||
real, dimension( * ) | tau, | ||
real, dimension( ldc, * ) | c, | ||
integer | ldc, | ||
real, dimension( * ) | work, | ||
integer | lwork, | ||
integer | info ) |
SORMBR
Download SORMBR + dependencies [TGZ] [ZIP] [TXT]
!> !> If VECT = 'Q', SORMBR 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', SORMBR 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 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) 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). !>
[in] | VECT | !> VECT is CHARACTER*1 !> = 'Q': apply Q or Q**T; !> = 'P': apply P or P**T. !> |
[in] | 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. !> |
[in] | TRANS | !> TRANS is CHARACTER*1 !> = 'N': No transpose, apply Q or P; !> = 'T': Transpose, apply Q**T or P**T. !> |
[in] | M | !> M is INTEGER !> The number of rows of the matrix C. M >= 0. !> |
[in] | N | !> N is INTEGER !> The number of columns of the matrix C. N >= 0. !> |
[in] | K | !> K is INTEGER !> If VECT = 'Q', the number of columns in the original !> matrix reduced by SGEBRD. !> If VECT = 'P', the number of rows in the original !> matrix reduced by SGEBRD. !> K >= 0. !> |
[in] | A | !> A is REAL 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 SGEBRD. !> |
[in] | 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)). !> |
[in] | TAU | !> TAU is REAL 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 SGEBRD in the array argument TAUQ or TAUP. !> |
[in,out] | C | !> C is REAL 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. !> |
[in] | LDC | !> LDC is INTEGER !> The leading dimension of the array C. LDC >= max(1,M). !> |
[out] | WORK | !> WORK is REAL array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. !> |
[in] | 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. !> |
[out] | INFO | !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> |
Definition at line 192 of file sormbr.f.